Spin Dynamics Simulations Research Articles

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.

The impact of low-energy phonon lifetimes on the magnetic relaxation in a dysprosocenium single-molecule magnet.

Developing molecular spin technologies requires microscopic knowledge of their spin-dynamics. Calculation of phonon modes, phonon scattering and spin-phonon coupling for a dysprosocenium single-molecule magnet (SMM) give simulations of spin-dynamics that agree with experiment. They show that low-energy phonon scattering is a significant contribution to the high-performance of dysprosocenium SMMs.

Light-induced ultrafast spin transport in multilayer metallic films originates from sp - d spin exchange coupling

Ultrafast interaction between the femtosecond laser pulse and the magnetic metal provides an efficient way to manipulate the magnetic states of matter. Numerous experimental advancements have been made on multilayer metallic films in the last two decades. However, the underlying physics remains unclear. Here, relying on an efficient ab initio spin dynamics simulation algorithm, we revealed the physics that can unify the progress in different experiments. We found that light-induced ultrafast spin transport in multilayer metallic films originates from the sp - d spin-exchange interaction, which can induce an ultrafast, large, and pure spin current from ferromagnetic metal to nonmagnetic metal without charge carrier transport. The resulting trends of spin demagnetization and spin flow are consistent with most experiments. It can explain a variety of ultrafast light-spin manipulation experiments with different systems and different pump-probe technologies, covering a wide range of work in this field.

Discovery of ultrafast spontaneous spin switching in an antiferromagnet by femtosecond noise correlation spectroscopy

Owing to their high magnon frequencies, antiferromagnets are key materials for future high-speed spintronics. Picosecond switching of antiferromagnetic spin systems has been viewed a milestone for decades and pursued only by using ultrafast external perturbations. Here, we show that picosecond spin switching occurs spontaneously due to thermal fluctuations in the antiferromagnetic orthoferrite Sm0.7Er0.3FeO3. By analysing the correlation between the pulse-to-pulse polarisation fluctuations of two femtosecond optical probes, we extract the autocorrelation of incoherent magnon fluctuations. We observe a strong enhancement of the magnon fluctuation amplitude and the coherence time around the critical temperature of the spin reorientation transition. The spectrum shows two distinct features, one corresponding to the quasi-ferromagnetic mode and another one which has not been previously reported in pump-probe experiments. Comparison to a stochastic spin dynamics simulation reveals this new mode as smoking gun of ultrafast spontaneous spin switching within the double-well anisotropy potential.

Accelerating micromagnetic and atomistic simulations using multiple GPUs

It is shown that micromagnetic and atomistic spin dynamics simulations can use multiple graphical processing units (GPUs) not only to reduce computation time but also to allow for a larger simulation size than is possible on a single GPU. While interactions that depend on neighboring spins, such as exchange interactions, may be implemented efficiently by transferring data between GPUs using halo regions or direct memory accesses, implementing the long-range demagnetizing interaction is the main difficulty in achieving good performance scaling, where the data transfer rate between GPUs is a significant bottleneck. A multi-GPU convolution algorithm is developed here, which relies on single-GPU FFTs executed in parallel. It is shown that even for micromagnetic simulations where the demagnetizing interaction computation time dominates, good performance scaling may be achieved, with speedup factors up to 1.8, 2.5, and 3.1, for two, three, and four GPUs, respectively. The code developed here can be used for any number of GPUs in parallel, with performance scaling strongly dependent on the inter-GPU data transfer rate and connection topology. This is further improved in micromagnetic simulations, which include a spin transport solver, obtaining speedup factors up to 1.96, 2.8, and 3.7, for two, three, and four GPUs, respectively. The best case scenario is obtained for atomistic simulations, where the demagnetizing interaction is implemented with spin-averaged cells. Using a single workstation with four GPUs, it is shown that atomistic spin dynamics simulations with up to 1 × 109 spins and atomistic Monte Carlo simulations with up to 2 × 109 spins are possible, with near-ideal performance scaling.

