Magnetism doi: 10.3390/magnetism6030023

Authors: Iosif Galanakis

The emergence of all-d-metal Heusler alloys has opened up new pathways for the design of advanced functional materials. In this work, we employ first-principles electronic structure calculations to systematically investigate the electronic and magnetic properties of 27 all-d-metal Heusler compounds following the stoichiometry X2YZ, where X= Co, Rh, Ir, Y= V, Cr, Mn, and Z= Ti, Zr, Hf. Electronic band structure calculations show a consistent minority-spin pseudogap across the series, the width and characteristics of which are strongly dependent on the d-band broadening introduced by 4d (Rh, Zr) and 5d (Ir, Hf) transition metals. Magnetically, these materials largely follow the Mt=Zt−24 Slater–Pauling rule, driven by exactly 12 occupied minority-spin bands at the Γ point. Notably, substituting Co with Rh or Ir significantly redistributes the magnetization, drastically reducing the X-site spin magnetic moment while amplifying the spin magnetic moments on the Y-site atoms. This study provides a comprehensive understanding of the interplay between structural symmetry, orbital hybridization, and magnetism in all-d-metal Heuslers, highlighting their promise for future spintronic applications.

Magnetism doi: 10.3390/magnetism6030022

Authors: Yutaka Itoh

We report on the finite temperature staggered spin susceptibility χ(Q) as a function of the mode–mode coupling constant y1 in the self-consistent renormalization theory of two-dimensional antiferromagnetic spin fluctuations with zero-point quantum fluctuations just at the quantum critical point (y0 = 0). We find that the value y1 = 0.1 is a criterion to classify the effect of the zero-point spin fluctuations on the temperature dependence of χ(Q) into a Curie law for weak y1< 0.1 and a Curie–Weiss type or a power law type for strong y1> 0.1. The absence of a Curie–Weiss temperature can serve as an identifying criterion for QCP (y0 = 0) in systems with weak mode–mode coupling (y1< 0.1). Experimental application on the y1 classification is shown to several itinerant layered antiferromagnetic systems through an analysis of nuclear spin–lattice relaxation rates.

Magnetism doi: 10.3390/magnetism6030021

Authors: Georgios Samourgkanidis

This study investigates the use of magnetoelastic sensing for vibration-based structural health monitoring (SHM) of cementitious beam specimens under intact and damaged conditions. Prismatic mortar beams with dimensions of 160 × 40 × 40 mm3 were fabricated following standardized preparation procedures and equipped with annealed amorphous ferromagnetic ribbons, Metglas 2826MB3, for nondestructive magnetoelastic vibration sensing. The specimens were tested under free-vibration conditions in a simply supported configuration, and their vibration response was measured using a detection coil and subsequently analyzed using MATLAB software. The undamaged specimen exhibited a dominant resonance frequency at 6531 Hz, which closely corresponded to the fourth bending mode predicted by Euler–Bernoulli beam theory. Controlled notch-shaped cracks with varying locations and depths were subsequently introduced to evaluate the sensitivity of the sensing system to structural damage. Experimental results showed that the frequency shift is strongly influenced by the location of damage relative to the modal nodes, with maximum sensitivity observed between nodal regions and minimal variation near the nodes. Furthermore, increasing notch-shaped crack depth produced progressively larger frequency shifts, revealing a monotonic and non-linear relationship between damage severity and dynamic response. Polynomial fitting and 3D surface analysis further highlighted the combined influence of crack location and depth on the measured frequency variation. The findings confirm that the magnetoelastic sensor is capable of accurately detecting and magnetically transmitting the vibration state and damage-induced changes in cementitious structures, demonstrating high sensitivity and strong potential for application in vibration-based structural health monitoring systems, particularly in materials characterized by strong vibration damping.

Magnetism doi: 10.3390/magnetism6020020

Authors: Abhiyan Oli Igor Dubenko Alexander Granovsky Dushmantha K. Gusthigngnhadurage Muhammad A. Iqbal Margaret P. Hill Shane Stadler Naushad Ali Saikat Talapatra

We investigated the structural, magnetic, magnetocaloric, and magnetotransport properties of Ni50Mn35In15 Heusler alloys via partial substitution of Ni with 3 at.% Bi (Ni47Bi3Mn35In15) and 3 at.% Si (Ni47Si3Mn35In15) synthesized by arc melting. X-ray diffraction confirms a predominantly L21 cubic structure (space group Fm-3m), while SEM/EDX analysis verifies compositional homogeneity. Temperature-dependent magnetization measurements reveal that the Bi-substituted alloy exhibits a first-order magnetostructural transition associated with the martensitic transformation, followed by a second-order magnetic phase transition from ferromagnetic to paramagnetic behavior near the Curie temperature. In contrast, the Si-substituted alloy shows a single second-order transition with negligible thermal hysteresis, indicating suppression of the martensitic phase. The Curie temperature decreases from 324 K for the parent alloy to 313 K and 286 K for the Bi- and Si-substituted alloys, respectively. A maximum magnetic entropy change of 6.0 Jkg−1K−1 and 4.5 Jkg−1K−1 is observed for the Bi- and Si-substituted alloys, respectively, under an applied magnetic field change of 50 kOe, with corresponding relative cooling power values of 303 Jkg−1 and 345 Jkg−1. These results demonstrate that lattice expansion (Bi) and contraction (Si) distinctly modify Mn–Mn exchange interactions, enabling tunable magnetocaloric performance in Ni–Mn–In Heusler alloys.

Magnetism doi: 10.3390/magnetism6020019

Authors: Imre Bakonyi Franz D. Czeschka Alexander T. Krupp Mario Basletić

In a previous paper, in-plane magnetoresistance results were reported on a thin strip-shaped foil sample of nanocrystalline (nc) Ni metal. These studies have now been complemented by a measurement of the temperature dependence of the resistivity as well as the field dependence of the resistivity and the Hall effect on the same sample at 3 K and 300 K in polar magnetic fields up to 140 kOe, i.e., with the magnetic field perpendicular to the strip plane. Due to the strong contribution of grain-boundary scattering in the nc state, the residual resistivity was about 11% of the room-temperature value. The polar magnetoresistance (PMR) showed similar behavior to the previously reported transverse magnetoresistance (TMR), yielding an anisotropic magnetoresistance (AMR) value in good agreement with the AMR previously deduced from the in-plane MR data. As to the Hall effect, the results for the ordinary (Ro) and the anomalous (Rs) Hall coefficient fitted rather well with the rather dispersed reported data of bulk Ni at both temperatures. However, a closer look at the Rs values for nc-Ni revealed that at 300 K it is larger and at 3 K it is smaller than the corresponding bulk Ni values obtained on samples with the same zero-field resistivity as our nc-Ni foil. These deviations may be attributed to the nanocrystalline state containing a large density of grain boundaries.

Magnetism doi: 10.3390/magnetism6020018

Authors: Gary M. Wysin

I analyze the nonlinear Hamiltonian equations of motion for a one-dimensional chain of transverse magnetic nano-islands, seeking solutions for different types of static domain walls (DWs) connecting uniform static states. The system of elongated magnetic islands oriented transverse (y-direction) to the chain direction (x-direction) experiences an applied magnetic field transverse to the chain. The macro-spin model includes dipole interactions between islands, their uniaxial and easy-plane anisotropies, and Oersted energy of the applied field. DWs can form most easily between pairs of degenerate uniform states, described by their local magnetizations as oblique, y-parallel, and y-alternating. The DWs between oblique states are well described with scalar φ4 theory. General DW structures are found via a numerical energy relaxation scheme. At some anisotropy and field parameters, nearest-neighbor dipole interactions drive antiferromagnetic order inside the DW itself.

Magnetism doi: 10.3390/magnetism6020017

Authors: Mohamed Elkattan

The development of efficient and accurate methods for analyzing electromagnetic scattering by cylindrical objects has theoretical and practical relevance due to its importance in photonics, optoelectronics, antennas, and remote sensing applications. Modal methods are a category of semi-analytical solvers used in modelling electromagnetic scattering problems. Modal methods have several advantages compared to fully numerical methods, and they are very useful for problems with translational symmetry. In this paper, the interaction of electromagnetic waves with a cylinder with an impedance surface situated between two homogeneous half-spaces with different electromagnetic properties is studied. A forward model of the addressed scattering problem is presented. A theoretical formulation of the problem is deduced within a flexible and comprehensive framework that can be extended to solve other related cylindrical configurations. Furthermore, the modal solver developed within the proposed framework can be further developed to consider other forms of source excitations. Moreover, the impedance-dominant scenario has been investigated, and a convergent scheme has been derived for the special case within this regime.

Magnetism doi: 10.3390/magnetism6020016

Authors: Volker Ziemann

Rare-earth-based permanent magnets have the unique ability to create Tesla-strength magnetic fields without the need for power supplies. Moreover, Halbach showed that the fields of assemblies of magnets can be calculated analytically, because the permeability of permanent magnets is very close to unity. But that only worked in the absence of materials with a non-unity permeability, which implies that numerical tools must be employed to account, for example, for materials used to shield stray fields. Here we employ the method of images to derive analytic expressions for the magnetic field of Halbach multipoles that are enclosed in infinite-permeability shielding.

Magnetism doi: 10.3390/magnetism6020015

Authors: Murat Tas Ersoy Şaşıoğlu Iosif Galanakis

There were some errors in the original publication [...]

Magnetism doi: 10.3390/magnetism6010014

Authors: Ayoub Koufi Younes Ziat Hamza Belkhanchi

In this work, the electronic, structural, and magnetic properties of Ti-, V-, Cr-, Mn-, and Ni-doped AgZnF3 perovskites are systematically investigated using the Korringa–Kohn–Rostoker method combined with the coherent potential approximation (KKR-CPA) within the generalized gradient approximation (GGA). Transition metal dopants (Ti and V) at a concentration of 5% substituting the Zn site introduce 3d states that cross the Fermi level in the majority-spin channel, resulting in half-metallic behavior. Ferromagnetic stability is predicted for Ti-, V-, Cr-, and Mn-doped AgZnF3 at a doping concentration of 5%. The TM-doped AgZnF3 alloys exhibit noticeable variations in exchange splitting between the t2g and e_g states of the TM-3d orbitals. In Ti-doped AgZnF3, the calculated spin magnetic moments follow the expected trend based on crystal-field splitting theory. Furthermore, a clear correlation is observed between the nature of the transition metal dopant (Ti, V, Cr, Mn, and Ni) and the total magnetic moment of the system.

Magnetism doi: 10.3390/magnetism6010013

Authors: Neil Collings Martin R. Parker

This paper outlines a simple theoretical argument for the possibility of a quantum linear Voigt effect at low temperatures in certain media in the optical regime. An unlikely starting point for the ensuing argument arises out of a long-established hydrodynamic Lorentz field-modified classical dispersion theory whose Voigt component of the optical conductivity, when subjected to the Uncertainty Principle, results in a modified form in the quantum region. In contrast to its classical, second-order counterpart, this quantum Voigt conductivity is shown to have a (modular) linear field dependence.

Magnetism doi: 10.3390/magnetism6010012

Authors: Yunfei Sun Jincheng Zeng Yongfang Deng Weitao Ning Zihang Li Weiyi Xia Yirong Cai Qingchang Wu

In this study, Nd-Fe-B magnets with different degrees of alignment were prepared by adjusting the strength of the alignment magnetic field. The mechanism of influence of alignment degree on the densification of magnets was systematically investigated. The shrinkage rates of the magnets after sintering were calculated, and the results showed that the unoriented magnets exhibited similar shrinkage in different directions, displaying isotropic shrinkage behavior. With the increase in the degree of alignment, the magnets showed significant differences in shrinkage across different directions, presenting anisotropic shrinkage characteristics. In addition, the microstructural analysis revealed that the alignment degree also exerted a certain influence on the micromorphology of the magnets. The grain size parallel to the c-axis was larger than that parallel to the a-axis, which indicates that the alignment degree plays a crucial role in the anisotropic densification of the Nd-Fe-B magnets.

Magnetism doi: 10.3390/magnetism6010011

Authors: Qurban Ali Shah Syed Ingo Hahn

This paper presents a detailed parametric optimization of a spoke-type double stator and single-rotor (DSSR)-type axial flux permanent magnet (AFPM) motor based on the design of experiment (DoE) method coupled with 3D finite element analysis (FEA). Design variables are selected, and their individual effects on the output characteristics of the spoke-type DSSR AFPM motor are analyzed. The interactive effects of the design variable pairs are also investigated to understand their mutual influence on the spoke-type DSSR AFPM motor’s output characteristics. For the optimal design of the spoke-type DSSR AFPM motor, different values of each design variable are determined using Latin Hypercube Sampling (LHS) and analyzed using the 3D FEA method.

Magnetism doi: 10.3390/magnetism6010010

Authors: Gerardo F. Goya

With 2026 already firmly underway, I am pleased to share with you some of the most significant achievements of Magnetism throughout 2025 [...]

Magnetism doi: 10.3390/magnetism6010009

Authors: Ghada Mahmoud Ibrahim Asmaa Sobhy Sabik Adel Saad Nada

This paper presents a comparative modeling and analysis of an induction furnace for melting aluminum (Al) and copper (Cu), focusing on their electromagnetic behavior and heating performance. The study employs ANSYS Maxwell software version 16.0 with the finite element method (FEM) to simulate eddy current generation, Joule heating, and current density distribution in the metallic workpieces. The effects of coil geometry, input current, and operating frequency (50–100 kHz) on heating efficiency and skin depth are investigated. Estimated heating times based on ohmic losses are provided, revealing significant differences between aluminum and copper due to their distinct electrical and thermal properties. The results demonstrate that higher frequencies concentrate heating near the surface, reducing skin depth, while copper exhibits more uniform heating than aluminum. These findings offer practical insights for optimizing induction furnace design and operation for different non-ferrous metals.

