Nonuniform Magnetization Research Articles

Weyl Anomaly Induced Current in Boundary Quantum Field Theories.

We show that when an external magnetic field parallel to the boundary is applied, the Weyl anomaly gives rises to a new anomalous current in the vicinity of the boundary. The induced current is a magnetization current in origin: the movement of the virtual charges near the boundary give rise to a nonuniform magnetization of the vacuum and hence a magnetization current. Unlike other previously studied anomalous current phenomena such as the chiral magnetic effect or the chiral vortical effect, this induced current does not rely on the presence of a material system and can occur in vacuum. Similar to the Casimir effect, our discovered phenomenon arises from the effect of the boundary on the quantum fluctuations of the vacuum. However this induced current is purely quantum mechanical and has no classical limit. We briefly comment on how this induced current may be observed experimentally.

Twisted magnetization states and inhomogeneous resonance modes in a Fe/Gd ferrimagnetic multilayer

Static and dynamic magnetic properties of a ferrimagnetic [Fe(35A)/Gd(50A)]x12 superlattice were investigated in a wide 4-300 K temperature range using magneto-optical Kerr effect (MOKE) and ferromagnetic resonance (FMR) techniques. The multilayer structure was sputtered on a transparent glass substrate which made it possible to perform MOKE measurements on both Fe and Gd terminated sides of the superlattice. These experiments allowed us to detect a transition between field-aligned and canted magnetic states on both sides of the film and to distinguish between the bulk and surface twisted phases of the superlattice. As a result, the experimental H-T magnetic phase diagram of the system was obtained. FMR studies at frequencies 7-36 GHz demonstrated a complex evolution of absorption spectra as temperature decreased from room down to 4 K. Two spectral branches were detected in the sample. Theoretical simulations show that the observed spectral branches correspond to different types of inhomogeneous resonance modes in the multilayer with non-uniform magnetization precession inside Gd layers.

Damping of linear spin-wave modes in magnetic nanostructures: Local, nonlocal, and coordinate-dependent damping

A general perturbation theory for the description of weak damping of linear spin-wave modes in magnetic nanostructures is developed. This perturbative approach allows one to account for the usual uniform Gilbert damping, as well as for the spatially nonuniform (coordinate-dependent) and nonlocal (magnetization-texture-dependent) Gilbert-like dissipation mechanisms. Using the derived general expression, it is possible to calculate the damping rate of a particular spin-wave mode if the frequency and the spatial profile of this mode, along with the relevant parameters of a magnetic material, are known. The examples demonstrating the applications of the developed general formalism include (i) generalization of the damping rate of a spin-wave mode propagating in a magnetic sample for the case of a nonuniform static magnetization or/and bias magnetic field, (ii) calculation of a damping rate of a gyrotropic mode in a vortex-state magnetic nanodot, (iii) evaluation of the spin diffusion influence on the damping rate of spin-wave modes in a conducting ferromagnet, and (iv) calculation of damping rates of spin-wave modes in a ferromagnetic film in the presence of a spin pumping into an adjacent nonmagnetic metal layer. The developed formalism is especially useful in micromagnetic simulations, as it allows one to calculate damping rates of spin-wave modes based on the numerical solution of a conservative eigenmode problem.

Magnetization distribution in a spin ladder-shaped quantum nanomagnet

The quantum nanomagnets show interesting site-dependent magnetic properties as a function of the temperature and the external magnetic field. In the paper we present the results of calculations for a finite quantum spin ladder with two legs, consisting of 12 spins S=1/2, with open ends. We describe our system with isotropic quantum Heisenberg model and perform exact numerical diagonalization of the Hamiltonian to use canonical ensemble approach. Our analysis focuses on the site-dependent magnetization in the system, presenting magnetization distributions for various interaction parameters. We discuss extensively the temperature and magnetic field dependences of individual site magnetizations. The interesting behaviour, with pronounced non-uniformity of magnetization across the ladder, is found.

The Vortex State in Geologic Materials: A Micromagnetic Perspective

AbstractA wide variety of Earth and planetary materials are very good recorders of paleomagnetic information. However, most magnetic grains in these materials are not in the stable single domain grain size range but are larger and in nonuniform vortex magnetization states. We provide a detailed account of vortex phenomena in geologic materials by simulating first‐order reversal curves (FORCs) via finite‐element micromagnetic modeling of magnetite nanoparticles with realistic morphologies. The particles have been reconstructed from focused ion beam nanotomography of magnetite‐bearing obsidian and accommodate single and multiple vortex structures. Single vortex (SV) grains have fingerprints with contributions to both the transient and transient‐free zones of FORC diagrams. A fundamental feature of the SV fingerprint is a central ridge, representing a distribution of negative saturation vortex annihilation fields. SV irreversible events at multiple field values along different FORC branches determine the asymmetry in the upper and lower lobes of generic bulk FORC diagrams of natural materials with grains predominantly in the vortex state. Multivortex (MV) FORC signatures are modeled here for the first time. MV grains contribute mostly to the transient‐free zone of a FORC diagram, averaging out to create a broad central peak. The intensity of the central peak is higher than that of the lobes, implying that MV particles are more abundant than SV particles in geologic materials with vortex state fingerprints. The abundance of MV particles, as well as their single domain‐like properties point to MV grains being the main natural remanent magnetization carriers in geologic materials.

