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Enhancing stability, magnetic anisotropy, and coercivity of manganese aluminum: Machine learning, ab initio , and micromagnetic modeling

The binary manganese aluminum (MnAl) alloy with L⁢1 0 crystal structure is a promising rare earth (RE) element-free permanent magnetic material because of its exceptional magnetic properties. However, experimentally synthesizing it in a stable bulk form is extremely challenging. Here, in this study, an alternative method of stabilizing the material, a pathway for experimental synthesis and validation, is proposed and theoretically verified. This is done by partially substituting Mn and Al sites with Fe and Ni and identifying its enhanced phase stability, saturation magnetization density, magnetic anisotropy, and coercivity from density functional theory (DFT), machine learning (ML) crystal graph convolution neural network (CGCNN), and micro-magnetic modeling. When considering a fixed 50% Ni, the magnetic anisotropy increases with the increasing Fe content but decreases the formation energy. The calculated formation energies, elastic constants, and phonon frequencies demonstrate that the binary and quaternary compositions are stable. Most importantly, in 50% Fe and Ni-substituted-equiatomic phase, magnetic anisotropy constants and saturation magnetization density increase by 56% and 23% as compared to the MnAl. Further, the coercivity of the equiatomic phase predicted with micro-magnetic modeling is higher by 17% than the parent compound.

Bhandari, Churna [Ames National Laboratory, and Io

Accurate machine-learning predictions of coercivity in high-performance permanent magnets

Increased demand for high-performance permanent magnets in the electric vehicle and wind-turbine industries has prompted the search for cost-effective alternatives. Discovering magnetic materials with the desired intrinsic and extrinsic permanent magnet properties presents a significant challenge to researchers because of issues with the global supply of rare-earth elements, material stability, and a low maximum magnetic energy product BH max . While first-principles density functional theory (DFT) predicts materials’ magnetic moments, magnetocrystalline anisotropy constants, and exchange interactions, it cannot compute extrinsic properties such as coercivity (H c ). Although it is possible to calculate H c theoretically with micromagnetic simulations, the predicted value is larger than the experiment by almost an order of magnitude due to the Brown paradox. To circumvent these issues, we employ machine-learning (ML) methods on an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling. The use of a large experimental dataset enables realistic H c predictions for materials such as Ce-doped Nd 2 ⁢Fe 14 ⁢B, comparing favorably against micromagnetically simulated coercivities. Remarkably, our ML model accurately identifies uniaxial magneto-crystalline anisotropy as the primary contributor to H c . With DFT calculations, we predict the Nd-site-dependent magnetic anisotropy behavior in Nd 2 ⁢Fe 14 ⁢B, confirming that Nd 4⁢g sites mainly contribute to uniaxial magnetocrystalline anisotropy, and also calculate the Curie temperature (T c ). Finally, both calculated results are in good agreement with the experiments. The coupled experimental dataset and ML modeling with DFT input predict H c with far greater accuracy and speed than was previously possible using micromagnetic modeling. Further, we reverse engineer the grain-boundary and intergrain exchange coupling with micromagnetic simulations by employing the ML predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Interface‐Induced Stability of Nontrivial Topological Spin Textures: Unveiling Room‐Temperature Hopfions and Skyrmions

Topological spin configurations, such as soliton-like spin texture and Dirac electron assemblies, have recently emerged in fundamental science and technology. Achieving stable topological spin textures at room temperature is crucial for their use as long-range information carriers. However, their creation and manipulation are hindered by multi-step field training and competing interactions. Thus, a spontaneous ground state for multidimensional topological spin textures is desirable, with skyrmions forming swirling, hedgehog-like spin structures in two dimensions and hopfions as their twisted 3D counterparts. Here, the first observation of robust and reproducible topological spin textures of hopfions and skyrmions observed at room temperature and in zero magnetic field is reported, which are stabilized by geometric confinement and protected by interfacial magnetism in a ferromagnet/topological insulator/ferromagnet trilayer heterostructure. These skyrmion-hopfion configurations are directly observed at room temperature with Lorenz transmission electron microscopy. Using micromagnetic modeling, the experimental observations of hopfion-skyrmion assemblies are reproduced. This model reveals a complete picture of how spontaneously organized skyrmion lattices encircled by hopfion rings are controlled by surface electrons, uniaxial anisotropy, and Dzyaloshinskii-Moriya interaction. This study provides evidence that topological chiral spin textures can facilitate the development of magnetic topological carriers, paving the way for ultralow-power and high-density information processing.