Magnetism doi: 10.3390/magnetism6010008

Authors: Gabin Dimitri Ngantso Abdelmajid Kadiri Mounirou Karimou

We investigate a ferrimagnetic/ferroelectric bilayer in which a mixed-spin Heisenberg ferrimagnet is coupled to a three-state ferroelectric layer allowing for a nonpolar state. Using Monte Carlo simulations, we analyze how magnetic and electric single-ion anisotropies, together with interfacial magnetoelectric coupling, control phase transitions and hysteresis properties. We show that electric anisotropy, by tuning the population of nonpolar ferroelectric sites, strongly shifts the ferrimagnetic critical temperature, while magnetic anisotropy reciprocally affects the ferroelectric transition. Increasing the magnetoelectric coupling enhances both ordering temperatures and may induce a common transition. At fixed temperature, magnetic and electric hysteresis loops evolve from square to slim and nearly reversible shapes as anisotropies are varied. These results highlight the relevance of three-state ferroelectricity for describing polarization suppression and tunable magnetoelectric response in hybrid bilayers.

Magnetism doi: 10.3390/magnetism6010007

Authors: Satoru Hayami

We investigate the role of single-ion anisotropy in stabilizing higher-order skyrmion crystal phases in centrosymmetric magnets under D3d symmetry. Using a classical spin model that incorporates both a local single-ion anisotropy arising from the two-dimensional crystal symmetry and a D3d-type magnetic anisotropy originating from the D3d point-group symmetry, we perform simulated annealing calculations to explore the ground-state spin configurations. We find that a skyrmion crystal with a skyrmion number of two is stabilized over a wide range of parameters of single-ion anisotropy and D3d-type anisotropy. We also show that the skyrmion core position shifts from an interstitial site to an on-site location as the magnitude of the easy-axis single-ion anisotropy increases. Furthermore, we demonstrate that the magnetic field drives a variety of topological phase transitions depending on the sign and magnitude of the single-ion and D3d-type anisotropies. These results provide a possible microscopic understanding of how complex topological spin textures can be stabilized in centrosymmetric D3d magnets, suggesting that multiple phases with topological spin textures could emerge even in the absence of the Dzyaloshinskii–Moriya interaction.

Magnetism doi: 10.3390/magnetism6010006

Authors: Juharni Liliany N. Pamasi Ni’matil Mabarroh Azusa N. Hattori Hidekazu Tanaka Nobuyoshi Hosoito Satoru Yoshimura Ken Hattori

A magnetic vortex, characterized by curling in-plane magnetization, is generally unstable in two-dimensional (2D) ferromagnetic thin films. Here, we demonstrated that this vortex could be stable in three-dimensional (3D) pyramid-shaped Fe thin films and elucidated mechanistic origin of the stable vortex. Magnetization measurements reveal characteristic M−H hysteresis loops with a pronounced bending and a gradual slope near zero magnetization, contrasting strongly with the abrupt switching seen in 2D films. By decomposing the magnetization processes on each facet in pyramid, we identify the sequence of vortex formation, stabilization, and annihilation. The key factor is the 3D geometry: non-coplanar facet junctions at the ridge lines act as structural singularities that naturally pin domain walls (DWs). These ridge lines restrict DW motion, confine local magnetic structures, and mediate inter-facet interactions, creating geometrical constraints enhancing vortex stability. Vortex formation is driven by magnetostatic energy minimization, as in 2D films. However, ridge-induced weakening of inter-facet exchange becomes the dominant factor in the 3D pyramidal structure. Overall, the interplay of shape anisotropy, magnetostatic, exchange, and Zeeman energies under 3D constraints provides a clear framework for vortex stability, offering the first mechanistic insight into stable vortices in 3D ferromagnetic films and supporting future 3D magnetic devices.

Magnetism doi: 10.3390/magnetism6010005

Authors: Nikolaos Maniotis

This work presents a micromagnetic investigation of monolayer L10 FePt and FePt/Fe bilayer thin films to clarify the role of thickness, composition, and exchange coupling in their magnetic behavior. Simulations were performed using the Landau–Lifshitz–Gilbert formalism implemented in OOMMF, with realistic material parameters and geometries. For FePt monolayers, film thicknesses of 1–20 nm were examined, revealing a non-monotonic coercivity trend: the coercive field increased from 35 mT at 1 nm to 136 mT at 10 nm and decreased to 69 mT at 20 nm. This evolution indicates a transition from localized reversal to domain-wall-mediated switching once the film exceeds the exchange length (10–20 nm). Additional simulations varying Fe concentration (48–68%) through the exchange stiffness constant showed that higher Fe content strengthens magnetic coupling and increases coercivity. Bilayer systems combining a 2 nm FePt layer with Fe layers of 10 and 12 nm exhibited rectangular, saturated loops, confirming strong exchange coupling and exchange-spring behavior. The results identify 2 nm FePt as the optimal thickness for achieving full saturation, balanced coercivity, and thermal stability in FePt/Fe thin-film architectures.

Magnetism doi: 10.3390/magnetism6010004

Authors: Satoru Hayami

We theoretically investigate multiple-Q instabilities in centrosymmetric hexagonal magnets, formulated as superpositions of independent six ordering wave vectors related by sixfold rotational and mirror symmetries. By employing a spin model that incorporates biquadratic interactions and an external magnetic field, we establish a comprehensive low-temperature phase diagram hosting single-Q, double-Q, triple-Q, and sextuple-Q states, as well as skyrmion crystals with topological charges of one and two. The field evolution of the magnetization, scalar spin chirality, and finite wave-vector magnetic amplitudes reveals a hierarchical buildup of multiple-Q order, accompanied by first-order transitions between topologically distinct and trivial phases. At large biquadratic coupling, all six symmetry-related ordering wave vectors coherently participate, giving rise to two sextuple-Q states under magnetic fields and to another spontaneous sextuple-Q state even at zero field. The latter zero-field sextuple-Q state represents a fully developed sixfold interference pattern stabilized solely by the biquadratic interaction, characterized by alternating skyrmion- and antiskyrmion-like cores with vanishing uniform scalar spin chirality. These findings establish a unified framework for understanding hierarchical multiple-Q ordering and demonstrate that the interplay between bilinear and biquadratic interactions under hexagonal symmetry provides a generic route to complex noncoplanar magnetism in centrosymmetric itinerant systems.

Magnetism doi: 10.3390/magnetism6010003

Authors: Conrad Rizal

Magnetooptics (MO) explores light—matter interactions in magnetized media and has advanced rapidly with progress in materials science, spectroscopy, and integrated photonics. This review highlights recent developments in fundamental principles, experimental techniques, and emerging applications. We revisit the canonical MO effects: Faraday, MO Kerr effect (MOKE), Voigt, Cotton—Mouton, Zeeman, and Magnetic Circular Dichroism (MCD), which underpin technologies ranging from optical isolators and high-resolution sensors to advanced spectroscopic and imaging systems. Ultrafast spectroscopy, particularly time-resolved MOKE, enables femtosecond-scale studies of spin dynamics and nonequilibrium processes. Hybrid magnetoplasmonic platforms that couple plasmonic resonances with MO activity offer enhanced sensitivity for environmental and biomedical sensing, while all-dielectric magnetooptical metasurfaces provide low-loss, high-efficiency alternatives. Maxwell-based modeling with permittivity tensor (ε) and machine-learning approaches are accelerating materials discovery, inverse design, and performance optimization. Benchmark sensitivities and detection limits for surface plasmon resonance, SPR and MOSPR systems are summarized to provide quantitative context. Finally, we address key challenges in material quality, thermal stability, modeling, and fabrication. Overall, magnetooptics is evolving from fundamental science into diverse and expanding technologies with applications that extend far beyond current domains.

Magnetism doi: 10.3390/magnetism6010002

Authors: Roberto Zivieri Israa Medlej Giancarlo Consolo

Recently, nanoscale magnetic materials have attracted widespread attention due to their intriguing properties in both theoretical and experimental contexts [...]

Magnetism doi: 10.3390/magnetism6010001

Authors: Sayem UI Alam Shuhui Li Yang-Ki Hong Zhenghao Liu Md Abdul Wahed Chang-Dong Yeo Jung-Kun Lee Seungdeog Choi Hayan Shin Hyunkyung Lee Haein Choi-Yim

Permanent magnet synchronous machines (PMSMs) are the preferred choice for electric vehicles (EVs), hybrid EVs, and wind turbines because of their high torque density, efficiency, and wide constant-power speed range. Conventional PMSMs rely heavily on rare-earth (RE) permanent magnets like Nd-Fe-B, which offers high remanence and coercivity but comes with high costs, supply chain issues, and environmental concerns. To address these challenges, this paper explores the potential of tetragonal Fe2Ni2N, a newly developed RE-free permanent magnet, as a replacement for commercial Nd-Fe-B (N35) in high-performance PMSMs. Fe2Ni2N shows a remanent flux density of 1.2 T and coercivity of 0.957 MA/m, closely matching those of commercial N35 magnets. Finite element analysis (FEA) in Ansys Maxwell was performed on both surface-mounted (SPM) and interior-mounted (IPM) PMSMs under EV-representative operating conditions. Results demonstrate that Fe2Ni2N-based machines have similar demagnetization resistance, torque, and efficiency to those with N35 magnets, with slight performance advantages at low speeds and nearly identical performance at high speeds. Furthermore, system-level parameters such as DC bus voltage and stator current were analyzed, showing that increased voltage extends the constant torque region while higher current enhances torque output but can slightly reduce efficiency at elevated speeds. These findings confirm that Fe2Ni2N is a promising RE-free alternative to Nd-Fe-B for sustainable, high-performance PMSMs. Results show that Fe2Ni2N-based machines have similar demagnetization resistance, torque, and efficiency to those with N35 magnets, with slight performance benefits at low speeds and nearly identical results at high speeds. Furthermore, system-level parameters, such as DC bus voltage and stator current, were analyzed. The results show that increased voltage extends the constant-torque region, while higher current enhances torque output but can slightly reduce efficiency at elevated speeds. These findings confirm that Fe2Ni2N is a promising RE-free alternative to Nd-Fe-B for sustainable, high-performance PMSMs.

Magnetism doi: 10.3390/magnetism5040031

Authors: Chaimae El Mortajine Mohamed Amine Dabachi Soufian Lakrit Hasnaa Oubnaki Amine Faid Mostafa Bouzi

The present paper investigates the generation of the alternating almost zero and strong homogeneous magnetic fields for rotary magnetic refrigeration. In order to achieve an alternating magnetic field with eight regions, a soft magnetic rod is inserted in the bore. Four high-flux-density regions (FDRs) for magnetization and four low-flux-density regions for demagnetization of magnetocaloric materials are obtained by the proposed design. The design procedure for the four-pole structure and its implementation using 3D finite-element simulation are presented. To meet the predefined requirements, some magnet segments are replaced with high-permeability soft magnetic material. The proposed magnetic design for the rotary refrigerator allows good field distribution in the air gap, a high ratio of high-field-to-permanent-magnet volume, a minimized low-field volume, reduced magnet usage to the permanent-magnet volume, reduction of the amount of magnet material used, and increased flux density between the low- and high-field regions.

Magnetism doi: 10.3390/magnetism5040030

Authors: Nikita A. Buznikov Pavel A. Ivanov Ilya V. Komarov Andrey N. Lagarkov Sergey A. Maklakov Sergey S. Maklakov Alexey V. Osipov Konstantin N. Rozanov Artem O. Shiryaev Polina A. Zezyulina

Microwave permeability of amorphous Co67Fe7B26 films deposited on a flexible substrate was studied in a wide range of film thicknesses up to 1.40 μm. Microwave permeability measurements were carried out using the coaxial technique in the frequency range from 0.1 to 10 GHz. It was found that both the static permeability and the ferromagnetic resonance frequency depend weakly on the film thickness. Analysis of the microwave data showed that the studied films possess in-plane magnetic anisotropy. The influence of the skin effect on the frequency dependence of the microwave permeability was modeled using an analytical approach. It was demonstrated that the decrease in the peak of the imaginary part of the microwave permeability with film thickness growth is related to the skin effect. The results obtained may be useful for microwave applications of soft magnetic CoFeB films.

Magnetism doi: 10.3390/magnetism5040029

Authors: Steffen Kühn

This article demonstrates that magnetic force and Newton’s law of universal gravitation can be derived from the solution of Maxwell’s equations for moving point charges. For this purpose, a plasma droplet model is postulated, consisting of an aggregation of point charges undergoing Brownian motion within a very small three-dimensional volume. As the velocity of the charges is random due to the Brownian motion, it is described by a probability distribution. It is shown that a non-zero velocity standard deviation leads to the magnetic force, while Newton’s law of universal gravitation can be derived from a non-zero velocity variance. This suggests that magnetism and gravitation might be closely related.

Magnetism doi: 10.3390/magnetism5040028

Authors: Chenyu Zhao Yun Xu Lixin Jiao Linhai Hu Haoran Lv Peng Yang

Transcranial magnetic stimulation (TMS) is a non-invasive neuromodulation technique extensively utilized in neuroscience and clinical medicine; however, its underlying mechanisms require further elucidation. Due to ethical safety considerations, low cost, and physiological similarities to humans, rodent models have become the primary subjects for TMS animal studies. Nevertheless, existing TMS coils designed for rodents face several limitations, including size constraints that complicate coil fabrication, insufficient stimulation intensity, suboptimal focality, and difficulty in adapting coils to practical experimental scenarios. Currently, many studies have attempted to address these issues through various methods, such as adding magnetic nanoparticles, constraining current distribution, and incorporating electric field shielding devices. Integrating the above methods, this study designs a small arc-shaped TMS coil for the frontoparietal region of rats using the inverse boundary element method, which reduces the coil’s interference with experimental observations. Compared with traditional geometrically scaled-down human coil circular and figure-of-eight coils, this coil achieves a 79.78% and 57.14% reduction in half-value volume, respectively, thus significantly improving the focusing of stimulation. Meanwhile, by adding current density constraints while minimizing the impact on the stimulation effect, the minimum wire spacing was increased from 0.39 mm to 1.02 mm, ensuring the feasibility of the coil winding. Finally, coil winding was completed using 0.05 mm × 120 Litz wire with a 3D-printed housing, which proves the practicality of the proposed design method.