Excitation and coherent control of magnetization dynamics in magnetic tunnel junctions using acoustic pulses

We experimentally study magnetization dynamics in magnetic tunnel junctions driven by femtosecond-laser-induced surface acoustic waves. The acoustic pulses induce a magnetization precession in the free layer of the magnetic tunnel junction through magnetoelastic coupling. The frequency and amplitude of the precession show a pronounced dependence on the applied magnetic field and the laser excitation position. Comparing the acoustic-wave-induced precession frequencies with precession induced by charge currents and with micromagnetic simulations, we identify spatially non-uniform magnetization modes localized close to the edge regions as being responsible for the optically induced magnetization dynamics. The experimental scheme even allows us to coherently control the magnetization precession using two acoustic pulses. This might prove important for future applications requiring ultrafast spin manipulation. Additionally, our results directly pinpoint the importance of acoustic pulses since they could be relevant when investigating optically induced temperature effects in magnetic structures.

Magnetooptical Visualization and Mapping of Magnetic Stray Fields over the Surface of Composite Permanent Magnets Using Gadolinium–Cobalt Amorphous Films

Stray fields of magnetic systems with a known degree of structural and magnetic nonuniformities have been mapped using indicator amorphous films with a perpendicular anisotropy. The characteristic magnetooptical patterns have been determined, which correspond to the distribution of the magnetic-field component normal to the plane of the indicator films. The theoretical patterns of model magnetic systems that are similar to the studied systems in the degree of the structural and magnetic nonuniformity have been calculated. The validity of the magnetooptical visualization has been confirmed by comparison of the experimental and theoretical patterns. The possibility of the express monitoring of the parameters of the magnetic system has been shown using a laboratory model of a magnetooptical visualizer by the observation of the magnetooptical contrast of gadolinium–cobalt indicator films under the action of an ac magnetic field.

Coexistence of metallic edge states and antiferromagnetic ordering in correlated topological insulators

We investigate the emergence of anti-ferromagnetic ordering and its effect on the helical edge states in a quantum spin Hall insulator, in the presence of strong Coulomb interaction. Using dynamical mean-field theory, we show that the breakdown of lattice translational symmetry favours the formation of magnetic ordering with non-trivial spatial modulation. The onset of a non-uniform magnetization enables the coexistence of spin-ordered and topologically non-trivial states. An unambiguous signature of the persistence of the topological bulk property is the survival of bona fide edge states. We show that the penetration of the magnetic order is accompanied by the progressive reconstruction of gapless states in sub-peripherals layers, redefining the actual topological boundary within the system.

Printing ferromagnetic domains for untethered fast-transforming soft materials

Soft materials capable of transforming between three-dimensional (3D) shapes in response to stimuli such as light, heat, solvent, electric and magnetic fields have applications in diverse areas such as flexible electronics1,2, soft robotics3,4 and biomedicine5-7. In particular, magnetic fields offer a safe and effective manipulation method for biomedical applications, which typically require remote actuation in enclosed and confined spaces8-10. With advances in magnetic field control 11 , magnetically responsive soft materials have also evolved from embedding discrete magnets 12 or incorporating magnetic particles 13 into soft compounds to generating nonuniform magnetization profiles in polymeric sheets14,15. Here we report 3D printing of programmed ferromagnetic domains in soft materials that enable fast transformations between complex 3D shapes via magnetic actuation. Our approach is based on direct ink writing 16 of an elastomer composite containing ferromagnetic microparticles. By applying a magnetic field to the dispensing nozzle while printing 17 , we reorient particles along the applied field to impart patterned magnetic polarity to printed filaments. This method allows us to program ferromagnetic domains in complex 3D-printed soft materials, enabling a set of previously inaccessible modes of transformation, such as remotely controlled auxetic behaviours of mechanical metamaterials with negative Poisson's ratios. The actuation speed and power density of our printed soft materials with programmed ferromagnetic domains are orders of magnitude greater than existing 3D-printed active materials. We further demonstrate diverse functions derived from complex shape changes, including reconfigurable soft electronics, a mechanical metamaterial that can jump and a soft robot that crawls, rolls, catches fast-moving objects and transports a pharmaceutical dose.