hopfions

Universal Electronic‐Structure Relationship Governing Intrinsic Magnetic Properties in Permanent Magnets

An electronic-structure-centered perspective is presented on permanent-magnet (PM) design, highlighting two key levers, that is, saturation magnetization (M s ), governed by 3d-band filling and exchange physics, and magnetocrystalline anisotropy energy (MAE), arising from spin-orbit coupling (SOC) on anisotropic orbital populations. Reviewing current practices, including DFT-based MAE/J ij extraction, atomistic-spin and micromagnetic modeling, and high-throughput machine learning (ML) pipelines, three bottlenecks limiting predictive discovery is identified that is i) electronic-structure accuracy for small MAE (sensitive to functional choice, Hubbard U, and many-body effects), ii) finite-temperature and kinetic realism (phonon/magnon renormalization, ordering kinetics), and iii) descriptor and multiscale decoupling (lack of SOC-weighted and orbital-resolved fingerprints). Deep dives into the electronic-structure of Nd─Fe─B and Fe─N show how these fingerprints govern magnetic performance, motivating DFT- and quantum-mechanics-based descriptors for discovery. Unbiased, structure-driven exploration, coupled with high-throughput simulations, ML, generative AI, and reasoning models, accelerates candidate identification and propagates insights across scales. Addressing supply-chain risks, on future needs of designing “critical-element-free” magnets with tailored microstructure and high energy products is emphasized. By integrating electronic fingerprints, AI reasoning, and multiscale modeling, a practical roadmap is provided for rare-earth-lean or rare-earth free, high-performance, sustainable PMs.

Singh, Prashant [Ames Laboratory, and Iowa State U

Electrical Detection of Spin-Hall-Induced Auto-oscillations in Lithium Aluminate Ferrite Thin Films

Ferrimagnetic insulators with ultralow damping are of great interest for their potential applications in energy-efficient computing devices. Here, we report the direct electrical detection of magnetic auto-oscillations in unpatterned ultralow damping ferrimagnetic insulator epitaxial Li 0.5 Al 0.5 Fe 2 O 4 thin films, driven by a current in a proximal Pt nanowire. Auto-oscillations occur for only one current polarity, consistent with the spin-Hall effect inducing the oscillation state. Micromagnetic modeling shows good agreement with the experimental frequency and field dispersions, showing only one dominant oscillation mode, in contrast to the multiple modes typically observed in transition-metal nanowire-type spin-Hall nanooscillators. This study illustrates a new material system for neuromorphic computing and magnonics, a simple material platform with the direct-current generation of high-frequency (~10 GHz) signals and their electrical detection.

36 MATERIALS SCIENCE

Direct measurement of reduced exchange stiffness and its impact on magnetic vortex behavior in PyGd alloys

Thin films composed of sputtered transition metal/rare earth (TM/RE) ferrimagnets have emerged as promising building blocks for future spintronic devices, offering tunable magnetic properties critical for data storage, memory, and logic applications. However, understanding how the combination of TM and RE elements influences effective magnetic properties, such as exchange stiffness (Aex), remains challenging. Magnetic vortices provide a versatile tool for probing these properties in thin film systems. By combining magnetic imaging via soft x-ray microscopy and micromagnetic modeling, we quantify the effective exchange stiffness in PyGd ferrimagnetic disks with varying Gd concentrations. Our results indicate a reduction in Aex to below 3 pJ/m for a 20% Gd concentration when compared to reference Py, and values below 2 pJ/m for 30% Gd, reflecting weak Ni–Gd exchange coupling. These findings highlight the critical role of rare earth content in tuning the exchange stiffness. The reduced exchange stiffness facilitates a linear field response of the magnetization up to the edge of the disk, as well as significant deformations in the vortex core itself when compared to films with larger Aex. Our results are in line with, albeit lower than, recent measurements of the exchange stiffness in intermixed PyGd. This reduced exchange stiffness has implications for the development of spintronic devices based on ferrimagnetic skyrmions.