Magnetism doi: 10.3390/magnetism5040027

Authors: Yang Zhang Chunguang Fan Chenglong Yu

This study proposes a semi-analytic harmonic modeling method that significantly improves the accuracy and efficiency of complex magnetic field modeling by integrating numerical and analytical approaches. Compared to traditional methods such as the equivalent charge method and finite element method, this approach optimizes the distribution of surface and body charges in the magnetic dipole model and introduces a finite and variable permeability model to accommodate material non-uniformity. Through harmonic expansion and analytical optimization, the method more accurately reflects the characteristics of real magnets, providing an efficient and precise solution for complex magnetic field problems, particularly in the design of high-performance magnets such as Halbach arrays. In this study, the effectiveness of the new modeling method is verified through the combination of simulation and experiment: the magnetic field distribution of the new Halbach array is accurately simulated, and the applicability of the model in the description of complex magnetic fields is analyzed. The dynamic response ability of the optimized model is verified by modeling and simulating the variation of the permeability under actual conditions. The distribution of scalar potential energy with permeability was simulated to evaluate the adaptability of the model to the real physical field. Through the comparative analysis of simulation and experimental results, the advantages of the new method in modeling accuracy and efficiency are clearly pointed out, and the effectiveness of the semi-analytic harmonic modeling method and its wide application potential in the design of new magnetic fields are proved. In this study, a semi-analytic harmonic modeling method is proposed by combining numerical and analytical methods, which breaks through the efficiency bottleneck of traditional modeling methods, and achieves the unity of high precision and high efficiency in the magnetic field modeling of the new Halbach array, providing a new solution for the study of complex magnetic field problems.

Magnetism doi: 10.3390/magnetism5040026

Authors: Arsalan Arif Farhan Arif Zuhair Abbas Ghulam Jawad Sirewal Muhammad Saleem Qasim Ali Mukhtar Ullah

This paper proposes a method to analyze the effect of the rotor’s harmonic winding design and the output of a brushless wound rotor synchronous machine (WRSM) for optimal excitation power transfer. In particular, the machine analyzed by the finite-element method was a 48-slot eight-pole 2D model. The subharmonic magnetomotive force was additionally created in the air gap flux, which induces voltage in the harmonic winding of the rotor. This voltage is rectified and fed to the field winding through a full bridge rectifier. Eventually, a direct current (DC) flows to the field winding, removing the need for external excitation through brushes and sliprings. The effect of the number of harmonic winding turns is analyzed and the field winding turns were varied with respect to the available rotor slot space. Optimization of the harmonic excitation part of the machine will maximize the rotor excitation for regulation purposes and optimize the torque production at the same time. Two-dimensional finite-element analysis has been performed in ANSYS Maxwell 19 to obtain the basic results for the design of the machine.

Magnetism doi: 10.3390/magnetism5040025

Authors: Patricia Lázpita Natalia Ahiova Río-López David Mérida Emily (Leonie Quinlyn Nowalaja) Ammerlaan Uli Zeitler Volodymyr Chernenko Jon Gutiérrez

Heusler-type metamagnetic shape memory alloys (MMSMAs) exhibit a large functional response associated with a first-order martensitic transformation (MT). The strong magneto-structural coupling combined with the presence of mixed magnetic interactions enables controlling this MT by means of a magnetic field, resulting in different multifunctional properties, among them giant magnetoresistance, metamagnetic shape memory effect (MMSM), or inverse magnetocaloric effect (MCE). Not only the shift rate of MT as a function of the magnetic field but also its eventual suppression are key parameters in order to develop these effects. Here we present our findings concerning a detailed study of the magnetic field-induced MT and its suppression in MnNi(Fe)Sn MMSMAs, by applying strong steady magnetic fields up to 33 T. These measurements will lead to the creation of the T-μ0H phase diagrams of the MT. Moreover, we will also give light to the effect of Fe—content and, as a direct consequence, the magnetic coupling on the suppression of the magnetostructural transformation.

Magnetism doi: 10.3390/magnetism5040024

Authors: Satoru Hayami

We study unconventional multipole moments arising from noncollinear magnetic structures within an augmented framework encompassing electric, magnetic, magnetic toroidal, and electric toroidal multipoles. Employing a tight-binding model for an s-p hybridized orbital system, we analyze two spiral magnetic textures and classify the resulting multipoles according to magnetic point group symmetry. Different spiral wave types, such as cycloidal and proper-screw forms, activate distinct multipole components, with odd-parity multipoles emerging from local s-p parity mixing induced by magnetically driven inversion-symmetry breaking. Calculated multipole structure factors reveal finite-q peaks originating from higher-order magnetic-dipole-scattering processes and their characteristic couplings between Fourier components of the magnetic dipole texture. Our results demonstrate that magnetic ordering can generate parity-mixed states without intrinsic structural inversion asymmetry, offering new pathways to realize cross-correlation phenomena in functional magnetic materials.

Magnetism doi: 10.3390/magnetism5030023

Authors: Shu Kondo Takuya Masuda Masaki Sakaguchi Yasutaka Hayamizu M. M. A. Alam Toshio Tagawa

Natural convection of liquid metals under magnetic fields is a phenomenon of interest in various industrial and scientific applications, including fusion reactor blankets and magnetohydrodynamic (MHD) power systems. While the application of a magnetic field generally suppresses convection and reduces the heat transfer rate, recent studies have reported cases where the Nusselt number increases under certain magnetic field conditions. In this study, we conduct numerical simulations of natural convection in an annular container filled with a liquid metal, subject to a circumferential static magnetic field. The governing equations, incorporating both temperature and electromagnetic fields, are solved using a high-order finite difference scheme. The results show that, within a specific range of parameters, the Nusselt number increases at moderate Hartmann numbers, even under low Rayleigh number conditions. Notably, this enhancement in heat transfer occurs alongside a reduction in kinetic energy, indicating that convective strength is not necessarily the dominant factor. Further analysis confirms that this phenomenon weakens and eventually vanishes as the Rayleigh number approaches 106. These findings provide evidence that magnetic field-induced heat transfer enhancement can occur without a corresponding increase in convective motion, thereby challenging conventional assumptions in magnetoconvection theory.

Magnetism doi: 10.3390/magnetism5030022

Authors: Liubov Zhemchuzhna Lovely Joseph Andrii Iurov Godfrey Gumbs Danhong Huang

We have carried out detailed theoretical and numerical calculations and developed a physics-based model for quantitatively describing the Landau levels of several pseudospin-1 structures with a flat band and a finite bandgap in their electronic-energy spectrum under a strong and uniform magnetic field. We have investigated the Landau-level-based dynamics, as well as the corresponding eigenstates, for gapped graphene, a dice lattice with both a zero and finite bandgap and, eventually, for the Lieb lattice, which represents a separate type of square lattice with a very special non-symmetric (elevated) location of the flat band which intersects the conduction band at its lowest point. Exact analytical consideration of Landau-level states has been performed and explained when dealing with all types of considered lattices. Our model could be further generalized for treating cases with an arbitrary position for the flat band between the valence and conduction bands. Our current results have direct implications for a deep-level investigation of the quantum Hall effect, as well as other magnetic and topological properties of these novel materials.

Magnetism doi: 10.3390/magnetism5030021

Authors: Andrzej Skumiel

This article describes systems generating high-frequency rotating magnetic fields for magnetic hyperthermia treatments. It covers two- and three-phase device systems powered by rectangular signals. A passive bandpass filter tuned to a specific frequency (100 kHz) is placed between the magnetic circuits and the DC power source powering the device. The paper compares the electrical parameters of both solutions, including the supply voltage, magnetic field strength amplitude H, and magnetizing current IL as a function of the supply voltage (Udc). At a fixed supply voltage Udc, the magnetizing current IL and the rotating magnetic field strength amplitude H are approximately twice as large for the three-phase system as for the two-phase system. The relationships between the magnetizing currents IL and the magnetic field strength amplitude H as a function of the supply voltage Udc are linear.

Magnetism doi: 10.3390/magnetism5030020

Authors: Easir Arafat Babak Porkar Mona Ghassemi

High-voltage transmission lines are the backbone of modern power systems, facilitating the delivery of electricity from diverse generation sources, including conventional power plants and renewable energy systems, to consumers. As the electricity demand grows, the expansion of transmission infrastructure becomes essential to connecting new consumers with power suppliers. However, traditional transmission lines require significant right-of-way, posing challenges related to land use and environmental impact, as well as limited loadability. To address this issue, compact unconventional High Surge Impedance Loading (HSIL) transmission lines offer a viable solution by reducing right-of-way requirements while enhancing line natural power, mainly leading to less voltage drop. Before the implementation of the new unconventional HSIL lines, it is crucial to assess key parameters, such as magnetic field distribution under the lines, to ensure compliance with environmental and safety standards. This paper presents a numerical analysis of the magnetic field characteristics of compact unconventional HSIL transmission lines with different subconductor configurations. The results show that the proposed HSIL designs can reduce the magnetic field at ground level by up to 71.74% compared to a conventional 500 kV line near the center, as well as by up to 74% at the right-of-way edge, while maintaining magnetic field levels well below the limits set by ICNIRP and state-specific regulations. This study evaluates the magnetic field distribution within the right-of-way, providing insights into the electromagnetic performance and potential implications for transmission line design.

Magnetism doi: 10.3390/magnetism5030019

Authors: Fuxi Zhou Zheng He Donger Cheng Han Ge Wenjing Zhang Xiao Wang Pengfei Zhou Wanju Luo Zhengdong Fu Xinzhi Liu Liusuo Wu Lunhua He Yanchun Zhao Erxi Feng

Geometrically frustrated magnets exhibit exotic excitations due to competing interactions between spins. The spinel compound MgCr2O4, a three-dimensional Heisenberg antiferromagnet, hosts both spin-wave and spin-resonance modes, but the origin of its resonant excitations remains debated. Suppressing magnetic order via non-magnetic doping can help isolate these modes in neutron scattering studies. We synthesized Ga3+ and Cd2+-doped MgCr2O4 via solid-state reaction and analyzed their structure and magnetism. Ga3+ doping (0–20%) causes anomalous lattice shrinkage due to site disorder from Ga3+ occupying both Mg2+ and Cr3+ sites. Magnetically, Ga3+ doping drives the system from the antiferromagnetic order to a spin-glass state, fully suppressing magnetic ordering at 20% doping. In contrast, Cd2+ replaces only Mg2+, expanding the lattice and meantime inducing strong spin-glass behavior. At 10% Cd2+, long-range antiferromagnetic order is entirely suppressed. Thus, 10% Cd-doped MgCr2O4 offers an ideal platform to study the resonant magnetic excitations without any spin-wave interference.

Magnetism doi: 10.3390/magnetism5030018

Authors: André Bülau Daniela Walter Karl-Peter Fritz

Quantum sensing based on NV-centers in diamonds has been demonstrated many times in multiple publications. The majority of publications use lasers in free space or lasers with fiber optics, expensive optical components such as dichroic mirrors, or beam splitters with dichroic filters and expensive detectors, such as Avalanche photodiodes or single photon detectors, overall, leading to custom and expensive setups. In order to provide an inexpensive NV-based magnetometer setup for educational use in schools, to teach the three topics, fluorescence, optically detected magnetic resonance, and Zeeman splitting, inexpensive, miniaturized, off-the-shelf components with high reliability have to be used. The cheaper such a setup, the more setups a school can afford. Hence, in this work, we investigated LEDs as light sources, considered different diamonds for our setup, tested different color filters, proposed an inexpensive microwave resonator, and used a cheap photodiode with an appropriate transimpedance amplifier as the basis for our quantum magnetometer. As a result, we identified cheap and functional components and present a setup and show that it can demonstrate the three topics mentioned at a hardware cost <EUR 100.

Magnetism doi: 10.3390/magnetism5030017

Authors: Rupam Tamang Shivraj Gurung Dibya Prakash Rai Samy Brahimi Samir Lounis

Recently, a new class of magnetic material, termed altermagnets, has caught the attention of the magnetism and spintronics community. The magnetic phenomenon arising from these materials differs from traditional ferromagnetism and antiferromagnetism. It generally lacks net magnetization and is characterized by unusual non-relativistic spin-splitting and broken time-reversal symmetry. This leads to novel transport properties, such as the anomalous Hall effect, the crystal Nernst effect, and spin-dependent phenomena. Spin-dependent phenomena such as spin currents, spin-splitter torques, and high-frequency dynamics emerge as key characteristics in altermagnets. This paper reviews the main aspects pertaining to altermagnets by providing an overview of theoretical investigations and experimental realizations. We discuss the most recent developments in altermagnetism and prospects for exploiting its unique properties in next-generation devices.