Numerical Calculation of Non-uniform Magnetization Using Experimental Magnetic Field Data

A relation between the distance from the surface of a magnet and the number of cells required for a numerical calculation in order to secure the error below a certain threshold is derived. We also developed a method to obtain the magnetization at each part of the magnet from the experimentally measured magnetic field. This method is applied to three magnets with distinct patterns on magnetic-field-viewing film. Each magnet showed a unique pattern of magnetization. We found that the magnet that shows symmetric magnetization on the magnetic-field-viewing film is not uniformly magnetized. This method can be useful comparing the magnetization between magnets that yield typical magnetic field and those that yield atypical magnetic field.

Development of Prototype High Gradient Small Aperture Quadrupole Magnets for HEPS-TF

A test facility named HEPS-TF for new storage-ring-based high energy photon source with low beam emittance is now under construction in China. Two prototype quadrupole magnets with small aperture and high field gradient are important devices in HEPS-TF. The bore diameters of the prototypes are both 25 mm, and the field gradients are 80 and 90 T/m, respectively. A lot of effort was spent to obtain an optimized pole shape, which meets the stringent field quality requirement, the mechanical boundary condition, and is also convenient to be machined. The influence of magnetic property nonuniformity of the core material on the field quality was studied. The design and manufacture of these prototype quadrupole magnets are finished. The field measurement results show that the field quality of these prototypes meets the specifications. The detailed two-dimensional (2-D) and 3-D magnetic design, field simulation, and field error analysis of the two prototypes are presented, and field measurement results are also described.

Spin current and second harmonic generation in non-collinear magnetic systems: the hydrodynamic model

We report a theoretical study of the second harmonic generation in a noncollinearly magnetized conductive medium with equilibrium spin current. The hydrodynamic model is used to unravel the mechanism of a novel effect of the double frequency signal generation that is attributed to the spin current. According to our calculations, this second harmonic response appears due to the ‘non-adiabatic’ spin polarization of the conduction electrons induced by the oscillations in the non-uniform magnetization forced by the electric field of the electromagnetic wave. Together with the linear velocity response this leads to the generation of the double frequency spin current. This spin current is converted to the electric current via the inverse spin Hall effect, and the double-frequency electric current emits the second harmonic radiation. Possible experiment for detection of the new second harmonic effect is proposed.

On a neutral particle with permanent magnetic dipole moment in a magnetic medium

We investigate quantum effects that stem from the interaction of a permanent magnetic dipole moment of a neutral particle with an electric field in a magnetic medium. We consider a long non-conductor cylinder that possesses a uniform distribution of electric charges and a non-uniform magnetization. We discuss the possibility of achieving this non-uniform magnetization from the experimental point of view. Besides, due to this non-uniform magnetization, the permanent magnetic dipole moment of the neutral particle also interacts with a non-uniform magnetic field. This interaction gives rise to a linear scalar potential. Then, we show that bound states solutions to the Schrodinger-Pauli equation can be achieved.

Torque‐ripple reduction of SRM using optimised voltage vector in DTC

High torque ripple is inherent in switched reluctance motors (SRMs) because of the motor's doubly salient structure and highly non-uniform torque and magnetisation characteristics. Direct torque control (DTC) for SRM is one of the torque ripple reduction strategies which gets wide attention for its simpleness and effectiveness. In this study, aiming at the torque ripple phenomenon of DTC for SRM, a novel method for torque-ripple reduction is proposed. With the new methods, sector zones were redivided into 9 and 12 sector zones based on six sector zones and new control rules were adopted. Consequently, the proposed methods make the selection of voltage vector more precise. A 12/8-pole three-phase SRM drive system was designed to verify the effectiveness of the proposed new methods. The results verified that the improved DTC algorithms with 9 and 12 sector zones could indeed minimise the torque ripple to a great extent.

Magnetization Reversal Modes in Short Nanotubes with Chiral Vortex Domain Walls.

Micromagnetic simulations of magnetization reversal were performed for magnetic nanotubes of a finite length, L, equal to 1 and 2 μm, 50 and 100 nm radii, R, and uniaxial anisotropy with “easy axis” parallel to the tube length. I.e., we considered relatively short nanotubes with the aspect ratio L/R in the range 10–40. The non-uniform curling magnetization states on both ends of the nanotubes can be treated as vortex domain walls (DW). The domain wall length, Lc, depends on the tube geometric parameters and the anisotropy constant Ku, and determines the magnetization reversal mode, as well as the switching field value. For nanotubes with relative small values of Lc (Lc/L < 0.2) the magnetization reversal process is characterized by flipping of the magnetization in the middle uniform state. Whereas, for relative large values of Lc, in the reverse magnetic field, coupling of two vortex domain walls with opposite magnetization rotation directions results in the formation of a specific narrow Néel type DW in the middle of the nanotube. The nanotube magnetization suddenly aligns to the applied field at the switching field, collapsing the central DW.