Jacob, Liyan

Quantitative phase retrieval and characterization of magnetic nanostructures via Lorentz (scanning) transmission electron microscopy

Magnetic materials phase reconstruction using Lorentz transmission electron microscopy (LTEM) measurements have traditionally been achieved using longstanding methods such as off-axis holography (OAH) fast-Fourier transform technique and the transport-of-intensity equation (TIE). The increase in access to processing power alongside the development of advanced algorithms have allowed for phase retrieval of nanoscale magnetic materials with greater efficacy and resolution. Specifically, reverse-mode automatic differentiation (RMAD) and the extended electron ptychography iterative engine (ePIE) are two recent developments of phase retrieval that can be applied to analyzing micro-to-nano- scale magnetic materials. This work evaluates phase retrieval using TIE, RMAD, and ePIE in simulations of Permalloy (Ni 80 Fe 20 ) nanoscale islands, or nanomagnets. Extending beyond simulations, we demonstrate total phase retrieval and image reconstructions of a NiFe nanowire using OAH and RMAD in LTEM and ePIE in Lorentz-mode-4D scanning transmission electron microscopy experiments and determine the saturation magnetization through corroborations with micromagnetic modeling. Finally, we demonstrate the efficacy of these methods in retrieving the total phase and highlight its use in characterizing and analyzing the proximity effect of the magnetic nanostructures.

Lorentz transmission electron microscopy

Skyrmion lattice manipulation with electric currents and thermal gradients in MnSi

The skyrmion lattice (SkL) in MnSi was studied using small-angle neutron scattering and under the influence of a radial electric current in a Corbino geometry. In response to the applied current, the SkL undergoes an angular reorientation with respect to the MnSi crystal lattice. The reorientation is nonmonotonic with increasing current, with the SkL rotating first in one direction and then the other. The SkL reorientation was studied at different sample locations and found to depend on the local current density as inferred from a finite-element analysis. Here, the nonmonotonic response indicates the presence of two competing effects on the SkL, most likely due to the presence of both radial electric and thermal currents. Such a scenario is supported by micromagnetic simulations, which show how these effects can act constructively or destructively to drive the SkL rotation, depending on the direction of the electric current. In addition, the simulations also suggest how the direction of the skyrmion flow may affect the SkL orientation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Coupling-dependent antiferromagnetic-ferromagnetic ordering in a pinwheel artificial spin ice

Nanopatterned magnetic thin films offer a platform for exploration of tailored magnetic properties such as emergent long-range order. A prominent example is artificial spin ice (ASI), where an arrangement of nanoscale magnetic elements, acting as macrospins, interact via their dipolar fields. In this study, we discuss the transition from antiferromagnetic (AFM) to ferromagnetic (FM) long-range order in a square lattice ASI as the magnetic elements are gradually rotated through 45⁢° to a “pinwheel” configuration. The AFM-FM transition is observed experimentally using synchrotron radiation x-ray spectromicroscopy and occurs for a certain rotation angle of the nanomagnets, dependent on the dipolar coupling strength determined by the separation of the magnets in the lattice. Large-scale magnetic dipole simulations show that the point-dipole approximation fails to capture the correct AFM-FM transition angle. However, excellent agreement with experimental data is obtained using a dumbbell-dipole model, which better reflects the actual dipolar fields of the magnets. This model also explains the coupling dependence of the transition angle, another feature not captured by the point-dipole model. Our findings resolve a discrepancy between measurement and theory in previous work on “pinwheel” ASIs and establish the coupling dependence of the AFM-FM transition. The revised dipole model, with a more accurate representation of the stray field, offers more precise control of magnetic order in artificial spin systems.

