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.

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.

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

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.

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.

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.

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.

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.

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.

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.