Nonlinear Magnetization Research Articles

Multiple nonlinear wave solutions of a generalized Heisenberg ferromagnet model and their interactions

Under investigation in this paper is a generalized Heisenberg ferromagnet (HF) equation which is named the Zhanbota-IIA equation. It is one of the integrable generalizations of the HF equation that plays an important role in nonlinear magnetization dynamics. Through the establishment of the N-fold Darboux transformation, a series of solutions will be obtained, including multi-solitons, one- and two-breathers, first- and higher-order rogue waves. Dynamic behaviors of those solutions will be analyzed, including several structures of rogue waves such as fundamental structure, triangular structure, ring structure and ring-fundamental structure, the coexistence of rogue waves and breathers, i.e. semi-rational solution and the interaction of two breathers.

Design of gradient coils based on the target field method in a high-permeability shield considering sidewall apertures

The combination of high-permeability ferrite and coils is often used to nullify ambient magnetic fields and is widely used in applications such as magnetic resonance imaging and high-sensitivity magnetic sensors. We propose the design method of transverse gradient coils based on the target field method in a high-permeability shield considering sidewall apertures (TFM-HPSCSA), which are installed in the ferrite shield to zero the residual magnetic field gradient. TFM-HPSCSA coils enable an innovative combination of magnetic field gradient linearity and structural luminescence. The coil current density distribution is set to avoid the central sidewall apertures. As a result, the contour distribution of the stream function under the optimized weight coefficients is calculated to obtain the wire alignments of the dBy/dx, dBy/dy and dBy/dz gradient coils. The deviations of the experimentally measured values from the finite element simulations of the three types coils are 0.63%, 1.17% and 0.48%, respectively, which verified the validity and the accuracy of the proposed method. In comparison to the traditional saddle gradient coil designed under the free space condition, the proposed dBy/dx coil produces a 30.5% improvement in the percentage range of regions with 5% magnetic field gradient nonlinearity. The increased linear range of the gradient magnetic field contributes to the improvement of the residual field nulling range in magnetic sensors and magnetic shielding systems in practical applications.

Functional magnetic particle imaging (fMPI) of cerebrovascular changes in the rat brain during hypercapnia

Objective. Non-invasive functional brain imaging modalities are limited in number, each with its own complex trade-offs between sensitivity, spatial and temporal resolution, and the directness with which the measured signals reflect neuronal activation. Magnetic particle imaging (MPI) directly maps the cerebral blood volume (CBV), and its high sensitivity derives from the nonlinear magnetization of the superparamagnetic iron oxide nanoparticle (SPION) tracer confined to the blood pool. Our work evaluates functional MPI (fMPI) as a new hemodynamic functional imaging modality by mapping the CBV response in a rodent model where CBV is modulated by hypercapnic breathing manipulation. Approach. The rodent fMPI time-series data were acquired with a mechanically rotating field-free line MPI scanner capable of 5 s temporal resolution and 3 mm spatial resolution. The rat’s CBV was modulated for 30 min with alternating 5 min hyper-/hypocapnic states, and processed using conventional fMRI tools. We compare our results to fMRI responses undergoing similar hypercapnia protocols found in the literature, and reinforce this comparison in a study of one rat with 9.4T BOLD fMRI using the identical protocol. Main results. The initial image in the time-series showed mean resting brain voxel SNR values, averaged across rats, of 99.9 following the first 10 mg kg−1 SPION injection and 134 following the second. The time-series fit a conventional General Linear Model with a 15%–40% CBV change and a peak pixel CNR between 12 and 29, 2–6× higher than found in fMRI. Significance. This work introduces a functional modality with high sensitivity, although currently limited spatial and temporal resolution. With future clinical-scale development, a large increase in sensitivity could supplement other modalities and help transition functional brain imaging from a neuroscience tool focusing on population averages to a clinically relevant modality capable of detecting differences in individual patients.