Artificial spin ice

Emulating 2D Materials with Magnons

Spin waves (magnons) in two-dimensional (2D) materials have received increasing interest due to their unique states and potential for tunability. However, many interesting features of these systems, including Dirac points and topological states, occur at high frequencies, where experimental probes are limited. Here, we study a crystal formed by patterning a hexagonal array of holes in a perpendicularly magnetized thin film. Through simulation, we find that the magnonic band structure imitates that of graphene, but additionally has some kagomelike character and includes a few flat bands. Surprisingly, its nature can be understood using a nine-band tight-binding Hamiltonian. This clear analogy to 2D materials enables band-gap engineering in 2D, topological magnons along 1D phase boundaries, and spectrally isolated modes at 0D point defects. Interestingly, the 1D phase boundaries allow access to the valley degree of freedom through a magnonic analog of the quantum valley Hall insulator. These approaches can be extended to other magnonic systems, but are potentially more general due to the simplicity of the model, which resembles existing results from electron, phonon, photon, and cold-atom systems. This finding brings the physics of spin waves in 2D materials to more experimentally accessible scales, augments it, and outlines a few principles for controlling magnonic states.

Ferrimagnets

Enhancement of magnetic domain wall velocity via resonant dissipation of standing wave modes of domain wall structure with perpendicular magnetic anisotropy

The dynamic behaviors of magnetic domain walls have significant implications for developing advanced spintronic devices. In this study, we investigate the intriguing resonance phenomenon within the magnetic domain wall structure, focusing on the dissipation mechanism and its impact on domain wall dynamic motion. By applying a static external magnetic field, we observe a remarkable amplification of domain wall velocity through the resonant excitations of the flexure modes. The resonance of the flexure mode exerts an indirect influence on the domain wall velocity through energy dissipation, leading to a significant enhancement from the predictions of the one-dimensional Walker model. We establish a robust model platform rooted in energy dissipation allows comprehensive understanding the dramatic enhancement of domain wall velocity observed during width-directional flexure mode resonance. By directly quantifying energy dissipation, our approach provides highly effective and accurate estimates of domain wall velocity, surpassing previous methods that focus solely on the instantaneous dynamics of the domain wall structure. These findings offer crucial insights into the fundamental mechanisms governing the dynamics of domain walls and other magnetic systems, such as magnetic skyrmions, bubbles, and magnetic vortices, paving the way for development and optimization of next-generation spintronic devices.

Collective dynamics

Integrating adaptive learning with post hoc model explanation and symbolic regression to build interpretable surrogate models

Abstract We develop a materials informatics workflow to build an interpretable surrogate model for micromagnetic simulations. Our goal is to predict the energy barrier of a moving isolated skyrmion in rare-earth-free $$\hbox {Mn}_4$$ Mn 4 N. Our approach integrates adaptive learning with post hoc model explanation and symbolic regression methods. We discuss an unexplored acquisition function (information condensing active learning) within the adaptive learning loop and compare it with the known standard deviation function for efficient navigation of the search space. Model-agnostic post hoc explanation techniques then uncover trends learned by the trained model, which we then leverage to constrain the expressions used for symbolic regression. Graphical abstract

Biswas, Ankita

Nanomagnet shape effects on magnetic reversal in artificial spin ice

We use micromagnetic simulations to study the influence of the shape of elongated nanomagnets that vary from rectangular to elliptical shapes in an artificial spin ice array. For weakly interacting ellipselike islands, the magnetic hysteresis loops align with the Stoner-Wohlfarth model, demonstrating nearly uniform magnetization at remanence and nearly coherent rotation. As expected, nonelliptical weakly interacting islands show deviations from the model due to the curling and pinning of the magnetization at the island edge. We find that increasing interisland coupling leads to an increasingly complex magnetic reversal process due to an interplay between internal and external degrees of freedom as the shape of the islands varies. Furthermore, our results open a roadmap for tailoring systems with desired magnetic properties by choosing the appropriate nanomagnet shape.

