Magnetism

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. Full article

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. Full article

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. Full article

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. Full article

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) ų 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 T_N = 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. Full article

Measurements of specific heat and magnetization in single crystals were used to map out the magnetic phase diagram of Gd_1−xEr_xB₄ (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. Full article

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. Full article

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. Full article

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. Full article

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 $S^2$—and is thus characterized by the integer Hopf index $Q_H$. 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 $Q_H=-1$, 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 Cu${}_2$OSeO${}_3$) 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. Full article

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. Full article

A novel micro-solenoid resonator has been designed, simulated, and measured. The solenoid core consisted of a Duroid^TM 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. Full article

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 Mn_0.30NbS₂. The results of the X-ray study showed the possible existence of an intermediate 2$\sqrt{3}$a₀·2$\sqrt{3}$a₀ 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. Full article

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. Full article

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. Full article

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. Full article

The properties of a superconducting spin valve Fe1/Cu/Fe2/Cu/Pb on a piezoelectric PMN–PT substrate ([Pb(Mg_1/3Nb_2/3)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. Full article

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 $\beta$-${\mathrm{YbAlB}}_4$, ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, and strongly correlated layered cobalt oxide $\left[{\mathrm{BiBa}}_{0.66}{\mathrm{K}}_{0.36}{\mathrm{O}}_2\right]{\mathrm{CoO}}_2$. Analyzing ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, we show that the $T/B$ scaling behavior of $S/T$ is violated at the antiferromagnetic phase (AF) transition. The residual resistivity ${\rho }_0$ and the density of states $N_0$ 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 ${\rho }_0$ and $N_0$ and leads to the violation of particle–hole symmetry. The particle–hole asymmetry generates the asymmetrical part $\mathsf{\Delta }{\sigma }_d\left(V\right)$ of tunneling differential conductivity ${\sigma }_d\left(V\right)$, $\mathsf{\Delta }{\sigma }_d\left(V\right)={\sigma }_d\left(V\right)-{\sigma }_d(-V)$, 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. Full article

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. Full article