Atomistic Spin Dynamics Research Articles

Magnetic ordering and dynamics in monolayers and bilayers of chromium trihalides: atomistic simulations approach

We analyze magnetic properties of monolayers and bilayers of chromium iodide, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CrI}_3$$\\end{document}, in two different stacking configurations: AA and rhombohedral ones. Our main focus is on the corresponding Curie temperatures, hysteresis curves, equilibrium spin structures, and spin wave excitations. To obtain all these magnetic characteristic, we employ the atomistic spin dynamics and Monte Carlo simulation techniques. The model Hamiltonian includes isotropic exchange coupling, magnetic anisotropy, and Dzyaloshinskii-Moriya interaction. As the latter interaction is relatively weak in pristine \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CrI}_3$$\\end{document}, we consider a more general case, when the Dzyaloshinskii-Moriya interaction is enhanced externally (e.g. due to gate voltage, mechanical strain, or proximity effects). An important issue of the analysis is the correlation between hysteresis curves and spin configurations in the system, as well as formation of the skyrmion textures.

Characterizing the diffuse continuum excitations in the classical spin liquid h−YMnO3

We extend previous inelastic neutron scattering results on the geometrically frustrated antiferromagnet hexagonal-YMnO3, which has been suggested to belong to the class of classical spin liquids. We expand the energy transfer range of the diffuse signal up to 6.9 meV within a wide temperature range around the ordering temperature, TN. The two distinct diffuse signals in the a−b plane, the signal localized at Γ′ and the scattering intensity connecting Γ′ points over the M′, are shown to be only weakly energy dependent. In addition, an external magnetic field of up to 10.5 T applied along c is shown to have no effect on the diffuse signal. In the orthogonal scattering plane, the signals are shown to be dependent on l only through the magnetic form factor, showing that the correlations are purely two-dimensional, and supporting the origin of this to be the frustrated Mn3+ triangles. This result is corroborated by atomistic spin dynamics simulations showing similar scattering vector and temperature behaviors. Lastly, data for the spin wave scattering in the (h,0,l) plane allow for a discussion of the magnetic ground state where better agreement is found between the data and an ordered structure of the Γ1 or Γ3 symmetry, albeit crystal electric field arguments dismiss the Γ1 as a possibility. Published by the American Physical Society 2024

Ultrafast antiferromagnetic switching of Mn2Au with laser-induced optical torques

Ultrafast manipulation of the Néel vector in metallic antiferromagnets most commonly occurs by generation of spin-orbit (SOT) or spin-transfer (STT) torques. Here, we predict another possibility for antiferromagnetic domain switching by using novel laser optical torques (LOTs). We present results of atomistic spin dynamics simulations from the application of LOTs for all-optical switching of the Néel vector in the antiferromagnet Mn2Au. The driving mechanism takes advantage of the sizeable exchange enhancement, characteristic of antiferromagnetic dynamics, allowing for picosecond 90 and 180-degree precessional toggle switching of the Néel vector with laser fluences on the order of mJ/cm2. A special symmetry of these novel torques greatly minimises the over-shooting effect common to precessional spin switching by SOT and STT methods. We demonstrate the opportunity for LOTs to produce deterministic, non-toggle switching of single antiferromagnetic domains. Lastly, we show that even with sizeable ultrafast heating by laser in metallic systems, there exist a large interval of laser parameters where the LOT-assisted toggle and preferential switchings in magnetic grains have probabilities close to one. The proposed protocol could be used on its own for all-optical control of antiferromagnets for computing or memory storage, or in combination with other switching methods to lower energy barriers and/or to prevent over-shooting of the Néel vector.