Nonreciprocal photonic quantum router via synthetic magnetism

Nonreciprocal photon transmissions at the single-quantum level play crucial roles in optical information processing. Here, we propose to develop a nonreciprocal photonic quantum router via synthetic magnetism, which can route photons of an input quantum state in one direction but block them in the other direction. Our model is based on a superconducting circuit of linearly coupled microwave cavities, and the Lorentz reciprocity is broken by synthesizing an effective magnetic field for photons. As a result, an input quantum signal from a given direction can be delivered on-demand to either of the two output ports, but it from the opposite direction is completely absorbed. Our scheme does not involve strong static magnetic fields and optical nonlinearity for generating the desired optical nonreciprocity. It is, therefore, expected to be a key ingredient for the construction of on-chip quantum networks.

Stationary quantum entanglement and steering between two distant macromagnets

Generating and manipulating magnon quantum states for quantum information processing is a central topic in quantum magnonics. The conventional strategy amplifies the nonlinear interaction among magnons to manifest their quantum correlations at cryogenic temperatures, which is challenging for magnets with vanishingly small nonlinearities. Here we propose an unconventional approach to prepare entangled states of two distant magnon modes by applying a two-tone Floquet field to each magnet inside a microwave cavity. The Floquet driving can effectively generate parametric interaction between magnons and photons, and thus opens an indirect entanglement channel between the two magnon modes mediated by cavity photons. By optimizing the relative ratio of the magnon–photon coupling and the detuning between the magnon modes, the two magnon modes can reach a stationary and robust entanglement, of which the strength is enhanced compared with entanglement generated via magnetic nonlinearities. Furthermore, one-way steering between the two magnets is realized by engineering unequal damping rates of the two magnets while the steering asymmetry can be efficiently modulated by tuning the coupling strength of magnons and cavity photons. The essential physics of our findings universally applies to a wide class of magnets with small nonlinearities and may find promising applications in engineering robust magnon quantum states for quantum information science.

Harmonic signals of magnetic nanoparticle in suspension for biosensing application: Comparison of properties between Brownian- and Néel-dominant regions

We have studied harmonic signals caused by the nonlinear AC magnetization (M-H) curve of magnetic nanoparticles (MNPs) suspended in solution. First, numerical simulations were performed for wide ranges of the MNP parameters and the excitation fields that are commonly used in biosensing applications. As an example, the third harmonic signal was mainly studied. Because the AC M-H curve for the suspended MNPs is affected by both Brownian and Néel relaxations, we demonstrated the condition that determines the dominant relaxation. We emphasize that the MNP’s behavior changes from Brownian-dominant to Néel-dominant relaxation when the amplitude of the excitation field is increased, even when the MNP parameters are fixed. The properties of the harmonic signals in the Brownian- and Néel-dominant cases were compared, and the differences between the two cases were clarified. The relationships among the higher harmonic signals were also presented. Next, an analytical expression for the third harmonic signal was obtained for both the Brownian- and Néel-dominant cases. In the Néel-dominant case, the alignment of the easy axes caused by the AC field was taken into account. We demonstrated good agreement between the simulation and the analysis results. Finally, harmonic signals were measured using a commercial MNPs sample. Reasonable agreement was obtained between experiment and analysis. The results obtained will be useful for biosensing applications.

Bose-Einstein condensation in honeycomb dimer magnets and Yb2Si2O7

An asymmetric Bose-Einstein condensation (BEC) dome was observed in a recent experiment on the quantum dimer magnet ${\mathrm{Yb}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}\mathrm{e}$ [G. Hester et al., Phys. Rev. Lett. 123, 027201 (2019)], which is modeled by a ``breathing'' honeycomb lattice Heisenberg model with possible anisotropies. We report a remarkable agreement between key experimental features and predictions from numerical simulations of the magnetic model. Both critical fields, as well as critical temperatures of the BEC dome, can be accurately captured, as well as the occurrence of two regimes inside the BEC phase. Furthermore, we investigate the role of anisotropies in the exchange coupling and the $g$ tensor. While we confirm a previous proposal that anisotropy can induce a zero-temperature phase transition at magnetic fields smaller than the fully polarizing field strength, we find that this effect becomes negligible at temperatures above the anisotropy scale. Instead, the two regimes inside the BEC dome are found to be due to a nonlinear magnetization behavior of the isotropic breathing honeycomb Heisenberg antiferromagnet. Our analysis is performed by combining the density matrix renormalization group (DMRG) method with the finite-temperature techniques of minimally entangled typical thermal states (METTS) and quantum Monte Carlo (QMC).

