Magnetism

The quantum states of a spin $\frac{1}{2}$ (a qubit) are parametrized by the space ${\mathbf{CP}}^1\sim S^2$, 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, ${\mathbf{CP}}^{2j}$. Here we study the state of a single angular momentum/spin in the limit $j\to \infty$. A special class of states, $|j,\mathbf{n}⟩\in {\mathbf{CP}}^{2j}$, with spin oriented towards definite spatial directions, $\mathbf{n}\in S^2$, i.e., $(\widehat{\mathbf{J}}·\mathbf{n})|j,\mathbf{n}⟩=j|j,\mathbf{n}⟩$, are found to behave as classical angular momenta, $j\mathbf{n}$, in this limit. Vice versa, general spin states in ${\mathbf{CP}}^{2j}$ 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. Full article

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. Full article

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 $T_C$ 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 ${\mathrm{Fe}}_{2-y}$Co_yP_1−xSi_x 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 $T_C$ 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 ${\mathrm{Fe}}_{2-y}$Co_yP, ${\mathrm{Fe}}_{2-y}$Co_yP_0.92Si_0.08 and ${\mathrm{Fe}}_{2-y}$Co_yP_0.84Si_0.16, 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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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 $\mathsf{\Gamma }$ 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. Full article

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). Full article

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. Full article

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. Full article

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 i_d, 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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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 ${\mathrm{Co}}_2$MnZ, ${\mathrm{Rh}}_2$MnZ, and ${\mathrm{Ru}}_2$MnZ 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 $L{2}_1$ 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 ${\mathrm{Rh}}_2$Mn(Cr, Mo, W) compounds. Our findings suggest that these compounds hold significant promise for applications in spintronics and magnetoelectronics. Full article

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. Full article