Machine learning-based prediction of FeNi nanoparticle magnetization

This work proposes a computationally efficient approach for estimating the magnetization of Fe0.7Ni0.3 body-centered cubic (bcc) nanoparticles (NPs) at room temperature using machine-learning algorithms, in terms of the average magnetic moment per atom, ⟨μ⟩. The magnetization data of isolated NPs were generated using atomistic spin dynamics (ASD) simulations for various nanoparticle shapes (cubes, spheres, octahedra, cones, cylinders, ellipsoids, flakes, and pyramids, with or without nanovoids) and FeNi distributions (random, core-shell, onion, sandwich, and Janus with different boundary planes). More than 1600 NPs were created and split into training and testing sets (70%-30% split), with features including the number of Ni/Fe surface and core atoms, potential energy distributions, pair correlation functions, and coordination distributions. Several machine-learning algorithms, including Random Forest (RF), Elastic Net, Support Vector Regression (SVR), and Gradient Boosting Regression (CatBoost), were applied to predict the average magnetic moment per atom of these NPs. The best-performing models, CatBoost and RF, achieved R2 scores of up to 0.86, demonstrating their accuracy in predicting NP magnetization. Feature analysis highlighted the significance of the interface between Fe and Ni clusters, Fe-Fe interactions, and the presence of Fe on the surface as critical contributors to overall magnetization. Random alloy spherical NPs without porosity exhibited the highest ⟨μ⟩ ∼ 1.6μB due to reduced Ni-Ni interactions. Applying machine-learning methods significantly reduces computational time and memory requirements compared to traditional ASD simulations. This allows for rapid prediction of NPs with desired magnetic properties, making them suitable for various technological applications.

Stability and dynamics of magnetic skyrmions in FM/AFM heterostructures

Magnetic skyrmions have garnered attention for their potential roles in spintronic applications, such as information carriers in computation, data storage, and nano-oscillators due to their small size, topological stability, and the requirement of small electric currents to manipulate them. Two key challenges in harnessing skyrmions are the stabilization requirement through a strong out-of-plane field, and the skyrmion Hall effect (SkHE). Here, we present a systematic model study of skyrmions in ferromagnetic/antiferromagnetic (FM/AFM) multilayer structures by employing both atomistic Monte Carlo and atomistic spin dynamics simulations. We demonstrate that skyrmions stabilized by exchange bias have superior stability to field-stabilized skyrmions due to the formation of a magnetic imprint within the AFM layer. Additionally, stacking two skyrmion hosting FM layers between two AFM layers suppresses the SkHE and enables the transport of AFM-coupled skyrmions with high velocity in the order of a few km/s. This proposed multilayer configuration could serve as a pathway to overcome existing limitations in the development of skyrmion-based devices, and the insights obtained through this study contribute significantly to the broader understanding of topological spin textures in magnetic materials. Published by the American Physical Society 2024

Atomistic spin dynamics simulations of magnonic spin Seebeck and spin Nernst effects in altermagnets

Magnon band structures in altermagnets are characterized by an energy splitting of modes with opposite chirality, even in the absence of applied external fields and relativistic effects, because of an anisotropy in the Heisenberg exchange interactions. We perform quantitative atomistic spin dynamics simulations based on electronic structure calculations on rutile RuO2, a prototypical “d-wave” altermagnet, to study magnon currents generated by thermal gradients. We report substantial spin Seebeck and spin Nernst effects, i.e., longitudinal or transverse spin currents, depending on the propagation direction of the magnons with respect to the crystal, together with a finite spin accumulation associated with nonlinearities in the temperature profile. Our findings are consistent with the altermagnetic spin-group symmetry, as well as predictions from linear spin-wave theory and semiclassical Boltzmann transport theory. Published by the American Physical Society 2024

Proximity coupling induced two dimensional magnetic order in EuO-based synthetic ferrimagnets

