Magnetism

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

We investigate the role of single-ion anisotropy in stabilizing higher-order skyrmion crystal phases in centrosymmetric magnets under D_3d symmetry. Using a classical spin model that incorporates both a local single-ion anisotropy arising from the two-dimensional crystal symmetry and a D_3d-type magnetic anisotropy originating from the D_3d 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 D_3d-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 D_3d-type anisotropies. These results provide a possible microscopic understanding of how complex topological spin textures can be stabilized in centrosymmetric D_3d magnets, suggesting that multiple phases with topological spin textures could emerge even in the absence of the Dzyaloshinskii–Moriya interaction. Full article

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. Full article

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. Full article

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. Full article

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 ($\epsilon$) 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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article