Artificial spin ice

Exascale-Enabled Models and Algorithms for Microelectronics Applications (MicroEleX) v1

The MicroEleX code package contains a variety of models and algorithms for physical modeling of microelectronic circuitry, including electrostatics, electrodynamics, superconducting physics, micromagnetics, multi-ferroic systems, and quantum transport. MicroEleX leverages the AMReX software framework to provide scalability on GPU-based supercomputing architectures. The code is open source and designed to be algorithmically flexible so developers can incorporate enhanced or customized physics.

Nonaka, Andy

Advances in relaxation and memory effects of magnetic nanoparticles for biomedical applications

Functionalized magnetic nanoparticles are pivotal in magnetic resonance imaging, computed tomography, controlled drug delivery, and hyperthermia treatments due to their exceptional magnetic relaxation and functional properties. The magnetic core composition and structure significantly affects the complex magnetic properties of these nanoparticles necessitating a thorough examination of magnetism fundamentals related to these systems. One important aspect is the ability of magnetic nanoparticles to retain previous magnetic state configurations known as memory effect, primarily governed by domain structure and magnetic anisotropy. Despite its relevance to advanced applications, comprehensive studies on magnetic relaxation and memory effects remain limited. Here, the present review aims to bridge this gap by investigating relaxation mechanisms, synthesis strategies, and applications, fostering further innovation. It investigates the memory effects and their dependence on particle composition and morphology along with key synthesis techniques for large-scale production in industrial adoption. Structured into focused sections on magnetic properties and their influence on biomedical and technological applications, this review provides essential insights into memory effects, magneto-relaxation mechanisms, influencing factors, and both experimental and theoretical methodologies. It also delves into computational modelling and AI-driven design, which are revolutionizing the prediction, discovery, and optimization of materials with tailored properties.

36 MATERIALS SCIENCE

On the origin of stable remanence in pseudo-single domain grains

A critique is presented of the quantitative model for the magnetic moment of pseudo-single domain grains (hypothetical magnetite grains larger than the critical size threshold for single domain behavior, yet also difficult to demagnetize), derived by Stacey and Banerjee (1974). Evidence from theoretical studies in micromagnetics demonstrates that the spin orientations in such grains are too complex to permit ready prediction of the magnetic moments. However, this limitation in the theory may be overcome by experiments involving rare earth-cobalt alloys and yttrium iron garnet crystals; these studies have suggested that surface anisotropy is the predominant cause of the high coercivity of pseudo-single domain grains.

Banerjee, S. K.

Spin–orbit torque in a three-fold-symmetric bilayer and its effect on magnetization dynamics

Field-free switching of perpendicular magnetization has previously been observed in an epitaxial L1 1 -ordered CoPt/CuPt bilayer and attributed to spin–orbit torque (SOT) arising from the crystallographic 3m point group of the interface. Using a first-principles nonequilibrium Green's function formalism combined with the Anderson disorder model, we calculate the angular dependence of the SOT in a CoPt/CuPt bilayer and find that the magnitude of the 3m SOT is about 20% of the conventional dampinglike SOT. We further study the magnetization dynamics in perpendicularly magnetized films in the presence of 3m SOT and Dzyaloshinskii–Moriya interaction, using the equations of motion for domain wall dynamics and micromagnetic simulations. For systems where strong interfacial DMI results in the Néel character of domain walls, we find that a very large current density is required to achieve deterministic switching, because reorientation of the magnetization inside the domain wall is necessary to induce the switching asymmetry. For thicker films with relatively weak interfacial DMI and the Bloch character of domain walls, deterministic switching is possible at much smaller current densities, which may explain the recent experimental findings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Numerical simulation projects in micromagnetics with Jupyter

We report a case study where an existing materials science course was modified to include numerical simulation projects on the micromagnetic behavior of materials. The Ubermag micromagnetic simulation software package is used in order to solve problems computationally. The simulation software is controlled through the Python code in Jupyter notebooks. Our experience is that the self-paced problem-solving nature of the project work can facilitate a better in-depth exploration of the course contents. We discuss which aspects of the Ubermag and the project Jupyter ecosystem have been beneficial for the students' learning experience and which could be transferred to similar teaching activities in other subject areas.

97 MATHEMATICS AND COMPUTING