Proximity effects allow for the adjustment of magnetic properties in a physically elegant way. If two thin ferromagnetic (FM) films are brought into contact, electronic coupling alters their magnetic exchange interaction at their interface. For a low-TC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_C$$\\end{document} rare-earth FM coupled to a 3d transition metal FM, even room temperature magnetism is within reach. In addition, magnetic proximity coupling is particularly promising for increasing the magnetic order of metastable materials such as europium monoxide (EuO) beyond their bulk TC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_C$$\\end{document}, since neither the stoichiometry nor the insulating properties are modified. We investigate the magnetic proximity effect at Fe/EuO and Co/EuO interfaces using hard X-ray photoelectron spectroscopy. By exciting the FM layers with circularly polarized light, magnetic dichroism is observed in angular dependence on the photoemission geometry. In this way, the depth-dependence of the magnetic signal is determined element-specifically for the EuO and 3d FM parts of the bilayers. In connection with atomistic spin dynamics simulations, the thickness of the EuO layer is found to be crucial, indicating that the observed antiferromagnetic proximity coupling is a short-ranged and genuine interface phenomenon. This fact turns the bilayer into a strong synthetic ferrimagnet. The increase in magnetic order in EuO occurs in a finite spatial range and is therefore particularly strong in the 2D limit—a counterintuitive but very useful phenomenon for spin-based device applications.

Tunable topological magnetism in superlattices of nonmagnetic B20 systems

We predict topological magnetic properties of B20 systems, that are organized in atomically thin multilayers. In particular, we focus on FeSi/CoSi and FeSi/FeGe superlattices with different numbers of layers and interface structures. We demonstrate that the absence of long-range magnetic order, previously observed in bulk FeSi and CoSi, is broken near the FeSi/CoSi interface, where a magnetic state with a nontrivial topological texture appears. Using the Heisenberg and Dzyaloshinskii-Moriya (DM) interactions calculated from first principles, we perform finite-temperature atomistic spin dynamics simulations for up to 2×106 spins to capture the complexity of noncollinear textures. Our simulations predict the formation of antiskyrmions in a [001]-oriented FeSi/CoSi multilayer, intermediate skyrmions in a [111]-oriented FeSi/CoSi system, and Bloch skyrmions in the FeSi/FeGe (001) system, with a size between 7 and 37 nm. These varieties of topological magnetic textures in the studied systems can be attributed to the complex asymmetric structure of the DM matrix, which is different from previously known magnetic materials. We demonstrate that through structural engineering both ferromagnetic and antiferromagnetic skyrmions can be stabilized, where the latter are especially appealing for applications due to the zero skyrmion Hall effect. The proposed B20 multilayers show a potential for further exploration and call for experimental confirmation. Published by the American Physical Society 2024

Current-driven dynamics of antiferromagnetic skyrmions: from skyrmion Hall effects to hybrid inter-skyrmion scattering

Antiferromagnetic (AFM) skyrmions have emerged as a highly promising avenue in the realm of spintronics, particularly for the development of advanced racetrack memory devices. A distinguishing feature of AFM skyrmions is the cancellation of their net topological charge, leading to an anticipated absence of the skyrmion Hall effect (SkHE). Here, we unveil that the latter is finite under the influence of spin-transfer torque, depending on the direction of the injected current impinging on intrinsic AFM skyrmions emerging in Cr/Pd/Fe trilayer on Ir(111) surface. Hinging on first principles combined with atomistic spin dynamics simulations, we identify the origin of the SkHE, which is due to the ellipticity of the skyrmions, and we uncover that FM skyrmions in the underlying Fe layer act as effective traps for AFM skyrmions, confining them and affecting their velocity. These findings hold significant promise for spintronic applications, the design of multi-purpose skyrmion tracks while advancing our understanding of AFM–FM skyrmion interactions and hybrid soliton dynamics in heterostructures.