Magnetism doi: 10.3390/magnetism5030016

Authors: Kenichi Konishi Roberto Menta

The quantum states of a spin 12 (a qubit) are parametrized by the space CP1∼S2, the Bloch sphere. A spin j for a generic j (a 2j+1-state system) is represented instead by a point in a larger space, CP2j. Here we study the state of a single angular momentum/spin in the limit j→∞. A special class of states, |j,n⟩∈CP2j, with spin oriented towards definite spatial directions, n∈S2, i.e., (J^·n)|j,n⟩=j|j,n⟩, are found to behave as classical angular momenta, jn, in this limit. Vice versa, general spin states in CP2j do not become classical, even at a large j. We study these questions by analyzing the Stern–Gerlach processes, the angular momentum composition rule, and the rotation matrix. Our observations help to better clarify how classical mechanics emerges from quantum mechanics in this context (e.g., with the unique trajectories of a particle carrying a large spin in an inhomogeneous magnetic field) and to make the widespread idea that large spins somehow become classical more precise.

Magnetism doi: 10.3390/magnetism5030015

Authors: Satoru Hayami

A magnetic toroidal monopole, which characterizes time-reversal-odd polar-charge quantity, manifests itself not only in antiferromagnetism but also in time-reversal switching physical responses. We theoretically investigate an atomic-scale description of the magnetic toroidal monopole based on multipole representation theory, which consists of four types of multipoles. We show that the magnetic toroidal monopole degree of freedom is activated as the off-diagonal imaginary hybridization between the single-site orbitals with the same orbital angular momentum but different principal quantum numbers. We demonstrate that the expectation value of the magnetic toroidal monopole becomes nonzero when both electric and magnetic fields are applied to the system.

Magnetism doi: 10.3390/magnetism5020014

Authors: Stephan Erdmann Halil İbrahim Sözen Thorsten Klüner

Permanent magnetic materials are essential for technological applications, with the majority of available magnets being either ferrites or materials composed of critical rare-earth elements, such as well-known Nd2Fe14B. The binary Fe2P material emerges as a promising candidate to address the performance gap, despite its relatively low Curie temperature TC of 214 K. In this study, density functional theory was employed to investigate the effect of Si and Co substitution on the magnetic moments, magnetocrystalline anisotropy energy (MAE) and Curie temperature in Fe2−yCoyP1−xSix compounds. Our findings indicate that Si substitution enhances magnetic moments due to the increase in 3f-3f and 3f-3g interaction energies, which also contribute to higher TC values. Conversely, Co substitution leads to a reduction in magnetic moments, attributable to the inherently lower magnetic moments of Co. In all examined cases of different Si concentrations, such as hexagonally structured Fe2−yCoyP, Fe2−yCoyP0.92Si0.08 and Fe2−yCoyP0.84Si0.16, Co substitution increases the Curie temperatures by augmenting 3g-3g exchange interaction energies. Both Si and Co substitutions decrease the magnetocrystalline anisotropy energy, resulting in the loss of the easy magnetization direction at higher Co contents. However, higher Si concentrations appear to confer resilience against the loss. In summary, Si and Co substitutions effectively modify the investigated magnetic properties. Nonetheless, to preserve a high MAE, the extent of substitution should be optimized.

Magnetism doi: 10.3390/magnetism5020013

Authors: Marcos Gonçalves Maria E. K. Fuziki Jose M. Balthazar Giane G. Lenzi Angelo M. Tusset

This paper presents the results of investigating the application of magnetorheological fluids in controlling the lateral and angular vibrations of a high-speed elevator. Numerical simulations are performed for a mathematical model with two degrees of freedom. The lateral and rotational accelerations are analyzed for different travel speeds to determine passenger comfort levels. To attenuate the elevator vibrations, the introduction of a magnetorheological damper in parallel with the passive damper of the elevator rollers is considered. To semi-actively control the dissipative forces of the magnetorheological fluids, a State-Dependent Riccati Equation (SDRE control) is proposed. The numerical results demonstrate that using an MR damper makes it possible to reduce the acceleration levels of the elevator cabin, thus improving passenger comfort and reducing the elevator’s vibration levels and wear on the mechanical and electronic components of the elevator. In addition to the results, a detailed sensitivity analysis is presented.

Magnetism doi: 10.3390/magnetism5020012

Authors: Satoru Hayami

We investigate the role of high-harmonic wave-vector interactions, which affect the stability of the single-Q spiral state and often result in the formation of multiple-Q states. By performing simulated annealing for an effective spin model on a two-dimensional square lattice, we examine the modulation of the single-Q spiral spin configuration by the high-harmonic wave-vector interaction. As a result, we find that the interactions at particular high-harmonic wave vectors affect the stability of the single-Q spiral state. In particular, the incorporation of interactions at high-harmonic wave vectors formed by the sum of two mutually perpendicular ordering wave vectors can lead to the emergence of three double-Q states and a square skyrmion crystal. The present study unveils the importance of high-harmonic wave-vector interactions in order to realize complicated noncoplanar spin textures.

Magnetism doi: 10.3390/magnetism5020011

Authors: Marcos Antônio Sousa Mateus Aquino Gonçalves Thais Aparecida Sales Jessica Boreli dos Reis Lino Stéfany Gonçalves de Moura Joaquim Paulo da Silva Teodorico Castro Ramalho

This study approaches the characterization of Ferroxite and Hematite and the test of their magnetic properties on the degradation and adsorption of Atrazine, an herbicide of the triazine class. This herbicide was compared with a sample of Ferroxite in the absence of a magnetic field and with Hematite, a non-magnetic material which should not be attracted by the magnet. In the sample, the Atrazine determination was carried out by Fenton analysis. Preliminary results were satisfactory, gathering a reduction rate up to 85% for Ferroxite in the presence of a magnetic field and 53% for Hematite. The Fenton reaction, however, showed an 87% reduction rate for Ferroxite in the presence of a magnetic field, and 56% for Hematite. These findings have shown that there is a relation between the magnetic field intensity and the adsorption capacity for these materials.

Magnetism doi: 10.3390/magnetism5020010

Authors: Sharzeel Saleem Mir Lodro

This paper presents a comparative analysis of a long-term evolution advanced (LTE-A) and fifth-generation new radio (5G-NR), focusing on the effects of transient electromagnetic interference (EMI) caused by catenary–pantograph contact in a railway environment.A software-defined radio (SDR)-based prototype was developed to evaluate the performance of LTE-A and 5G-NR links under the influence of transient interference. The results show that both links experience considerable degradation due to interference at different centre frequencies. Performance degradation is proportional to the gain of interference. The measurement results show that both links experience considerable performance degradation in the presence of transient EMI.

Magnetism doi: 10.3390/magnetism5010009

Authors: Gary M. Wysin

A chain of dipole-coupled elongated magnetic islands whose long axes are oriented perpendicular to the chain is studied for its magnetization properties. With a magnetic field applied perpendicular to the chain, the competition between dipolar energy, shape anisotropy, and field energy leads to three types of uniform states with distinct magnetizations: (1) oblique to the chain, (2) perpendicular to the chain, and (3) zero due to having alternating dipoles. The response of these states to a slowly varying field is analyzed, focusing on their stability limits and related oscillation modes, and the dependencies on the dipolar and anisotropy constants. Based on identifiable transitions among the three states and their instability points, the theoretically predicted zero-temperature magnetization curves show significant dependence on the anisotropy. The model suggests a path for designing advanced materials with desired magnetic properties. Different geometries and magnetic media for the islands are considered.

Magnetism doi: 10.3390/magnetism5010008

Authors: Shadan Ghassemi Tabrizi Thomas D. Kühne

While either a spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin S and the irreducible representation Γ of the point group is limited by the complexity of the transformations between different coupling schemes that are related in terms of their site permutations. To overcome these challenges, we apply projection operators directly to uncoupled basis states, enabling the simultaneous treatment of spin and point-group symmetry without the need for recoupling transformations. This provides a simple and efficient approach for the exact diagonalization of isotropic spin models, which we illustrate, with applications in Heisenberg spin rings and polyhedra, including systems that are computationally inaccessible with conventional coupling techniques.

Magnetism doi: 10.3390/magnetism5010007

Authors: Tanguy Phulpin Rym Boulahbel Hafaliana Randrianjanaka Yann Leroy

Inductive Power Transfer (IPT) is evolving fast in many domains, but its efficiency, its extensive resource requirements, and its cost remain crucial problems for its development. Although the inverter is mainly responsible for its cost and material consumption, a considerable quantity of conductors is required for the coupling realization. Therefore, A drastic cost reduction is possible when comparing the traditional most efficient copper Litz wire with aluminum conductors for a similar volume and a lighter embedded system. However, alternative ribbon wire solutions are also characterized and seem promising as substitutes for such applications. First, standard electrical efficiency is evaluated for all cases, before the price and weight. To complement the results and as the alternative couplers imply different materials and production processes, a Life Cycle Assessment is performed. A comparison is carried out on copper and aluminum litz wires and copper and aluminum ribbons. Results demonstrate the promising interest in industrial application of such study, furthermore for systems requiring many couplers as Dynamic IPT (DIPT).

Magnetism doi: 10.3390/magnetism5010006

Authors: Nikolaos Maniotis Spyridon Mitropoulos Nikolaos Vordos Vassilios Tsiantos

In this study, the role of blood perfusion in modulating the thermal response of tumors during magnetic nanoparticle hyperthermia was investigated through computational modeling. The thermal dissipation of 15 nm magnetite nanoparticles was estimated using micromagnetic simulations of their hysteresis loops under a magnetic field of 20 mT and a frequency of 100 kHz. These calculations provided precise energy loss parameters, serving as inputs to simulate the temperature distribution in a tumor embedded within healthy tissue. Temperature-dependent blood perfusion rates, derived from experimental models, were integrated to differentiate the vascular dynamics in normal and cancerous tissues. The simulations were conducted using a bioheat transfer model on a 2D axisymmetric tumor geometry with magnetite nanoparticles dispersed uniformly in the tumor volume. Results showed that tumor tissues exhibit limited blood perfusion enhancement under hyperthermic conditions compared to healthy tissues, leading to localized heat retention favorable for therapeutic purposes. The computational framework validated these findings by achieving therapeutic tumor temperatures (41–45 °C) without significant overheating of surrounding healthy tissues, highlighting the critical interplay between perfusion and energy dissipation. These results demonstrate the efficacy of combining nanoparticle modeling with temperature-dependent perfusion for optimizing magnetic nanoparticle-based hyperthermia protocols.

Magnetism doi: 10.3390/magnetism5010005

Authors: Lucas G. Dos Santos Daina D. A. Buelvas Daniel F. Valezi Bruno L. S. Vicentin Christian M. M. Rocha Eduardo Di Mauro Felipe de A. La Porta

This study explores a sustainable approach to developing magnetic nanocomposites by synthesizing a mixed-phase iron oxide (IO) and recycled polyamide (RPA) composite from textile waste. The RPA/IO nanocomposite’s microstructural and magnetic properties were characterized using X-ray diffraction (XRD) with Rietveld refinement, scanning, transmission electron microscopy (SEM, TEM), and vibrating sample magnetometry (VSM). The proportions of the Fe3O4 and γ-Fe2O3 phases were found to be 23.2 wt% and 76.8 wt%, respectively. SEM and TEM showed a porous, agglomerated IO surface morphology with an average particle size of 14 nm. Magnetic analysis revealed ferrimagnetic and superparamagnetic behavior, with VSM showing saturation magnetization values of 21.81 emu g−1 at 5 K and 18.84 emu g−1 at 300 K. Anisotropy constants were estimated at 4.28 × 105 and 1.53 × 105, respectively, for IO and the composite, with a blocking temperature of approximately 178 K at 300 K. These results contribute to understanding the magnetic behavior of IO and their nanocomposites, which is crucial for their potential applications in emerging technologies.

Magnetism doi: 10.3390/magnetism5010004

Authors: Vasilios C. Ilioudis

In this paper, a new sensorless approach is proposed to address the speed and position estimation of the Synchronous Reluctance Machine (SynRM). The design of the sensorless control algorithm is developed on the basis of the modified SynRM mathematical model employing a simple sliding mode observer (SMO) and a modified EMF observer that are connected in series. All variables of the modified SynRM model are expressed in the arbitrary rotating frame, which is the so-called estimated γδ reference frame. The derived modified rotor flux terms contain angle error information in the form of trigonometric functions. Initially, the modified rotor flux is expressed as a function of saliency and the stator current id, including the angular deviation between the dq and γδ reference frames, which are rotating at synchronous and estimated speeds, respectively. A suitably designed SMO is utilized to estimate the modified stator flux components in the γδ reference frame. Once the SMO operates in sliding mode, the derived equivalent control inputs of the flux/current observer are used to obtain the required angular position and speed information of rotor by means of the modified EMF and Speed/Position observer. Only measures of stator voltages and currents are required for the speed and position estimation. In addition, Lyapunov Candidate Functions (LCFs) have been applied to determine the sliding mode existence conditions and the gains of the modified EMF observer. The SynRM observer–controller system is tested and evaluated in a wide speed range, even at very low speeds, in the presence of torque load disturbances. Simulation results demonstrate the overall efficacy and robustness of the proposed sensorless approach. Moreover, simulation tests verify the fast convergence and high performance of the modified EMF/speed/angle observer.