Minimum separation between two pump pulses for ultrafast double magnetization switching in GdFeCo

Femtosecond laser ultrafast thermally induced magnetization switching (TIMS) has also attracted much attention due to its ability to trigger a single switching at the picosecond timescale. Current studies have shown that after a TIMS excited by a laser pulse, excitation of the switch again via TIMS does not require equilibrium between the subsystems. In this work, the main investigation is on the various possible cases of magnetization dynamics in GdFeCo under two short-delayed pulse excitations, as well as the factors limiting the minimum separation for double TIMS. These conditions are relevant for the potential application of TIMS to memory devices as it affects both the speed limit at which rewritten data is available and demonstrates the importance of spatial confinement of a laser pulse to bit size. The results show that low energy and short pulse duration lasers are prerequisites for double TIMS in GdFeCo based on simulations of atomic spin dynamics. By changing the damping constants of the alloy, we can shorten the minimum pulse separation between two pump pulses for double TIMS to 2 ps to approach terahertz frequency of write/erase cycles.

Equivariant neural networks for spin dynamics simulations of itinerant magnets

I present a novel equivariant neural network architecture for the large-scale spin dynamics simulation of the Kondo lattice model. This neural network mainly consists of tensor-product-based convolution layers and ensures two equivariances: translations of the lattice and rotations of the spins. I implement equivariant neural networks for two Kondo lattice models on two-dimensional square and triangular lattices, and perform training and validation. In the equivariant model for the square lattice, the validation error (based on root mean squared error) is reduced to less than one-third compared to a model using invariant descriptors as inputs. Furthermore, I demonstrate the ability to simulate phase transitions of skyrmion crystals in the triangular lattice, by performing dynamics simulations using the trained model.

Singlet-triplet dephasing in radical pairs in avian cryptochromes leads to time-dependent magnetic field effects.

Cryptochrome 4a (Cry4a) has been proposed as the sensor at the heart of the magnetic compass in migratory songbirds. Blue-light excitation of this protein produces magnetically sensitive flavin-tryptophan radical pairs whose properties suggest that Cry4a could indeed be suitable as a magnetoreceptor. Here, we use cavity ring-down spectroscopy to measure magnetic field effects on the kinetics of these radical pairs in modified Cry4a proteins from the migratory European robin and from nonmigratory pigeon and chicken. B1/2, a parameter that characterizes the magnetic field-dependence of the reactions, was found to be larger than expected on the basis of hyperfine interactions and to increase with the delay between pump and probe laser pulses. Semiclassical spin dynamics simulations show that this behavior is consistent with a singlet-triplet dephasing (STD) relaxation mechanism. Analysis of the experimental data gives dephasing rate constants, rSTD, in the range 3-6 × 107s-1. A simple "toy" model due to Maeda, Miura, and Arai [Mol. Phys. 104, 1779-1788 (2006)] is used to shed light on the origin of the time-dependence and the nature of the STD mechanism. Under the conditions of the experiments, STD results in an exponential approach to spin equilibrium at a rate considerably slower than rSTD. We attribute the loss of singlet-triplet coherence to electron hopping between the second and third tryptophans of the electron transfer chain and comment on whether this process could explain differences in the magnetic sensitivity of robin, chicken, and pigeon Cry4a's.

Temperature dependent magnetic properties of crystallographically amorphous TbCo: An atomistic simulation study

Due to interesting properties such as perpendicular magnetic anisotropy (PMA), ferrimagnetism, etc., rare earth-transition metal(RE-TM) alloys attract considerable attention in ultrafast and terahertz spintronics applications. The magnetic properties of RE-TM alloys strongly depend on their composition and vary with temperature. Here, we model crystallographically amorphous ferrimagnetic TbCo using atomistic spin dynamics(ASD) simulations to study their temperature dependence on magnetic properties by varying the compositions. In this study, we investigate the temperature dependence of magnetisation, uniaxial anisotropy, and coercivity values of amorphous TbxCo100−x for the composition range Tb18Co82 to Tb36Co64. The monte carlo method is used to calculate the temperature dependence of magnetisation and calculate the magnetisation compensation temperature(TM) and curie temperature(Tc) values for different compositions. The temperature dependence of uniaxial anisotropy is calculated from the angular dependence of free energy curves calculated at different temperatures using constrained monte carlo methods. Further, we evaluate the temperature dependence of coercivity values by calculating the magnetic hysteresis at different temperatures using the LLG Heun method. The results show the magnetic properties of amorphous TbCo can be easily tuned by varying their composition and have a strong temperature dependence. These highly tunable magnetic properties make them promising candidates for spintronics applications.