Classification tasks using input driven nonlinear magnetization dynamics in spin Hall oscillator

The inherent nonlinear magnetization dynamics in spintronic devices make them suitable candidates for neuromorphic hardware. Among spintronic devices, spin torque oscillators such as spin transfer torque oscillators and spin Hall oscillators have shown the capability to perform recognition tasks. In this paper, with the help of micromagnetic simulations, we model and demonstrate that the magnetization dynamics of a single spin Hall oscillator can be nonlinearly transformed by harnessing input pulse streams and can be utilized for classification tasks. The spin Hall oscillator utilizes the microwave spectral characteristics of its magnetization dynamics for processing a binary data input. The spectral change due to the nonlinear magnetization dynamics assists in real-time feature extraction and classification of 4-binary digit input patterns. The performance was tested for the classification of the standard MNIST handwritten digit data set and achieved an accuracy of 83.1% in a simple linear regression model. Our results suggest that modulating time-driven input data can generate diverse magnetization dynamics in the spin Hall oscillator that can be suitable for temporal or sequential information processing.

Magnetic Bistability for a Wider Bandwidth in Vibro-Impact Triboelectric Energy Harvesters.

Mechanical energy from vibrations is widespread in the ambient environment. It may be harvested efficiently using triboelectric generators. Nevertheless, a harvester's effectiveness is restricted because of the limited bandwidth. To this end, this paper presents a comprehensive theoretical and experimental investigation of a variable frequency energy harvester, which integrates a vibro-impact triboelectric-based harvester and magnetic nonlinearity to increase the operation bandwidth and improve the efficiency of conventional triboelectric harvesters. A cantilever beam with a tip magnet was aligned with another fixed magnet at the same polarity to induce a nonlinear magnetic repulsive force. A triboelectric harvester was integrated into the system by utilizing the lower surface of the tip magnet to serve as the top electrode of the harvester, while the bottom electrode with an attached polydimethylsiloxane insulator was placed underneath. Numerical simulations were performed to examine the impact of the potential wells formed by the magnets. The structure's static and dynamic behaviors at varying excitation levels, separation distance, and surface charge density are all discussed. In order to develop a variable frequency system with a wide bandwidth, the system's natural frequency varies by changing the distance between the two magnets to reduce or magnify the magnetic force to achieve monostable or bistable oscillations. When the system is excited by vibrations, the beams vibrate, which causes an impact between the triboelectric layers. An alternating electrical signal is generated from a periodic contact-separation motion between the harvester's electrodes. Our theoretical findings were experimentally validated. The findings of this study have the potential to pave the way for the development of an effective energy harvester that is capable of scavenging energy from ambient vibrations across a broad range of excitation frequencies. The frequency bandwidth was found to increase by 120% at threshold distance compared to the conventional energy harvester. Nonlinear impact-driven triboelectric energy harvesters can effectively broaden the operational frequency bandwidth and enhance the harvested energy.