Magnetism doi: 10.3390/magnetism5010003

Authors: Sabina Andreea Fironda Ioana Cristina Badea Marian Burada Radu-Robert Piticescu Lidia Licu

Rare earth elements (REEs) possess unique physical and chemical properties that render them indispensable in various industries, including electronics, energy production and storage, hybrid and electric vehicles, metallurgy, and petro-chemical processing. The criticality of REE underscores the need to enhance the efficiency of primary resource extraction and promote circularity through increased recycling from secondary sources. This paper provides a brief overview of REE recovery from secondary sources, particularly waste from electronic and electric equipment (WEEE). The discussion encompasses direct reuse of magnets, short-loop recycling (direct recycling), hydro- and pyrometallurgical processes, highlighting microwave (MW) technology. Original results are presented, focusing on the recovery of neodymium (Nd) from permanent magnet scraps from hard disk drives (HDD-PC) using microwave-assisted liquid metal extraction (LME) with magnesium (Mg) as the extractant. The subsequent separation of Nd from the Mg-Nd alloy via vacuum Mg distillation that is reused in the process is described. The experimental study demonstrates that the LME process, conducted in a microwave furnace, is a viable method for recovering Nd from permanent magnet scraps, which are essential for reducing the environmental impact of REE extraction and promoting a circular economy. By separating Nd from the alloy through vacuum distillation (450–550 mmHg), at temperatures of 850–900 °C for 8 h, a Nd sponge with a content of 95–98 wt.% Nd was obtained. The extracted content of Nd in the Mg alloy increases with increasing temperature and holding time. It was found that ≈ 97% of the Nd in the scrap was extracted from 2 to 5 mm crushed scrap at 800 °C for 8 h, using a LiF-LiCl-MgF2 protecting flux in a furnace Ar atmosphere.

Magnetism doi: 10.3390/magnetism5010002

Authors: Satoru Hayami

We conduct a numerical investigation into the stability of a quadruple-Q skyrmion crystal, a structure generated by the superposition of four spin density waves traveling in distinct directions within three-dimensional space, hosted on a centrosymmetric body-centered tetragonal lattice. Using simulated annealing applied to an effective spin model that includes momentum-resolved bilinear and biquadratic interactions, we construct a magnetic phase diagram spanning a broad range of model parameters. Our study finds that a quadruple-Q skyrmion crystal does not emerge within the phase diagram when varying the biquadratic interaction and external magnetic field. Instead, three distinct quadruple-Q states with topologically trivial spin textures are stabilized. However, we demonstrate that the quadruple-Q skyrmion crystal can become the ground state when an additional high-harmonic wave–vector interaction is considered. Depending on the magnitude of this interaction, we obtain two types of quadruple-Q skyrmion crystals exhibiting the skyrmion numbers of one and two. These findings highlight the emergence of diverse three-dimensional multiple-Q spin states in centrosymmetric body-centered tetragonal magnets.

Magnetism doi: 10.3390/magnetism5010001

Authors: Mehrija Hasičić Spyridon Angelopoulos Aphrodite Ktena Evangelos Hristoforou

The present work aspires to contribute to the discussion on the relationship between macroscopic measurements and microstructure, helping establish a methodology that will allow the quantitative assessment of the effect of strain on magnetic properties in the plastic deformation regime. In particular, we study the effect of strain on the magnetization process as a result of varying the anisotropy profile at the grain level. Results on micromagnetic calculations of hysteresis loops for various configurations of magnetic anisotropy are shown and discussed against the interplay between the energy terms involved in the calculations, namely anisotropy, demagnetizing, and exchange. The results are in line with previously obtained results using vector Preisach modeling with the Stoner–Wohlfarth model acting both as a switching and rotation mechanism. The hysteresis loop phenomenology is consistent with the emergence of a hard phase in the form of a boundary around soft grains which is assumed to be the result of the onset of compressive stresses in the plastic region. Future research will be oriented toward the study of the effect of the secondary peak in differential permeability, which is observed experimentally in the plastic deformation region, and its dependence on the angle of misalignment between the hard boundary and the soft grain.

Magnetism doi: 10.3390/magnetism4040027

Authors: Satoru Hayami

We investigate the instability toward a double-Q state, which consists of a superposition of two spin density waves at different wave vectors, on a two-dimensional noncentrosymmetric square lattice in an in-plane external magnetic field. By performing the simulated annealing for the spin model with the Dzyaloshinskii–Moriya interaction and bond-dependent anisotropic interaction, we obtain four types of double-Q states depending on the sign of the bond-dependent anisotropic interaction. On the other hand, only the single-Q spiral state appears in the absence of the bond-dependent anisotropic interaction. The present results suggest that the interplay between the Dzyaloshinskii–Moriya interaction and bond-dependent anisotropic interaction can give rise to multiple-Q states for both zero and nonzero in-plane magnetic fields.

Magnetism doi: 10.3390/magnetism4040026

Authors: Murat Tas Ersoy Şaşıoğlu Iosif Galanakis

All-d metallic Heusler compounds are promising materials for nanoelectronic applications. Such materials combining 3d, 4d, and 5d atoms have not yet been studied. In this respect, we perform ab initio electronic structure calculations and focus on Co2MnZ, Rh2MnZ, and Ru2MnZ compounds, where Z represents transition metal atoms from groups 3B, 4B, 5B, and 6B of the periodic table. Our results demonstrate that most of these compounds exhibit a distinctive region of very low minority-spin state density at the Fermi level when crystallized in the L21 lattice structure. The Co-based compounds follow a Slater–Pauling behavior for their total spin magnetic moments, while the Ru-based compounds consistently deviate from the predicted Slater–Pauling values. Rh-based compounds show similarities to Co-based compounds for lighter Z atoms and to Ru-based compounds for heavier Z atoms. We find that the choice of the Z element within the same periodic table column has only a minor effect on the results, except for the Rh2Mn(Cr, Mo, W) compounds. Our findings suggest that these compounds hold significant promise for applications in spintronics and magnetoelectronics.

Magnetism doi: 10.3390/magnetism4040025

Authors: Konstantin Guslienko

Recent advances in the research area of 3D magnetic topological solitons (hopfions) in restricted geometries are reviewed. The description of the magnetic solitons is based on a macroscopic micromagnetic approach and the Landau–Lifshitz equation of the magnetization motion. The concepts of the gauge emergent vector potential and emergent magnetic field are widely used to calculate the 3D topological charge (the Hopf index) of magnetic textures. The relation of the magnetic hopfions with classical field theory is demonstrated, and a special role of the curvilinear toroidal coordinates in the description of the hopfions is underlined. The hopfion stability and dynamics in ferromagnetic films and dots are considered. A critical discussion of calculations of the magnetization emergent magnetic field and the Hopf index of the toroidal magnetic hopfions in restricted geometries is presented.

Magnetism doi: 10.3390/magnetism4040024

Authors: Satoru Hayami

We investigate the stability tendency of a magnetic skyrmion crystal in noncentrosymmetric tetragonal systems with the Dzyaloshinskii–Moriya interaction. We show that the stability region of the square skyrmion crystal on a square lattice depends on the Ising-type magnetic anisotropic interaction by performing the simulated annealing for the spin model. The easy-axis anisotropic interaction tends to narrow the region where the square skyrmion crystal is stabilized when the magnetic field is applied in the out-of-plane direction. In contrast, the easy-plane anisotropic interaction tends to enlarge the stability region. Meanwhile, the square skyrmion crystal induced by the easy-axis anisotropic interaction is robust compared with that induced by the easy-plane anisotropic interaction when the magnetic field is tilted from the out-of-plane to the in-plane direction. The results indicate that the instability toward the square skyrmion crystal in noncentrosymmetric crystals is sensitive to both magnetic anisotropy and magnetic fields.

Magnetism doi: 10.3390/magnetism4040023

Authors: Mehdi Abdolmaleki Pedram Asef Christopher Vagg

Rare-earth-based permanent magnets (PMs) have a vital role in numerous sustainable energy systems, such as electrical machines (EMs). However, their production can greatly harm the environment and their supply chain monopoly presents economic threats. Alternative materials are emerging, but the use of rare-earth PMs remains dominant due to their exceptional performance. Damage to magnet structure can cause loss of performance and efficiency, and propagation of cracks in PMs can result in breaking. In this context, prolonging the service life of PMs and ensuring that they remain damage-free and suitable for re-use is important both for sustainability reasons and cost management. This paper presents a new harmonic content diagnosis and motor performance analysis caused by various magnet structure defects or faults, such as cracked or broken magnets. The proposed method is used for modeling the successive physical failure of the magnet structure in the form of crack formation, crack growth, and magnet breakage. A surface-mounted permanent magnet synchronous motor (PMSM) is studied using simulation in Ansys Maxwell software (Version 2023), and different cracks and PM faults are modeled using the two-dimensional finite element method (FEM). The frequency domain simulation results demonstrate the influence of magnet cracks and their propagation on EM performance measures, such as stator current, distribution of magnetic flux density, back EMF, flux linkage, losses, and efficiency. The results show strong potential for application in health monitoring systems, which could be used to reduce the occurrence of in-service failures, thus reducing the usage of rare-earth magnet materials as well as cost.

Magnetism doi: 10.3390/magnetism4040022

Authors: Shadan Ghassemi Tabrizi Thomas D. Kühne

Spin Hamiltonians, like the Heisenberg model, are used to describe the magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities, such as heat capacities, magnetic susceptibilities or neutron-scattering spectra, can be calculated based on energies and eigenstates obtained by exact diagonalization (ED). Utilizing spin-rotational symmetry SU(2) to factor the Hamiltonian with respect to total spin S facilitates ED, but the conventional approach to spin-adapting the basis is more intricate than selecting states with a given magnetic quantum number M (the spin z-component), as it relies on irreducible tensor-operator techniques and spin-coupling coefficients. Here, we present a simpler technique based on applying a spin projector to uncoupled basis states. As an alternative to Löwdin’s projection operator, we consider a group-theoretical formulation of the projector, which can be evaluated either exactly or approximately using an integration grid. An important aspect is the choice of uncoupled basis states. We present an extension of Löwdin’s theorem for s=12 to arbitrary local spin quantum numbers s, which allows for the direct selection of configurations that span a complete, linearly independent basis in an S sector upon the spin projection. We illustrate the procedure with a few examples.

Magnetism doi: 10.3390/magnetism4040021

Authors: Tanguy Phulpin Wassim Kabbara Mohammed Terrah Mostafa-Kamel Smail Mohamed Bensetti

The efficiency of Dynamic Inductive Power Transfer (DIPT) depends mainly on the coupling coefficient within the coupler. In order to improve this parameter, a novel approach has been introduced that results in a significant increase of between 25% and 36% at minimal additional cost in the case of juxtaposed rectangular coil configuration on the road. This method involves the incorporation of a passive additional short-circuit coil adjacent to the primary coil for obtaining a higher coupling coefficient, as has been theoretically demonstrated. Simulations carried out on Comsol have optimized the dimensions of this additional coil, not only for cost effectiveness and minimal space utilization, but also for optimal efficiency. Experimental validation was performed at reduced power, using a 2 kW test bench, and confirmed the estimation. The efficiency improvement proposed in this paper is crucial for improving the global DIPT efficiency and then facilitating its social acceptance.

Magnetism doi: 10.3390/magnetism4040020

Authors: Bruno Barton-Singer

Two recently developed methods of modelling chiral magnetic soliton elliptical instability are applied in two novel scenarios: the tilted ferromagnetic phase of chiral magnets dominated by easy-plane anisotropy and the general case of the chiral magnet with tilted applied field and arbitrary uniaxial anisotropy. In the former case, the analytical predictions are found to exactly match previous numerical results. In the latter case, the instability of isolated chiral skyrmions has not yet been studied, although interestingly, the predictions correspond to previous numerical investigation into the phase diagram.

Magnetism doi: 10.3390/magnetism4030019

Authors: Carlo Burkhardt Francisco Ortiz Kaies Daoud Tomas Björnfot Fredrik Ahrentorp Jakob Blomgren Allan Walton

This work describes an automated pilot plant for the extraction of rare-earth (RE) permanent magnets from computer hard-disk drives (HDDs), demonstrating a commercially viable way to exploit these abundant sources of end-of-life (EOL) magnets. A mobile approach is provided for the on-site destruction of the HDDs in server farms, in compliance with the European Data Protection Regulation (GDPR), enabling both separation of the magnets and automated shredding of the data carrier. This fully automated process identifies (both optically and magnetically) the location of the rare-earth magnets and cuts off the corner of the hard drive containing the rare-earth material in the voice coil motor. This allows for a significant reduction in magnet extraction time (6 s per HDD) compared to previously reported semi-automated (2 min) and manual (5 min) dismantling times. This work will also help to transfer the experience gained in the mobile pilot plant to other future sources of EOL materials such as drive motors and mixed electronic scrap.

Magnetism doi: 10.3390/magnetism4030018

Authors: Satoru Hayami

We investigate the emergence of magnetic skyrmion crystals with swirling topological spin textures in itinerant magnets with an emphasis on momentum-resolved multi-spin interactions. By performing the simulated annealing for the effective spin model with the two-spin and four-spin interactions on a two-dimensional triangular lattice, we show that various types of four-spin interactions become the microscopic origin of the magnetic skyrmion crystal with the skyrmion numbers of one and two. We find that the four-spin interactions between the different wave vectors lead to the skyrmion crystal with the skyrmion number of one, whereas those at the same wave vectors lead to the skyrmion crystals with the skyrmion number of one and two. Our results indicate that the multi-spin interactions arising from the itinerant nature of electrons provide rich topological spin textures in magnetic metals.

Magnetism doi: 10.3390/magnetism4030017

Authors: Carlos Moya Jorge Ara Amílcar Labarta Xavier Batlle

NiO nanoparticles have garnered significant interest due to their diverse applications and unique properties, which differ markedly from their bulk counterparts. NiO nanoparticles are p-type semiconductors with a wide bandgap, high discharge capacity, and high carrier density, making them ideal for use in batteries, sensors, and catalysts. Their ability to generate reactive oxygen species also imparts disinfectant and antibiotic properties. Additionally, the higher Néel temperature of NiO compared with other antiferromagnetic materials makes it suitable for high-temperature applications in spintronic devices and industrial settings. This review focuses on the critical role of structure and composition in determining the magnetic properties of NiO nanoparticles. It examines how finite-size surface effects, morphology, crystallinity, and nickel distribution influence these properties. Fundamental physical properties and characterization techniques are discussed first. Various synthesis methods and their impact on NiO nanoparticle properties are then explored. Their magnetic phenomenology is examined in detail, highlighting the effects of finite size, particle composition and surface, and crystal quality. The review concludes with a summary of key insights and future research directions for optimizing NiO nanoparticles in technological applications.