Dzyaloshinskii–Moriya interaction and field-free sub-10 nm topological magnetism in Fe/bismuth oxychalcogenides heterostructures

Abstract Topological magnetism with strong robustness, nanoscale dimensions and ultralow driving current density (∼ 106 A/m2) is promising for applications in information sensing, storage, and processing, and thus sparking widespread research interest. Exploring candidate material systems with nanoscale size and easily tunable properties is a key for realizing practical topological magnetism-based spintronic devices. Here, we propose a class of ultrathin heterostructures, Fe/Bi2O2 X (X = S, Se, Te) by deposing metal Fe on quasi-two-dimensional (2D) bismuth oxychalcogenides Bi2O2 X (X = S, Se, Te) with excellent ferroelectric/ferroelastic properties. Large Dzyaloshinskii–Moriya interaction (DMI) and topological magnetism can be realized. Our atomistic spin dynamics simulations demonstrate that field-free vortex–antivortex loops and sub-10 nm skyrmions exist in Fe/Bi2O2S and Fe/Bi2O2Se interfaces, respectively. These results provide a possible strategy to tailor topological magnetism in ultrathin magnets/2D materials interfaces, which is extremely vital for spintronics applications.

Impact of dimensionality on the magnetocaloric effect in two-dimensional magnets

Magnetocaloric materials, which exploit reversible temperature changes induced by magnetic field variations, are promising for advancing energy-efficient cooling technologies. The potential integration of two-dimensional materials into magnetocaloric systems represents an emerging opportunity to enhance the magnetocaloric cooling efficiency. In this study, we use atomistic spin dynamics simulations based on first-principles parameters to systematically evaluate how magnetocaloric properties transition from three-dimensional (3D) to two-dimensional (2D) ferromagnetic materials. We find that 2D features such as reduced Curie temperature, sharper magnetic transition, and higher magnetic susceptibility are beneficial for magnetocaloric applications, while the relatively higher lattice heat capacity in 2D can compromise achievable adiabatic temperature changes. We further propose GdSi2 as a promising 2D magnetocaloric material. Our calculation predicts that GdSi2 exhibits an isothermal entropy change ΔSM of 22.5 J kg−1 K−1 and an adiabatic temperature change ΔTad of 6.2 K, near the hydrogen liquefaction temperature (TC≈25 K). Our analysis offers valuable theoretical insights into the magnetocaloric effect in 2D ferromagnets and demonstrates that 2D ferromagnets hold promise for cooling and thermal management applications in compact and miniaturized nanodevices.

Zero-field magnetic skyrmions in exchange-biased ferromagnetic–antiferromagnetic bilayers

We report on the stabilization of ferromagnetic skyrmions in zero external magnetic fields, in exchange-biased systems composed of ferromagnetic–antiferromagnetic (FM-AFM) bilayers. By performing atomistic spin dynamics simulations, we study cases of compensated, uncompensated, and partly uncompensated FM-AFM interfaces, and investigate the impact of important parameters such as temperature, inter-plane exchange interaction, Dzyaloshinskii–Moriya interaction, and magnetic anisotropy on the skyrmions appearance and stability. The model with an uncompensated FM-AFM interface leads to the stabilization of individual skyrmions and skyrmion lattices in the FM layer, caused by the effective field from the AFM instead of an external magnetic field. Similarly, in the case of a fully compensated FM-AFM interface, we show that FM skyrmions can be stabilized. We also demonstrate that accounting for interface roughness leads to stabilization of skyrmions both in compensated and uncompensated interface. Moreover, in bilayers with a rough interface, skyrmions in the FM layer are observed for a wide range of exchange interaction values through the FM-AFM interface, and the chirality of the skyrmions depends critically on the exchange interaction.

Ultrafast opto-magnetic effects in the extreme ultraviolet spectral range

Coherent light-matter interactions mediated by opto-magnetic phenomena like the inverse Faraday effect (IFE) are expected to provide a non-thermal pathway for ultrafast manipulation of magnetism on timescales as short as the excitation pulse itself. As the IFE scales with the spin-orbit coupling strength of the involved electronic states, photo-exciting the strongly spin-orbit coupled core-level electrons in magnetic materials appears as an appealing method to transiently generate large opto-magnetic moments. Here, we investigate this scenario in a ferrimagnetic GdFeCo alloy by using intense and circularly polarized pulses of extreme ultraviolet radiation. Our results reveal ultrafast and strong helicity-dependent magnetic effects which are in line with the characteristic fingerprints of an IFE, corroborated by ab initio opto-magnetic IFE theory and atomistic spin dynamics simulations.