Determining perpendicular magnetic anisotropy in Fe/MgO/Fe magnetic tunnel junction: A DFT-based spin–orbit torque method

In our JunPy package, we have combined the first-principles calculated self-consistent Hamiltonian with divide-and-conquer technique to successfully determine the magnetic anisotropy (MA) in an Fe/MgO/Fe magnetic tunnel junction (MTJ). We propose a comprehensive analytical derivation to clarify the crucial roles of spin–orbit coupling that mediates the exchange and spin–orbit components of spin torque, and the kinetic and spin–orbit components of spin current accumulation. The angular dependence of cumulative spin–orbit torque (SOT) indicates a uniaxial MA corresponding to the out-of-plane rotations of magnetic moments of the free Fe layers. Different from the conventional MA energy calculation and the phenomenological theory for a whole MTJ, our results provide insight into the orbital-resolved SOT for atomistic spin dynamics simulation in emergency complex magnetic heterojunctions.

Spin-phonon decoherence in solid-state paramagnetic defects from first principles

Paramagnetic defects in diamond and hexagonal boron nitride possess a combination of spin and optical properties that make them prototypical solid-state qubits. Despite the coherence of these spin qubits being critically limited by spin-phonon relaxation, a full understanding of this process is not yet available. Here we apply ab initio spin dynamics simulations to this problem and quantitatively reproduce the experimental temperature dependence of spin relaxation time and spin coherence time. We demonstrate that low-frequency two-phonon modulations of the zero-field splitting are responsible for spin relaxation and decoherence, and point to the nature of vibrations in 2-dimensional materials as the culprit for their shorter coherence time. These results provide an interpretation to spin-phonon decoherence in solid-state paramagnetic defects, offer a strategy to correctly interpret experimental results, and pave the way for the accelerated design of spin qubits.

A high-performance implementation of atomistic spin dynamics simulations on x86 CPUs

Atomistic spin dynamics simulations provide valuable information about the energy spectrum of magnetic materials in different phases, allowing one to identify instabilities and the nature of their excitations. However, the time cost of evaluating the spin-spin correlation functions in real space increases quadratically as the number of spins N, leading to significant computational effort, making the simulation of large spin systems very challenging. In this work, we propose to use a highly optimized general matrix multiply (GEMM) subroutine to calculate the dynamical spin-spin correlation function that can achieve near-optimal hardware utilization. Furthermore, we fuse the element-wise operations in the calculation of S(q,t) into the in-house GEMM kernel, which results in further performance improvements of 44% - 71% on several relatively large lattice sizes when compared to the implementation that uses the GEMM subroutine in OpenBLAS, which is the state-of-the-art open source library for Basic Linear Algebra Subroutine (BLAS).

Light-Induced Metastable Hidden Skyrmion Phase in the Mott Insulator Cu2 OSeO3.

The discovery of a novel long-lived metastable skyrmion phase in the multiferroic insulator Cu2 OSeO3 visualized with Lorentz transmission electron microscopy for magnetic fields below the equilibrium skyrmion pocket is reported. This phase can be accessed by exciting the sample non-adiabatically with near-infrared femtosecond laser pulses and cannot be reached by any conventional field-cooling protocol, referred as a hidden phase. From the strong wavelength dependence of the photocreation process and via spin-dynamics simulations, the magnetoelastic effect is identified as the most likely photocreation mechanism. This effect results in a transient modification of the magnetic free energy landscape extending the equilibrium skyrmion pocket to lower magnetic fields. The evolution of the photoinduced phase is monitored for over 15 min and no decay is found. Because such a time is much longer than the duration of any transient effect induced by a laser pulse in a material, it is assumed that the newly discovered skyrmion state is stable for practical purposes, thus breaking ground for a novel approach to control magnetic state on demand at ultrafast timescales and drastically reducing heat dissipation relevant for next-generation spintronicdevices.