Magnetism doi: 10.3390/magnetism4030016

Authors: Jessica R. P. Oliveira Eduardo Abreu Maria E. K. Fuziki Elaine T. de Paula Michel Z. Fidelis Rodrigo Brackmann Angelo M. Tusset Odivaldo C. Alves Giane G. Lenzi

This work presents an investigation of the degradation of paracetamol via heterogeneous photocatalysis, aiming to magnetically immobilize the catalyst in a continuous process. Catalyst immobilization was conducted on aggregated flower-like structures. The CoFe2O4@Nb5O2 catalyst was characterized using a Vibrating Sample Magnetometer (VSM). The effects of the magnetic immobilization of the catalyst, flow, residence time, adsorption, and photolysis were evaluated. Additionally, catalyst reuse cycles were analyzed. The results indicated that a longer residence time favors the degradation of paracetamol due to the increase in the contact time of the effluent catalyst. At a flow rate of 20 mL·min−1, a degradation of 27% was obtained. Photolysis and adsorption tests indicated that residence time was not an important factor for paracetamol degradation. For the photolysis test, in the first cycle, the values obtained were in the range of 6.0–8.5%. The adsorption results indicated ~10% removal.

Magnetism doi: 10.3390/magnetism4030015

Authors: Anwer S. Abd El-Hameed Dalia M. Elsheakh Gomaa M. Elashry Esmat A. Abdallah

In this article, a comprehensive review is presented of recent technological advancements utilizing electromagnetic sensors in the microwave range for detecting human vital signs and lung water levels. With the main objective of improving detection accuracy and system robustness, numerous advancements in front-end architecture, detection techniques, and system-level integration have been reported. The benefits of non-contact vital sign detection have garnered significant interest across a range of applications, including healthcare monitoring and search and rescue operations. Moreover, some integrated circuits and portable systems have lately been shown off. A comparative examination of various system architectures, baseband signal processing methods, system-level integration strategies, and possible applications are included in this article. Going forward, researchers will continue to focus on integrating radar chips to achieve compact form factors and employ advanced signal processing methods to further enhance detection accuracy.

Magnetism doi: 10.3390/magnetism4030014

Authors: Frank Zhigang Wang

In 1971, Chua defined an ideal memristor that links magnetic flux φ and electric charge q. In a magnetic lump with a current-carrying conductor, we found that the direct interaction between physical magnetic flux φ and physical electric charge q is memristive by nature in terms of a time-invariant φ-q curve being nonlinear, continuously differentiable and strictly monotonically increasing. Although we succeeded in demonstrating that the “ideal/real/perfect/… memristor” needs magnetism, the structure still suffers from two serious limitations: 1. a parasitic “inductor” effect and 2. bistability and dynamic sweep of a continuous resistance range. Then, we discussed how to overcome these two limitations to make a fully functioning ideal memristor with multiple or an infinite number of stable states and no parasitic inductance. We then gave a number of innovations to the current memristor structure, such as an “open” structure, nanoscale size, magnetic materials with cubic anisotropy (or even isotropy) and sequential switching of the magnetic domains. Contrary to the conjecture that “an ideal memristor may not exist or may be a purely mathematical concept”, we remain optimistic that an ideal memristor will be discovered in nature or will be made in the laboratory. Our finding of the memristive flux–charge interaction may advance the development and application of the memristor technology.

Magnetism doi: 10.3390/magnetism4030013

Authors: Shadan Ghassemi Tabrizi Thomas D. Kühne

Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters with spatial symmetry, analytical solutions exist, and a few Heisenberg systems have been solved in closed form. This paper presents a simple, generally applicable approach to analytically solve isotropic spin clusters, based on adapting the basis to both total spin and point group symmetry to factor the Hamiltonian matrix into sufficiently small blocks. We demonstrate applications to small rings and polyhedra, some of which are straightforward to solve by successive spin-coupling for Heisenberg terms only; additional interactions, such as biquadratic exchange or multi-center terms necessitate symmetry adaptation.

Magnetism doi: 10.3390/magnetism4030012

Authors: László F. Kiss Imre Bakonyi

The exact formulae for calculating the demagnetizing factors of a general ellipsoid along the three main axes a ≥ b ≥ c have been long known. According to these formulae, the demagnetizing factors depend only on the axial ratios b/a and c/a. Although the calculation of the demagnetizing factors is a straightforward task, the calculation itself is not a simple one. Therefore, tabular and graphical representations of these demagnetizing factor data have also been presented which can then be used for approximating the demagnetizing factors of a rectangular ferromagnetic slab with the same axial ratios. It turned out in our recent study, however, that, in some ranges of axial ratios (e.g., for very small c/a values), the available tables and graphs do not provide sufficient resolution for obtaining the demagnetizing factors with reasonable accuracy. It was decided to calculate these missing values, and they are presented here in both tabular and graphical form by giving instructions for how to obtain conveniently further interpolated data. In addition, the previous and current demagnetizing factor data have been replotted and fitted to a polynomial function with high accuracy. The functional form of these fitting polynomials is presented in a table for the whole range of the axial ratios b/a and c/a. By graphically displaying these functions, one can obtain, in a relatively simple manner, the demagnetizing factors of a general ellipsoid with known axial ratios without the need to directly calculate through the exact formulae. This may be helpful in obtaining a quick estimate for the demagnetizing factors of any rectangular ferromagnetic slab of interest.

Magnetism doi: 10.3390/magnetism4030011

Authors: Uta Rösel Dietmar Drummer

Multipolar bonded magnets based on a thermoset matrix provide the opportunity to expand the applications of bonded magnets, especially within the drive technology industry, in terms of the high thermal and chemical resistance, along with a higher utilisation of the magnetic potential. To realize the application of polymer bonded magnets based on thermosets within the drive technology industry, general design parameters in terms of the material, the process parameters, and the tool concept are needed. These allow for a fundamental realization of multipolar bonded magnets with complex geometries in drive technologies, based on thermosets as the matrix material. This paper investigates the impact of the material (matrix material and filler grade), the process conditions (holding pressure (ph) and heating time (th)), and the tool concept (gating position and system, sleeve material, pole division, and sample thickness) on the magnetic properties in terms of the remanence (BR) and the deviation (Δs) of the pole division, as well as the orientation of the fillers in the middle of the pole and at the pole pitch. For each parameter, an optimised value is derived. In the majority of the cases, this value is equal in terms of the magnetic properties and the orientation. In terms of the sleeve material and the sample thickness, the ideal value differs between the two criteria. Therefore, an optimised value for each criterion, as well as an overall value, is defined. In terms of the material, PF, along with a high filler grade; in terms of the process conditions, a high holding pressure (ph) and a low heating time (th); and in terms of the tool concept, a two-pinpoint gating system, located in the middle of the pole, a Ferro-Titanit-Cromoni sleeve material, a high pole division, as well as small sample thickness, should be selected to improve the properties of polymer bonded magnets based on thermosets.

Magnetism doi: 10.3390/magnetism4020010

Authors: Saikumar Dussa Sameehan S. Joshi Shashank Sharma Karri Venkata Mani Krishna Madhavan Radhakrishnan Narendra B. Dahotre

Additive manufacturing offers manufacturing flexibility for intricate components and also allows for precise control over the microstructure. This review paper explores the current state of the art in additive manufacturing techniques for Alnico permanent magnets, emphasizing the notable advantages and challenges associated with this innovative approach. Both the LPBF and L-DED processes have demonstrated promising results in fabricating Alnico with magnetic properties comparable with conventionally processed samples. The optimization of process parameters successfully reduced porosity and cracking in the LPBF processing of Alnico. The review further explored the significance of additive manufacturing process parameter optimization in managing the temperature gradient and solidification rate for a desired microstructure and enhanced magnetic properties. Other potential additive manufacturing methods suitable for the fabrication of Alnico were discussed, along with the challenges associated with the process. The insights provided also highlight how additive manufacturing holds the potential to replace post-processing techniques like solutionization, magnetic annealing, and tempering often necessary in Alnico production.

Magnetism doi: 10.3390/magnetism4020009

Authors: Tomasz Kubiak

The investigation and clarification of the properties of surface-functionalized superparamagnetic nanoparticles in a biological environment are key challenges prior to their medical applications. In the present work, electron paramagnetic resonance spectroscopy (EPR) combined with the spin labeling technique was utilized to better understand the behavior of nitroxides attached to magnetite nanoparticles dispersed in body fluid. EPR spectra of spin-labeled, silane-coated Fe3O4 nanoparticles in human serum and whole blood were recorded and analyzed for both room- and low-temperature values. In all cases, the obtained EPR signal consisted of a broad line from magnetite cores and a characteristic signal from the attached 4-Amino-2,2,6,6-tetramethylpiperidine-1-oxyl (4-amino-TEMPO). Even for liquid samples, the anisotropic components of magnetic tensors did not fully average out, which was reflected in the differences in the intensity of three narrow hyperfine lines from nitroxide. At 230 K the irregular slow-motion signal from the attached radical was also simulated using the EasySpin toolbox, which allowed to determine the parameters related to magnetic tensors and the dynamics of the spin label. The study showed that the anisotropy of the motion of the spin label 4-amino-TEMPO reflects its interactions with the surrounding medium and the manner of the attachment of the nitroxide to the surface of nanoparticles.

Magnetism doi: 10.3390/magnetism4020008

Authors: Lara B. Oliveira Teonis S. Paiva Hamilton A. Teixeira Clodoaldo I. L. de Araujo

Inspired in pyrochlore materials presenting residual entropy and featuring collective excitation behaving like emergent monopoles, geometrically frustrated arrays of nanomagnets, denominated artificial spin ices (ASIs), were proposed as an interesting platform to investigate such excitation at room temperature. However, in such artificial systems, emergent magnetic monopoles lack the same freedom present their natural counterpart, once energetic strings connecting opposite magnetic charges arise. In this work, we aim to experimentally investigate the proposed degeneracy obtained in connected square arrays of ASIs, a characteristic that allows a reduction in the string connecting monopole–antimonopole pairs in regular non-connected ASIs and could represent an important development for technological applications of connected nanomagnets. As in general those systems are developed by nanofabrication processes involving expensive and time-consuming physical vapour deposition techniques, we also present a new nanofabrication route using an electrodeposition technique for permalloy growth in different lattice geometries as an alternative for fast and low-cost ASI system production.

Magnetism doi: 10.3390/magnetism4020007

Authors: Andrey O. Leonov

The structure of skyrmion and spiral solutions, investigated within the phenomenological Dzyaloshinskii model of chiral magnets near the ordering temperatures, is characterized by the strong interplay between longitudinal and angular order parameters, which may be responsible for experimentally observed precursor effects. Within the precursor regions, additional effects, such as pressure, electric fields, chemical doping, uniaxial strains and/or magnetocrystalline anisotropies, modify the energetic landscape and may even lead to the stability of such exotic phases as a square staggered lattice of half-skyrmions, the internal structure of which employs the concept of the “soft” modulus and contains points with zero modulus value. Here, we additionally alter the stiffness of the magnetization modulus to favor one- and two-dimensional modulated states with large modulations of the order parameter magnitude. The computed phase diagram, which omits any additional effects, exhibits stability pockets with a square half-skyrmion lattice, a hexagonal skyrmion lattice with the magnetization in the center of the cells parallel to the applied magnetic field, and helicoids with propagation transverse to the field, i.e., those phases in which the notion of localized defects is replaced by the picture of a smooth but more complex tiling of space. We note that the results can be adapted to metallic glasses, in which the energy contributions are the same and originate from the inherent frustration in the models, and chiral liquid crystals with a different ratio of elastic constants.

Magnetism doi: 10.3390/magnetism4010006

Authors: Waled Albakosh Rawad Asfour Tarek S. Abdou Yas Khalil Salam K. Khamas

This article delves into the capabilities of 3D-printed millimeter-wave (mmWave) layered cylindrical dielectric resonator antennas (CDRAs). The proposed design yielded promising results, boasting a remarkable 53% impedance bandwidth spanning the frequency spectrum from 18 to 34 GHz. Furthermore, the axial ratio (AR) bandwidth achieved an impressive 17%, coupled with a maximum gain of 13.3 dBic. These notable results underscore the efficacy of the proposed design, positioning it as a viable solution for applications in Beyond 5G (B5G). A novel assembly technique was also investigated, employing additive manufacturing to seamlessly merge two layers with distinct dielectric constants into a singular layer. This innovative approach systematically eliminates the potential for air gaps between layers, enhancing the antenna’s overall performance. This approach exhibited potential, particularly in the performance of a millimeter-wave circularly polarized (CP) cylindrical DRA featuring a perforated coating layer. The synergy between measurements and simulations demonstrates a remarkable alignment, providing robust validation of the effectiveness of the proposed design.

Magnetism doi: 10.3390/magnetism4010005

Authors: Satoru Hayami

We report our numerical results on the stability of the skyrmion crystal phase in an external magnetic field for both in-plane and out-of-plane directions in a centrosymmetric host. We analyze a spin model with the two-spin symmetric anisotropic exchange interaction that arises from relativistic spin–orbit coupling on a triangular lattice. By performing simulated annealing, we construct magnetic phase diagrams when the magnetic field is tilted from the out-of-plane field direction to the in-plane field direction. We find a different stability tendency of the skyrmion crystal phase according to the directions of the in-plane field, which provides a signal of the two-spin symmetric anisotropic exchange interaction for stabilizing the skyrmion crystal phase. Our results indicate that the mechanism of the skyrmion crystal phase triggered by the two-spin symmetric anisotropic exchange interaction can be experimentally tested by applying the in-plane magnetic field.