Review of Hysteresis Models for Magnetic Materials

There are several models for magnetic hysteresis. Their key purposes are to model magnetization curves with a history dependence to achieve hysteresis cycles without a frequency dependence. There are different approaches to handling history dependence. The two main categories are Duhem-type models and Preisach-type models. Duhem models handle it via a simple directional dependence on the flux rate, without a proper memory. While the Preisach type model handles it via memory of the point where the direction of the flux rate is changed. The most common Duhem model is the phenomenological Jiles–Atherton model, with examples of other models including the Coleman–Hodgdon model and the Tellinen model. Examples of Preisach type models are the classical Preisach model and the Prandtl–Ishlinskii model, although there are also many other models with adoptions of a similar history dependence. Hysteresis is by definition rate-independent, and thereby not dependent on the speed of the alternating flux density. An additional rate dependence is still important and often included in many dynamic hysteresis models. The Chua model is common for modeling non-linear dynamic magnetization curves; however, it does not define classical hysteresis. Other similar adoptions also exist that combine hysteresis modeling with eddy current modeling, similar to how frequency dependence is included in core loss modeling. Most models are made for scalar values of alternating fields, but there are also several models with vector generalizations that also consider three-dimensional directions.

Tuning the Performance of Acoustically Actuated Magnetoelectric Antenna via Magnetic and Mechanical Stimuli

Magnetoelectric (ME) antenna operates at the acoustic wave resonance rather than EM wave resonance, thus it shows significant superiority for developing compact antennas and antenna arrays. The simulation of ME antenna involves the nonlinear coupling of Electrostatics, Solid Mechanics, and Magnetic physics, making it difficult to model such devices. This paper proposes a fully multi-field coupled model for the ME antenna, in which the nonlinear magnetostrictive model is taken into account. The nonlinear magnetization is solved and then AC and DC simulations are performed by coupling different physics. The effects of magnetic bias and pre-stress on the converse magnetoelectric (CME) coupling and near-field radiation are discussed for the first time, to regulate the performance of the ME antenna with fixed dimensions. The results indicate that the magnetic bias and pre-stress can change the resonance frequency, CME coefficient, and near-field radiation of ME antenna. Particularly, it should be noted that pre-stress has the opposite effect in the low and high regions of the bias field. The near-field radiation is significantly enhanced by applying a proper magnetic bias or pre-stress. This simulation may facilitate the understanding of nonlinear CME behavior and provide a basis for designing nonlinear active and tunable ME antenna.

Magnomechanical backaction corrections due to coupling to higher-order Walker modes and Kerr nonlinearities

The radiation pressurelike coupling between magnons and phonons in magnets can modify the phonon frequency (magnomechanical spring effect) and decay rate (magnomechanical decay) via dynamical backaction. Such effects have been recently observed by coupling the uniform magnon mode of a magnetic sphere (the Kittel mode) to a microwave cavity. In particular, the ability to evade backaction effects was demonstrated [C. A. Potts et al., Phys. Rev. B 107, L140405 (2023)], a requisite for applications such as magnomechanical-based thermometry. However, deviations were observed from the predicted magnomechanical decay rate within the standard theoretical model. In this work, we account for these deviations by considering corrections due to (i) magnetic Kerr nonlinearities and (ii) the coupling of phonons to additional magnon modes. Provided that such additional modes couple weakly to the driven cavity, our model yields a correction proportional to the average Kittel magnon mode occupation. We focus our results on magnetic spheres, where we show that the magnetostatic Walker modes couple to the relevant mechanical modes as efficiently as the Kittel mode. Our model yields excellent agreement with the experimental data.

Model Predictive Torque Control for Permanent- Magnet Synchronous Motors Using a Stator- Fixed Harmonic Flux Reference Generator in the Entire Modulation Range

To increase torque and power conversion of permanent-magnet synchronous motors (PMSMs) at high-speed operation, the dc-link voltage of the inverter must be fully utilized during steady-state and transient operations. This article proposes the incorporation of a harmonic reference generator (HRG) with a pulse clipping (PC) scheme into a model predictive control framework to achieve highest power output. The HRG calculates flux references in the stator-fixed coordinate system for an underlying continuous-control-set model-predictive flux control (CCS-MPFC). These reference trajectories contain the harmonic flux component induced by the voltage hexagon in the overmodulation range and specific switching states (e.g., six-step operation) of the inverter are ensured by the proposed PC scheme. This enables a seamless transition to the overmodulation range including six-step operation and increases the drive's power conversion to its maximum extent. Since the flux differential equation in the stator-fixed coordinate system, used as motor model for the HRG and CCS-MPFC, is able to represent PMSMs with linear and nonlinear magnetization, the proposed approach is well suited for the control of PMSMs with nonlinear magnetization. Extensive transient and steady-state experimental investigations on a highly utilized PMSM in the entire modulation and speed range prove the performance of the proposed approach.