Ultra-high spin emission from antiferromagnetic FeRh

An antiferromagnet emits spin currents when time-reversal symmetry is broken. This is typically achieved by applying an external magnetic field below and above the spin-flop transition or by optical pumping. In this work we apply optical pump-THz emission spectroscopy to study picosecond spin pumping from metallic FeRh as a function of temperature. Intriguingly we find that in the low-temperature antiferromagnetic phase the laser pulse induces a large and coherent spin pumping, while not crossing into the ferromagnetic phase. With temperature and magnetic field dependent measurements combined with atomistic spin dynamics simulations we show that the antiferromagnetic spin-lattice is destabilised by the combined action of optical pumping and picosecond spin-biasing by the conduction electron population, which results in spin accumulation. We propose that the amplitude of the effect is inherent to the nature of FeRh, particularly the Rh atoms and their high spin susceptibility. We believe that the principles shown here could be used to produce more effective spin current emitters. Our results also corroborate the work of others showing that the magnetic phase transition begins on a very fast picosecond timescale, but this timescale is often hidden by measurements which are confounded by the slower domain dynamics.

Kernel fusion in atomistic spin dynamics simulations on Nvidia GPUs using tensor core

In atomistic spin dynamics simulations, the time cost of constructing the space- and time-displaced pair correlation function in real space increases quadratically as the number of spins N, leading to significant computational effort. The GEMM subroutine can be adopted to accelerate the calculation of the dynamical spin–spin correlation function, but the computational cost of simulating large spin systems (>40000 spins) on CPUs remains expensive. In this work, we perform the simulation on a graphics processing unit (GPU), a hardware solution widely used as an accelerator for scientific computing and deep learning. We show that GPUs can accelerate the simulation up to 25-fold compared to multi-core CPUs when using the GEMM subroutine on both. To hide memory latency, we fuse the element-wise operation into the GEMM kernel using CUTLASS which can improve the performance by 26% ∼ 33% compared to the implementation based on cuBLAS. Furthermore, we perform the ‘on-the-fly’ calculation in the epilogue of the GEMM subroutine to avoid saving intermediate results on global memory, which makes large-scale atomistic spin dynamics simulations feasible and affordable.

Accounting for quantum effects in atomistic spin dynamics

Atomistic spin dynamics (ASD) is a standard tool to model the magnetization dynamics of a variety of materials. The fundamental dynamical model underlying ASD is entirely classical. In this paper, we present two approaches to effectively incorporate quantum effects into ASD simulations, thus enhancing their low-temperature predictions. The first allows to simulate the magnetic behavior of a quantum spin system by solving the equations of motion of a classical spin system at an effective temperature relative to the critical temperature. This effective temperature is determined from the microscopic properties of the system. The second approach is based on a semiclassical model where classical spins interact with an environment with a quantumlike power spectrum. The parameters that characterize this model can be calculated or extracted from experiments. This semiclassical model quantitatively reproduces the absolute temperature behavior of a magnetic system, thus accounting for the quantum mechanical aspects of its dynamics, even at low temperature. The methods presented here can be readily implemented in current ASD simulations with no additional complexity cost. Published by the American Physical Society 2024

Exploring the Fundamental Spatial Limits of Magnetic All-Optical Switching.