Magnetism doi: 10.3390/magnetism4010004

Authors: Julien Gasnier Christophe Dolabdjian

Studying the spatial response of a single-axis magnetometer could be the key parameter to optimize the ultimate performances of magnetic heads of detection. Indeed, the problem of non-orthogonality, misalignment, and 3D spatial response could be improved based on the knowledge of the 3D sensor spatial response. In that way, we have investigated the latter for our giant magneto-impedance (GMI) magnetometer, as a far-field pattern, by using a three-axis Helmholtz coil system. Firstly, we calibrate our device and secondly, we apply a specific 3D magnetic field to obtain this pattern. The latter helps to observe the directional or angular dependence of the sensor sensitivity versus the applied magnetic field, as we exemplified. The results confirm the excellent directivity of our off-diagonal GMI magnetometer. The evaluation of the associated error compared to an ideal vector magnetometer is also given and discussed.

Magnetism doi: 10.3390/magnetism4010003

Authors: Emily D. Williams Keith M. Taddei Kulugammana G. S. Ranmohotti Narendirakumar Narayanan Thomas Heitmann Joseph W. Kolis Liurukara D. Sanjeewa

Novel quantum materials offer the opportunity to expand next-generation computers, high-precision sensors, and new energy technologies. Among the most important factors influencing the development of quantum materials research is the ability of inorganic and materials chemists to grow high-quality single crystals. Here, the synthesis, structure characterization and magnetic properties of Na2Cu3(SeO3)4 are reported. It exhibits a novel two-dimensional (2D) structure with isolated layers of Cu nets. Single crystals of Na2Cu3(SeO3)4 were grown using a low-temperature hydrothermal method. Single-crystal X-ray diffraction reveals that Na2Cu3(SeO3)4 crystallizes in the monoclinic crystal system and has space group symmetry of P21/n (No.14) with a unit cell of a = 8.1704(4) Å, b = 5.1659(2) Å, c = 14.7406(6) Å, β = 100.86(2), V = 611.01(5) Å3 and Z = 2. Na2Cu3(SeO3)4 comprises a 2D Cu-O-Cu lattice containing two unique copper sites, a CuO6 octahedra and a CuO5 square pyramid. The SeO3 groups bridge the 2D Cu-O-Cu layers isolating the neighboring Cu-O-Cu layers, thereby enhancing their 2D nature. Magnetic properties were determined by measuring the magnetic susceptibility of an array of randomly oriented single crystals of Na2Cu3(SeO3)4. The temperature-dependent magnetic measurement shows an antiferromagnetic transition at TN = 4 K. These results suggest the fruitfulness of hydrothermal synthesis in achieving novel quantum materials and encourage future work on the chemistry of transition metal selenite.

Magnetism doi: 10.3390/magnetism4010002

Authors: Sueli H. Masunaga Vagner B. Barbeta Fábio Abud Milton S. Torikachvili Renato F. Jardim

Measurements of specific heat and magnetization in single crystals were used to map out the magnetic phase diagram of Gd1−xErxB4 (x = 0.2 and 0.4) solid solutions along the c-axis. While GdB4 orders antiferromagnetically (AF) at 41.7 K, with the easy plane of magnetization oriented perpendicularly to the c-axis, ErB4 displays AF ordering below 15.4 K, with the easy axis along c. Therefore, in solid solutions, the competition between the different spin anisotropies, as well as frustration, lead to a complex spin configuration. These measurements reveal that a 40% substitution of Er for Gd is sufficient for generating a phase diagram similar to the one for the ErB4 system, characterized by the occurrence of plateau phases and other exotic features attributed to the interplay of competing magnetic anisotropies.

Magnetism doi: 10.3390/magnetism4010001

Authors: Uta Rösel Dietmar Drummer

The applications of polymer-bonded magnets are increasing within drive technology mostly because of new concepts concerning the magnetic excitation of direct current (DC) or synchronous machines. To satisfy this rising demand for hard magnetic filler particles—mainly rare earth materials—in polymer-bonded magnets, a recycling strategy for thermoplastic-based bonded magnets has to be found that can be applied to polymer-bonded magnets. The most important factor for the recycling strategy is the filler material, especially when using rare earth materials, as those particles are associated with limited resources and high costs. However, thermoplastic-based bonded magnets reveal the opportunity to reuse the compound material system without separation of the filler from the matrix. Most known recycling strategies focus on sintered magnets, which leads to highly limited knowledge in terms of strategies for recycling bonded magnets. This paper illustrates the impact of different amounts of recycling material within the material system on material behavior and magnetic properties that can be achieved by taking different flow conditions and varying gating systems into account. The recycled material is generated by the mechanical reuse of shreds. We found that a supporting effect can be achieved with up to 50% recycled material in the material system, which leads to only minimal changes in the material’s behavior. Furthermore, changes in magnetic properties in terms of recycled material are affected by the gating system. To reduce the reduction in magnetic properties, the number of pin points should be as low as possible, and they should located in the middle. The filler orientation of the recycled material is minimally influenced by the outer magnetic field and, therefore, mainly follows the flow conditions. These flow conditions are likely to be affected by elastic flow proportions with increasing amounts of recycled material.

Magnetism doi: 10.3390/magnetism3040025

Authors: Kai Xu Youguang Guo Gang Lei Jianguo Zhu

The popularity of permanent magnet synchronous motors (PMSMs) has increased in recent years due to their high efficiency, compact size, and low maintenance needs. Calculating iron loss in PMSMs is crucial for designing and optimizing PMSMs to achieve high efficiency and a long lifespan, as this can significantly affect motor performance. However, multiple factors influence the accuracy of iron loss calculations in PMSMs, including the intricate magnetic behavior of the motor under different operating conditions, as well as the influence of the motor’s dynamic behavior during the operation process. This paper proposes a method based on particle swarm optimization (PSO) and a recurrent neural network (RNN) to estimate the iron loss in PMSMs, independent of the empirical iron loss formula. This method establishes an iron loss calculation model considering high-order harmonics, rotating magnetization, and temperature factors. Accounting for the multifactor influence, the model studies the law of loss change under different magnetic flux densities, frequencies, and temperature conditions. To avoid the deviation problem caused by conventional polynomial fitting, a multilayer RNN and PSO are used to train and optimize the neural network. Iron loss in complex cases beyond the measurement range can be accurately estimated. The proposed method helps achieve a PMSM iron loss calculation model with broad applicability and high accuracy.

Magnetism doi: 10.3390/magnetism3040024

Authors: Antonino Di Gerlando Claudio Ricca

The slot opening function, also called relative air gap permeance, is a function which, multiplied by the flux density distribution of a slotless geometry, gives the flux density distribution of a slotted configuration. Here, the magnetic field inside the air gap of a multi-slot surface facing a smooth one was studied, by solving the Laplace equation inside the air gap, in terms of a Fourier series. To obtain the Fourier coefficients, at first, the conformal mapping analytical solution of a single-slot configuration along the smooth surface, was considered. Then, the principle of superposition of the single-slot lost flux density distributions was applied to obtain the multi-slot distribution. The approach is valid in general, and in the case of interference among the flux density distributions of adjacent slots, where their mutual effect cannot be neglected. The field distributions obtained by using the proposed slot opening functions were compared with FEM simulations, showing satisfactory agreement. The numerical accuracy limits were also analysed and discussed.

Magnetism doi: 10.3390/magnetism3040023

Authors: Andrey O. Leonov

Magnetic hopfions are three-dimensional topological solitons embedded into a homogeneously magnetized background. The internal structure of hopfions is distinguished by the linked preimages—closed loops with a single orientation of the magnetization on the target space S2—and is thus characterized by the integer Hopf index QH. Alternatively, hopfions can be visualized as a result of the swirling of two-dimensional bimerons around the direction of an applied magnetic field. Since the bimeron consists of a circular core and an anti-skyrmion crescent, two hopfion varieties can be achieved with either bimeron constituent facing the hopfion interior. In bulk cubic helimagnets, however, the applied magnetic field leads to a spontaneous collapse of hopfions, i.e., the eigen-energy of hopfions has the minimum for zero hopfion radius R. Anti-hopfions with QH=−1, in this case, pass through the intermediate toron state with two-point defects. Here, we demonstrate that the competing cubic and exchange anisotropies inherent in cubic non-centrosymmetric magnets (e.g., in the Mott insulator Cu2OSeO3) as a third level of the hierarchy of energy scales following the exchange and Dzyaloshinskii–Moriya interactions, may shift the energy minimum into the region of finite hopfion radii.

Magnetism doi: 10.3390/magnetism3040022

Authors: Antonino Di Gerlando Simone Negri Claudio Ricca

This paper presents an analytical study of the air-gap magnetic field of a surface permanent magnet (SPM) linear, slot-less machine with a Halbach PM configuration, under the no-load condition. While other analytical formulations of the magnetic field generated by PMs are available, they exhibit some drawbacks, such as only providing a Fourier series, or being suitable to determine magnetic field average values, but not local magnetic field distributions. On the contrary, the proposed approach allows the determination of a unique, closed-form formulation for the slot-less machine air-gap field. This is obtained starting from the complex expression of the magnetic field of a conductor, inside the air gap, between two parallel smooth iron surfaces, obtained by means of the method of images. The magnetic field due to an infinitesimal conductor belonging to a current sheet is then integrated along a segment, providing the expression of the magnetic field due to the corresponding linear current density distribution, for current sheets perpendicular or parallel to the iron surfaces. Any Halbach PM segment disposition can, hence, be obtained via a suitable combination of field distributions generated by couples of current sheets with perpendicular and parallel orientation. Lastly, the no-load magnetic field expression with a Halbach array of PMs is retrieved. The proposed analytical model provides an accurate representation of the magnetic field distribution produced by any Halbach array, with an arbitrary number of segments and orientations. Additionally, the results obtained from the proposed analytical expressions are compared with FEM simulations realized by commercial software, and show an excellent agreement.

Magnetism doi: 10.3390/magnetism3040021

Authors: Reza Kamali-Sarvestani John D. Williams

A novel micro-solenoid resonator has been designed, simulated, and measured. The solenoid core consisted of a DuroidTM circuit board with a relative permittivity of 2.2. The resonator design incorporated four embedded copper vias with a radius of 125 µm and three surface conductors to form a rectangular coil. A pitch size of 250 µm was used for a 3.02 mm thick substrate. To enhance the resonator’s performance at higher frequencies, a capacitance was introduced in series through the via. This additional capacitor effectively couples the inductance, resistance, and stray capacitance. The optimization of the quality factor was investigated through pole transfer analysis, resulting in an increased resonance frequency of 12.25 GHz and an elevated Q-factor of 306. Moreover, besides its very high Q-factor, this resonator offers a simplified design and easy integration. An analytical lumped circuit model was employed to investigate the design, and the measured S-parameters closely matched the analytical model and electromagnetic simulation results. The tuned resonator exhibited a superior quality factor compared to other micro-resonators.

Magnetism doi: 10.3390/magnetism3030020

Authors: Fedor Mushenok Artem Shevchun Dmitriy Shovkun Maria Prokudina

Transition metal dichalcogenides are studied due to the possibility of creating nanoscale semiconductor devices, as well as fundamental issues of magnetic ordering. We researched the crystal structure and magnetic properties of niobium dichalcogenide Mn0.30NbS2. The results of the X-ray study showed the possible existence of an intermediate 23a0·23a0 structure between the “basic” superstructures. Also, two local maximums were found in the temperature dependence of the dynamic magnetic susceptibility. These features can indirectly confirm the presence of a transition superstructure and reflect the two-step nature of the magnetic ordering.

Magnetism doi: 10.3390/magnetism3030019

Authors: Priyamvada Jadaun Bart Soreé

Recent years have seen the emergence of moiré materials as an attractive platform for observing a host of novel correlated and topological phenomena. Moiré heterostructures are generated when layers of van der Waals materials are stacked such that consecutive layers are slightly mismatched in their lattice orientation or unit cell size. This slight lattice mismatch gives rise to a long-wavelength moiré pattern that modulates the electronic structure and leads to novel physics. The moiré superlattice results in flat superlattice bands, electron–electron interactions and non-trivial topology that have led to the observation of superconductivity, the quantum anomalous Hall effect and orbital magnetization, among other interesting properties. This review focuses on the experimental observation and theoretical analysis of orbital magnetism in moiré materials. These systems are novel in their ability to host magnetism that is dominated by the orbital magnetic moment of Bloch electrons. This orbital magnetic moment is easily tunable using external electric fields and carrier concentration since it originates in the quantum anomalous Hall effect. As a result, the orbital magnetism found in moiré superlattices can be highly attractive for a wide array of applications including spintronics, ultra-low-power magnetic memories, spin-based neuromorphic computing and quantum information technology.

Magnetism doi: 10.3390/magnetism3030018

Authors: Uta Rösel Dietmar Drummer

Multipolar bonded magnets based on thermosets offer the opportunity to expand the applications of bonded magnets with respect to an increasing chemical and thermal resistance compared to thermoplastics. To utilise this option, the correlation between the material system and the magnetic properties must be explored amongst other influencing factors. This paper investigates the magnetic properties and the orientation of thermoset- (epoxy resin and phenolic resin) based bonded ring magnets with a hard magnetic filler of strontium-ferrite-oxide. The influence of the matrix material and the filler grade on the magnetic properties is correlated with the material characterisation showing a high impact of the embedding of the fillers into the matrix on the orientation and with that the magnetic properties. Based on a network theory, it can be justified that the magnetic properties can be increased due to a phenolic resin and a high filler grade. Further, it was shown that the orientation along the sample depth is highly affected by the strength of the outer magnetic field and limited in terms of the high-tool temperature in a thermoset-based production. With that, the sample depth, which reveals a proper orientation, is restricted so far.