Extrapolation of System Matrices in Magnetic Particle Imaging.

Magnetic particle imaging exploits the non-linear magnetization of superparamagnetic iron-oxide particles to generate a tomographic image in a defined field-of-view. For reconstruction of the particle distribution, a time-consuming calibration step is required, in which system matrices get measured using a robot. To achieve artifact-free images, system matrices need to cover not only the field-of-view but also a larger area around it. Especially for large measurements- inevitable for future clinical application- this leads to long calibration time and high consumption of persistent memory. In this work, we analyze the signal in the outer part of the system matrix and motivate the usage of extrapolation methods to computationally expand the system matrix after restricting the calibration to the field-of-view. We propose a suitable extrapolation method and show its applicability on measured 2D and 3D data. In doing so, we achieve a considerable reduction of calibration time and consumption of persistent memory while preserving an artifact-free result.

Multi-scale dual domain network for nonlinear magnetization signal filtering in magnetic particle imaging

Magnetic particle imaging (MPI) realizes functional imaging by generating nonlinear response signals in the magnetic field through magnetic nanoparticles. MPI is a highly sensitive tracer-based imaging technology, which opens new possibilities for promising biomedical applications. However, in practice, the background signals, including random thermal noise from MPI receive chains and the harmonic interference caused by nonlinear components under a high-frequency excitation field, restrict the MPI performance. In this study, we propose a learning-based method by training a multi-scale dual-domain network to effectively filter the MPI signals. In the model, a multi-channel filtering module was designed to suppress the noise-related features in time and frequency domains. We constructed four different MPI signal datasets including simulated and measured noises acquired from a homemade MPI system to verify our method. The signal filtering tests were performed on synthetic and measured data. The experimental results indicated that our method can achieve the best performance among state-of-art signal filtering methods. Especially, on the dataset containing measured noise, our proposal improved the signal-to-noise ratio from 6.88 dB to 29.11 dB. Moreover, the percentage root means square difference was reduced from 51.26 to 3.96 and the root mean square error was reduced from 65.07×10-4 to 5.29×10-4.

Dynamic measurement of magnetic characteristics of switched reluctance motor

Introduction. Switched reluctance motor (SRM) is a type of electric motor featuring nonlinear magnetic characteristics. The flux linkage or inductance profile of SRM is usually required for the purpose of high control performance, and can be normally obtained through conventional static test by using DC or AC method when the rotor is locked. Problem. However, it is not practical to use the conventional method of measurement when the specific apparatus for locking the rotor is unavailable. Besides, due to the magnetic nonlinearity of SRM, the saturation effect makes it difficult to obtain the saturated magnetic characteristics, and the conventional static AC test fails to address this problem. Novelty. In this paper, a dynamic measurement method of the magnetization curves of SRM is proposed which allows the measurement take place while the motor is running with load. Methodology. Based on the conventional static AC test, the proposed measurement handles the saturation problem successfully by introducing a DC offset in the high frequency AC voltage. Phase inductance with different rotor positions and currents can be obtained by analyzing simple equivalent circuit. Practical value. Simulation is conducted in MATLAB/Simulink environment and the results have verified that the proposed dynamic measurement can effectively obtain the magnetic characteristics of SRM.