All-optical switching (AOS) results in ultrafast and deterministic magnetization reversal upon single laser pulse excitation, potentially supporting faster and more energy-efficient data storage. To explore the fundamental limits of achievable bit densities in AOS, we have used soft X-ray transient grating spectroscopy to study the ultrafast magnetic response of a GdFe alloy after a spatially structured excitation with a periodicity of 17 nm. The ultrafast spatial evolution of the magnetization in combination with atomistic spin dynamics and microscopic temperature model calculations allows us to derive a detailed phase diagram of AOS as a function of both the absorbed energy density and the nanoscale excitation period. Our results suggest that the minimum size for AOS in GdFe alloys, induced by a nanoscale periodic excitation, is around 25 nm and that this limit is governed by ultrafast lateral electron diffusion and by the threshold for optical damage.

Dzyaloshinskii-Moriya interactions, Néel skyrmions and V4 magnetic clusters in multiferroic lacunar spinel GaV4S8

Using ab initio density functional theory with static mean-field correlations, we calculate the Heisenberg and Dzyaloshinskii-Moriya interactions (DMI) for an atomistic spin Hamiltonian for the lacunar spinel, GaV4S8. The parameters describing these interactions are used in atomistic spin dynamics and micromagnetic simulations. The magnetic properties of the lacunar spinel GaV4S8, a material well-known from experiment to host magnetic skyrmions of Néel character, are simulated with these ab initio calculated parameters. The Dzyaloshinskii-Moriya contribution to the micromagnetic energy is a sum of two Lifshitz invariants, supporting the formation of Néel skyrmions and its symmetry agrees with what is usually expected for C3ν-symmetric systems. There are several conclusions one may draw from this work. One concerns the quantum nature of the magnetism, where we show that the precise magnetic state of the V4 cluster is crucial for understanding quantitatively the magnetic phase diagram. In particular, we demonstrate that a distributed-moment state of each V4 cluster explains well a variety of properties of GaV4S8, such as the band gap, observed Curie temperature and especially the stability of Néel skyrmions in the experimentally relevant temperature and magnetic-field range. In addition, we find that electronic correlations change visibly the calculated value of the DMI.

Theory of Defect-Induced Crystal Field Perturbations in Rare-Earth Magnets.

We present a theory describing the single-ion anisotropy of rare-earth (RE) magnets in the presence of point defects. Taking the RE-lean 1∶12 magnet class as a prototype, we use first-principles calculations to show how the introduction of Ti substitutions into SmFe_{12} perturbs the crystal field, generating new coefficients due to the lower symmetry of the RE environment. We then demonstrate that these perturbations can be described extremely efficiently using a screened point charge model. We provide analytical expressions for the anisotropy energy that can be straightforwardly implemented in atomistic spin dynamics simulations, meaning that such simulations can be carried out for an arbitrary arrangement of point defects. The significant crystal field perturbations calculated here demonstrate that a sample that is single phase from a structural point of view can nonetheless have a dramatically varying anisotropy profile at the atomistic level if there is compositional disorder, which may influence localized magnetic objects like domain walls or skyrmions.

Exploring intermixed magnetic nanoparticles: insights from atomistic spin dynamics simulations.

Binary nanoparticles, composed of both rare-earth elements with substantial magnetic properties and transition metals known for their high magnetic ordering temperatures, hold great promise as innovative materials for novel magnetic applications. In this study, we employ an atomistic spin dynamics framework to investigate how the magnetic properties change at finite temperatures in mixed NiGd nanoparticles. We specifically examine parameters such as saturation magnetization and spin-reorientation in relation to the nanoparticle's size, which ranges from 4 nm to 16 nm, and composition. Our findings reveal that Ni75Gd25 nanoparticles demonstrate exceptional magnetic properties at finite temperatures, marked by significantly increased saturation magnetizations and magnetic ordering temperatures. In contrast, nanoparticles containing 50% and 75% Gd contents exhibit notably reduced saturation magnetizations and magnetic ordering temperatures. Theoretical findings of our study shed light on the pivotal role that the Gd content plays in determining the magnetic behaviour at finite temperatures.