Magnetism doi: 10.3390/magnetism3030017

Authors: Irina Piyanzina Kirill Evseev Andrey Kamashev Rinat Mamin

Magneto-electric coupling is a desirable property for a material used in modern electronic devices to possess due to the favorable possibilities of tuning the electronic properties using a magnetic field and vice versa. However, such materials are rare in nature. That is why the so-called superlattice approach to creating such materials is receiving so much attention. In the superlattice approach, the functionality of a combined heterostructure depends on the interacting components and can be adjusted depending on the desired property. In the present paper, we present supercells of ferromagnetic thin films of Fe and Co deposited on ferroelectric and piezoelectric substrates of BaTiO3 and SrTiO3 that exhibit magnetism, ferroelectric polarization and piezoelectric effects. Within the structures under investigation, magnetic moments can be tuned by an external electric field via the ferroelectric dipoles. We investigate the effect of magnetoelectric coupling by means of ab initio spin-polarized and spin–orbit calculations. We study the structural, electronic and magnetic properties of heterostructures, and show that electrostriction can reduce the magnitude of the magnetization vector of a ferromagnet. This approach can become the basis for controlling the properties of one of the ferromagnetic layers of a superconducting spin valve, and thus the superconducting properties of the valve.

Magnetism doi: 10.3390/magnetism3030016

Authors: Andrey Kamashev Nadir Garif’yanov Aidar Validov Zvonko Jagličić Viktor Kabanov Rinat Mamin Ilgiz Garifullin

The properties of a superconducting spin valve Fe1/Cu/Fe2/Cu/Pb on a piezoelectric PMN–PT substrate ([Pb(Mg1/3Nb2/3)O3]0.7–[PbTiO3]0.3) in electric and magnetic fields have been studied. The magnitude of the shift of the superconducting transition temperature in the magnetic field H = 1 kOe equal to 150 mK was detected, while the full superconducting spin valve effect was demonstrated. Abnormal behavior of the superconducting transition temperature was observed, which manifests itself in the maximum values of the superconducting transition temperature with the orthogonal orientation of the magnetization vectors of ferromagnetic layers. This may indirectly indicate the formation of the easy axis of the magnetization vector of the Fe1-layer adjacent to the piezoelectric substrate PMN–PT. It was found that with an increase in the magnitude of the applied electric field to the PMN–PT substrate, the shift in the superconducting transition temperature of the Fe1/Cu/Fe2/Cu/Pb heterostructure increases. The maximum shift was 10 mK in an electric field of 1 kV/cm. Thus, it has been shown for the first time that a piezoelectric superconducting spin valve can function.

Magnetism doi: 10.3390/magnetism3030015

Authors: Vasily R. Shaginyan Alfred Z. Msezane Stanislav A. Artamonov

In this review, we consider the impact of magnetic field on the properties of strongly correlated heavy-fermion compounds such as heavy-fermion metals and frustrated insulators with quantum spin liquid. Magnetic field B can be considered a universal tool, allowing the exploration of the physics controlling the remarkable properties of heavy-fermion compounds. These vivid properties are T/B scaling, exhibited under the application of magnetic field B and at fixed temperature T, and the emergence of Landau Fermi liquid behavior under the application of magnetic field. We analyze the influence of quasiparticle–hole asymmetry on the properties of heavy-fermion (HF) compounds such as the universal scaling behavior of the thermopower S/T exhibited under the application of magnetic field B. We show that universal scaling is demonstrated by different HF compounds such as β-YbAlB4, YbRh2Si2, and strongly correlated layered cobalt oxide [BiBa0.66K0.36O2]CoO2. Analyzing YbRh2Si2, we show that the T/B scaling behavior of S/T is violated at the antiferromagnetic phase (AF) transition. The residual resistivity ρ0 and the density of states N0 experience jumps at the AF transition, causing two jumps in the thermopower and its sign reversal. Our consideration is based on the flattening of the single-particle spectrum that strongly affects ρ0 and N0 and leads to the violation of particle–hole symmetry. The particle–hole asymmetry generates the asymmetrical part Δσd(V) of tunneling differential conductivity σd(V), Δσd(V)=σd(V)−σd(−V), where V is the voltage bias. We demonstrate that in the presence of magnetic field, the quasiparticle–hole asymmetry vanishes, the LFL behavior is restored, and the asymmetry disappears. Our calculations of the mentioned properties of HF compounds, based on the fermion condensation theory, are in good agreement with the experiment and support our conclusion that the fermion condensation theory is capable of describing the properties of HF compounds, including those exhibited under the application of magnetic field.

Magnetism doi: 10.3390/magnetism3020014

Authors: Frank Denk Tobias Hofbauer

This document presents the process flow and the experimental conditions for calculating the static magnetic intermediate permeability of a specimen with a dedicated geometrical contour and surface for simulation parameter of metal detection systems. In this case, intermediate is explained and defined as probes with a magnetic permeability between 10 and 1000. An analysis of recent and current measurement standards as well as similar simulation principles leads to the contribution value of this new hybrid process flow. To calculate the permeability value in a first step, an electromagnetic circuit was constructed and excited with a defined electrical DC current with a dedicated tolerance for generating a static approximated homogenic magnetic field in a defined air gap space sector. Additionally, to the H-field generation part double copper coil, two magnetic ferrite cylinders with known permeability were used. The electrical and magnetic circuit has been modeled by an Ansys FEM Electronic Desktop software; the solver is magnetic static. Specifically, the simulated magnetic field distribution of the airgap was evaluated by using different Hall sensor elements with different tolerances. Subsequently, the electromagnetic circuit was expanded by implementing different cylindrical and cube shaped probes on a defined position inside the air gap sector with homogenic magnetization. Moreover, based on the analysis of the air gap structure without the probes, a detailed 3D-FEM model of the air gap magnetic field with special probes was established, which provides the environmental field distribution of the probes. The simulation models were compared with the corresponding Hall sensor measurements, which proved the high accuracy experimental validity of the models established in this paper. Finally, some key features related to parameter variations in the electromagnetic circuit were extracted, which can significantly reflect the characteristics of the robustness of the measurement principle. The main findings reported in this paper will be beneficial for magnetic parameter settings in electromagnetic simulation.

Magnetism doi: 10.3390/magnetism3020013

Authors: Kyyoul Yun

The magnetic characteristics of electromagnetic steel sheets used for motors are evaluated under ideal sinusoidal excitation. However, in actual equipment driving, excitation by pulse-width modulation (PWM) waves is the mainstream method. Therefore, it is necessary to clarify how the magnetic properties used in motors are changed by sinusoidal excitation and inverter excitation. To clarify the magnetic properties of the laminated core by inverter excitation, samples with different core sizes were prepared and the effects on the magnetic properties were then investigated. The magnetic properties were measured by changing only the input voltage VDC while maintaining the carrier frequency and modulation factor constant. As the results, the iron loss values of the small, medium, and large samples with inverter excitation were 6.05, 9.58, and 11.62 W/kg, respectively. The iron losses of the small, medium, and large toroidal cores with inverter excitation increased by 124.9, 256.1, and 332.0%, respectively, compared with the iron loss of each toroidal core with sinusoidal excitation. The larger the body, the higher the required voltage and iron loss. It can be inferred that a larger amount of energy was required to excite a larger toroidal core. This was because the change in magnetic flux density per unit time of the large toroidal core was greater than that of other cores. This indicates that the large toroidal core generated larger eddy currents than other cores. Therefore, it is possible to say that large toroidal cores generate greater eddy current losses than other cores.

Magnetism doi: 10.3390/magnetism3020012

Authors: Şerban Mişicu

I consider a proton–neutron fluid mixture placed in an ultra-strong external static magnetic field and derive the spin-independent, small-amplitude disturbances in infinitely extended systems. As a theoretical framework I adopt a hydrodynamical model for the proton and neutron fluids moving in a Skyrme mean-field derived from the time-dependent Hartree Fock formulation of the many-body nuclear problem. From the mass, momentum balance, and Maxwell equations, I set up a system of equations governing the electromagnetic field and the continuum-mechanical fields of the mixture. Next, the hydromagnetic equations are linearized, and the occurrence of small-amplitude distortions of the velocity field is analyzed for various orientations of the constant external magnetic induction with respect to the wave propagation vector. The derivation of the above equations is carried out for the inviscid case.

Magnetism doi: 10.3390/magnetism3020011

Authors: Stanislav Gritsutenko Nikolay Korovkin Yaroslav Sakharov Olga Sokolova

Recent history demonstrates that threat has no borders, though risk does, due to national and regional differences in vulnerabilities and exposure landscapes. The difference between well and poorly managed threat is striking. Inequalities in preparing for threats as a function of their type are still apparent. Compared to more concerning electromagnetic interference threats, the impact of geomagnetic disturbance (GMD) on power grid operation is not well studied. The need for detailed research of GMD negative impacts is expected to broaden awareness. The amplitude of geomagnetically induced currents (GICs) is treated as a uniform measure of danger that can be processed by various stakeholders. Hence, methods for increasing the accuracy of GIC representation are presented in this paper. A low-entropy signal is defined and it is shown that the feature of low signal entropy can be used for increasing the accuracy of the measurement equipment. At the end, a full-system view of GMD impact on power grid operation is given.

Magnetism doi: 10.3390/magnetism3020010

Authors: Lingqi Kong Alexander Schuchinsky Sumin Joseph Taylan Eker Yi Huang

Integration of the ferrite devices in the RF front-end and active antennas is hindered by the need for external magnets, biasing soft microwave ferrites. The hexaferrite-based self-biased nonreciprocal devices can operate without external magnets at mm-wave frequencies but the currently available hexaferrite materials inflict high RF losses at lower frequencies, particularly in the wireless communication bands. In this paper, the parameters of La-Co-substituted hexaferrite compounds are used for the self-biased circulators in the low GHz frequency bands, and a means of the dissipation loss reduction are discussed.

Magnetism doi: 10.3390/magnetism3020009

Authors: Juan Manuel Montes

This work is an attempt to modernise Weber’s electrodynamics to make it compatible with the high-velocity regime, and with the existence of a limiting velocity, c. For this purpose, starting from the law of energy conservation and the mass–energy equivalence, new expressions for potential energy and for kinetic energy are derived jointly which are consistent with an ultimate velocity of the value of c. The new potential energy, already reported by Phipps, becomes Weber’s expression in the limit of low velocities. The new kinetic energy differs from the relativistic expression, but, like the latter, it also becomes the Newtonian expression in the limit of low velocities. New expressions for force and linear momentum are also derived which complete a new mechanics. Phipps’ potential energy and new kinetic energy are applied to the problem of two interacting charges in a radial motion and orbital motion. The new framework is also applied to the problem of a charge moving between the two plates of a charged capacitor, obtaining a result similar to that obtained by means of Maxwell–Lorentz electromagnetism and relativistic mechanics. The metaphysical considerations that clearly differentiate the conventional framework from the new framework proposed here are discussed.

Magnetism doi: 10.3390/magnetism3020008

Authors: Anastasia V. Artemova Sergey S. Maklakov Artem O. Shiryaev Alexey V. Osipov Dmitry A. Petrov Konstantin N. Rozanov Andrey N. Lagarkov

The relationship between the chemical purity of one-size particles and microwave properties in ferromagnetic materials is not clearly studied. Ferromagnetic nanostructured iron powders were synthesized from iron nitrate solution using ultrasonic spray-pyrolysis and then reduced in H2 flow at 350, 400, 450, and 500 °C. A rise in the concentration of solutions of a precursor from 10 to 20 wt. % led to an increase in mean particle size. The interrelationship was studied between chemical composition and the microwave dispersion of the powders obtained. An increase in the temperature of reduction changes the chemical composition and increases the amplitude of complex microwave permeability, which was studied using solid-state physics methods (XRD, STA, SEM, and VNA). It was found that annealing at 400 °C is the optimal treatment that allows the production of iron powders, consisting of about 90% of α-Fe phase, possessing a particle surface with low roughness and porosity, and demonstrating intense microwave absorption. Annealing at a higher temperature (500 °C) causes an even higher increase in permeability but leads to the destruction of nanostructured spheres into smaller particles due to grain growth. This destruction causes an abrupt increase in permittivity and therefore significantly reduces potential applications of the product. The insight into chemical–magnetic relationships of these materials enhances the data for design applications in magnetic field sensing.

Magnetism doi: 10.3390/magnetism3010007

Authors: Uta Rösel Dietmar Drummer

To expand the range of applications of multipolar bonded magnets based on a thermoplastic matrix, the chemical and thermal resistance has to be increased and the reduced orientation in the rapid solidified surface layer has to be overcome. To meet these requirements, the matrix of multipolar bonded magnets can be based on thermosets. This paper investigates in the magnetic properties, especially in the orientation of hard magnetic fillers, the pole accuracy and the mechanical properties of multipolar bonded ring magnets based on the hard magnetic filler strontium-ferrite-oxide and compares the possibilities of thermoplastic (polyamide)- and thermoset (epoxy resin, phenolic resin)-based matrices. It was shown that the magnetic potential of the thermoset-based material can only be fully used with further magnetization. However, the magnetic properties can be increased using thermoset-based compounds compared to thermoplastics in multipolar bonded ring magnets. Further, a model of the orientation and pole accuracy is found in terms of thermoset-based multipolar magnets. In addition, the change of the mechanical properties due to the different matrix systems was shown, with an increase in E-Modulus, Et, and a reduction in tensile strength, σm, and elongation at break, εm, in terms of thermosets compared to thermoplastics.