Stabilization of PMSG-based wind turbine systems with sampling information: Dynamic delay partition method

This paper addresses the novel stabilization criteria for a nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS) with sampled-data information, subject to the uncertainty and controller gain variations. In this regard, the nonlinearity in PMSG-based WTS is conferred by the Takagi–Sugeno (T–S) fuzzy systems. Next, by employing the full advantages of the variable characteristic related to the sampling pattern, a novel looped-type asymmetric augmented Lyapunov-Krasovskii functional (LKF) is developed. Then, the dynamic delay partition method is the first time to be applied for the non-fragile sampled-data control design of proposed T–S fuzzy systems. Also, the less conservativeness stabilization criteria for T–S fuzzy systems are obtained in the form of linear matrix inequality. In the end, the numerical examples confirm the applicability and efficiency of the presented results.

Constitutive modeling of oriented and non-oriented magnetostrictive particulate composites

This study presents a mathematical framework for two-phase magnetostrictive composites composed of oriented or non-oriented magnetostrictive Terfenol-D particles embedded in passive polymer matrices. The phase constitutive behavior of the monolithic Terfenol-D with arbitrary crystal orientations is represented by a recently developed discrete energy averaged model. This unique Terfenol-D constitutive model results in close-form and linear algebraic equations accurately describing the nonlinear magnetostriction and magnetization in magnetostrictive composites subjected to a given loading or magnetic field increment. The effectiveness of this new mathematical framework in capturing magnetostrictive particle size orientation, phase volume fractions, mechanical loading conditions, and magnetic field excitations are validated using a series of experimental data available in literature. Compared to existing models that prevalently addressed particle orientation in composite constitutive level, the model framework in this study directly handles particle orientation in the phase constitutive level, and therefore achieves enhanced efficiency while maintaining comparable accuracy.

Long-Term Memory Recursive Least Squares Online Identification of Highly Utilized Permanent Magnet Synchronous Motors for Finite-Control-Set Model Predictive Control

Highly utilized permanent magnet synchronous motors (PMSM) characterized by their nonlinear magnetization due to (cross-)saturation effects are the common choice when highest power density is required. For precise torque and current control, these motors are usually characterized by extensive offline measurements on a test bench, finally resulting in look-up tables of the relations between torque, flux, and current. In contrast, this article proposes a long-term memory recursive least squares (LTM-RLS) current estimator optimized for finite-control-set (FCS) model predictive controllers (MPC). This approach is able to identify the differential inductance and flux linkage maps for online self-commissioning without additional signal injection in only few seconds. This is achieved by extending the local RLS identification with an additional long-term memory. By continuously adapting the flux linkage maps, a precise open-loop torque control can be realized without the knowledge of exact motor parameters except the stator resistance as datasheet parameter. Extensive experimental investigations demonstrate accurate predictions of the identified model and, thus, highest control performance of the FCS-MPC during transient and steady-state operation and small torque estimation errors of less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.2 \,\%$</tex-math></inline-formula> for speeds greater than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$50 \,\%$</tex-math></inline-formula> of the PMSM's nominal speed. Even for speeds of only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5 \,\%$</tex-math></inline-formula> of the nominal speed, the estimation error is less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$7 \,\%$</tex-math></inline-formula> .

Impact of interface stress on responsive deformation of magnetic hydrogel

A multiphysics model is presented to study the responsive deformation of the magnetic hydrogel subject to a magneto-chemo-mechanical coupled field. In this work, the influences of the surrounding solvent and the magnetic stress at the hydrogel-surrounding interface are particularly investigated on the performance of the magnetic hydrogel. The physicochemical processes of mass transfer, force balance, and magnetization are included. The constitutive relations are derived by the second law of thermodynamics, and the free energy density is proposed with nonlinear magnetization. The coupled partial differential equations are numerically solved by the finite element method. After that, the deformation patterns are compared with or without the interface stress, and then various parametric studies are performed to investigate the effects of the magnetic susceptibility, geometric shape, and surrounding size on the responsive deformation of the magnetic hydrogel. Results show that the interface stress contributes significantly to the final deformation pattern of the magnetic hydrogel, and the performance of the deformable magnetic hydrogel can be precisely controlled. The present findings offer predictive insights into the deformation mechanism of the magnetic hydrogel, and also provide guidance for developing the programmable magnetic hydrogel-based device.