Parameter design and characteristic analysis of the interior non-uniform airgap permanent magnet synchronous motor for electric vehicle

Parameter design and characteristic analysis of the interior non-uniform airgap permanent magnet synchronous motor for electric vehicle

Parameter design and characteristic analysis of the interior non-uniform airgap permanent magnet synchronous motor for electric vehicle

Aiming at the demand for high torque and wide speed range of permanent magnet synchronous motor (PMSM) used in electric vehicles, a PMSM with fractional slot concentrated winding and the rotor of non-uniform airgap is designed. Fourier harmonic analysis theorem is used to calculate the harmonic content and peak value of cogging torque of different rotor eccentricities. Combined with finite element simulation software, the influence of rotor of uniform airgap and the rotor of non-uniform airgap on the q axis and d axis magnetic circuit is analysed respectively, so the optimal rotor eccentricity is determined. Compared to the rotor of uniform airgap, the peak value of cogging torque and the waveform distortion rate is reduced, while the salient rate is increased. Performance test is done and results show that reasonable rotor eccentricity can effectively improve the motor of flux weakening capability and widening the operation region of high efficiency.

Electronic structure and quantum spin fluctuations at the magnetic phase transition in MnSi

The effect of spin fluctuations on the heat capacity and homogeneous magnetic susceptibility of the chiral magnetic MnSi in the vicinity of magnetic transition has been investigated by using the free energy functional of the coupled electron and spin subsystems and taking into account the Dzyaloshinsky-Moriya interaction. For helical ferromagnetic ordering, we found that zero-point fluctuations of the spin density are large and comparable with fluctuations of the non-uniform magnetization. The amplitude of zero-point spin fluctuations shows a sharp decrease in the region of the magnetic phase transition. It is shown that sharp decrease of the amplitude of the quantum spin fluctuations results in the lambda-like maxima of the heat capacity and the homogeneous magnetic susceptibility. Above the temperature of the lambda anomaly, the spin correlation radius becomes less than the period of the helical structure and chiral fluctuations of the local magnetization appear. It is shown that formation of a "shoulder" on the temperature dependence of the heat capacity is due to disappearance of the local magnetization. Our finding allows to explain the experimentally observed features of the magnetic phase transition of MnSi as a result of the crossover of quantum and thermodynamic phase transitions.

On second-harmonic generation in nonuniformly magnetized media

This paper presents a theoretical study of new effects of double-frequency optical signal generation in magnetic media with a nonuniform magnetization distribution. The study is based on the hydrodynamic approximation of the motion of conduction electrons in the field of an electromagnetic wave and equations for the mean electron spin. Within this approach, the mechanisms of the toroidal moment effect, which was experimentally discovered earlier in a system of magnetic particles with a vertical magnetization distribution as well as in a multilayered magnetic system (which is a collinear nonuniform magnetic system), are demonstrated. A new effect that appears due to the presence of equilibrium spin currents in a nonuniform magnetic system is studied in detail. This effect was predicted from the symmetry and can occur only in noncollinearly magnetized media. It is shown that this effect has a resonance nature with a resonance at a pump frequency equal to the plasma frequency of conduction electrons. Estimates of the susceptibility at the double frequency for the parameters of nickel and the typical scale of variation in the magnetization, which is equal to 10 nm, show that the susceptibility near the frequency of the plasma resonance at the chosen parameters is on the order of 10–9 esu, which holds up a hope of the experimental detection of this effect.

Mapping the magnonic landscape in patterned magnetic structures

We report the development of a hybrid numerical/analytical model capable of mapping the spatially varying distributions of the local ferromagnetic resonance (FMR) frequency and dynamic magnetic susceptibility in a wide class of patterned and compositionally modulated magnetic structures. Starting from the numerically simulated static micromagnetic state, the magnetization is deliberately deflected orthogonally to its equilibrium orientation, and the magnetic fields generated in response to this deflection are evaluated using micromagnetic software. This allows us to calculate the elements of the effective demagnetizing tensor, which are then used within a linear analytical formalism to map the local FMR frequency and dynamic magnetic susceptibility. To illustrate the typical results that one can obtain using this model, we analyze three micromagnetic systems boasting nonuniformity in either one or two dimensions, and successfully explain the spin-wave emission observed in each case, demonstrating the ubiquitous nature of the Schl\"omann excitation mechanism underpinning the observations. Finally, the developed model of local FMR frequency can be used to explain how spin waves could be confined and steered using magnetic nonuniformities of various origins, rendering it a powerful tool for the mapping of the graded magnonic index in magnonics.