Pseudo-Goldstone Modes and Dynamical Gap Generation from Order by Thermal Disorder.

Accidental ground state degeneracies-those not a consequence of global symmetries of the Hamiltonian-are inevitably lifted by fluctuations, often leading to long-range order, a phenomenon known as "order-by-disorder" (ObD). The detection and characterization of ObD in real materials currently lacks clear, qualitative signatures that distinguish ObD from conventional energetic selection. We show that for order by thermal disorder (ObTD) such a signature exists: a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. We demonstrate this in a minimal two-dimensional model that exhibits ObTD, the ferromagnetic Heisenberg-compass model on a square lattice. Using spin-dynamics simulations and self-consistent mean-field calculations, we determine the pseudo-Goldstone gap, Δ, and show that at low temperatures it scales as the square root of temperature, sqrt[T]. We establish that a power-law temperature dependence of the gap is a general consequence of ObTD, showing that all key features of this physics can be captured in a simple model of a particle moving in an effective potential generated by the fluctuation-induced free energy.

High-fidelity direct contrast synthesis from magnetic resonance fingerprinting.

This work was aimed at proposing a supervised learning-based method that directly synthesizes contrast-weighted images from the Magnetic Resonance Fingerprinting (MRF) data without performing quantitative mapping and spin-dynamics simulations. To implement our direct contrast synthesis (DCS) method, we deploy a conditional generative adversarial network (GAN) framework with a multi-branch U-Net as the generator and a multilayer CNN (PatchGAN) as the discriminator. We refer to our proposed approach as N-DCSNet. The input MRF data are used to directly synthesize T1-weighted, T2-weighted, and fluid-attenuated inversion recovery (FLAIR) images through supervised training on paired MRF and target spin echo-based contrast-weighted scans. The performance of our proposed method is demonstrated on in vivo MRF scans from healthy volunteers. Quantitative metrics, including normalized root mean square error (nRMSE), peak signal-to-noise ratio (PSNR), structural similarity (SSIM), learned perceptual image patch similarity (LPIPS), and Fréchet inception distance (FID), were used to evaluate the performance of the proposed method and compare it with others. In-vivo experiments demonstrated excellent image quality with respect to that of simulation-based contrast synthesis and previous DCS methods, both visually and according to quantitative metrics. We also demonstrate cases in which our trained model is able to mitigate the in-flow and spiral off-resonance artifacts typically seen in MRF reconstructions, and thus more faithfully represent conventional spin echo-based contrast-weighted images. We present N-DCSNet to directly synthesize high-fidelity multicontrast MR images from a single MRF acquisition. This method can significantly decrease examination time. By directly training a network to generate contrast-weighted images, our method does not require any model-based simulation and therefore can avoid reconstruction errors due to dictionary matching and contrast simulation (code available at:https://github.com/mikgroup/DCSNet).

Magnetic properties of Nd6Fe13Cu single crystals

The understanding of a coercivity mechanism in high performance Nd–Fe–B permanent magnets relies on the analysis of magnetic properties of all phases present in magnets. By adding Cu in such compounds, a new Nd6Fe13Cu grain boundary phase is formed; however, the magnetic properties of this phase and its role in the magnetic decoupling of matrix Nd2Fe14B grains are still insufficiently studied. In this work, we have grown Nd6Fe13Cu single crystals by the reactive flux method and studied their magnetic properties in detail. It is observed that below the Néel temperature (TN = 410 K), Nd6Fe13Cu is antiferromagnetic in zero magnetic field; whereas when a magnetic field is applied along the a-axis, a spin-flop transition occurs at approximately 6 T, indicating a strong competition between antiferromagnetic and ferromagnetic interactions in two Nd layers below and above the Cu layers. Our atomistic spin dynamics simulation confirms that an increase in the temperature and/or magnetic field can significantly change the antiferromagnetic coupling between the two Nd layers below and above the Cu layers, which, in turn, is the reason for the observed spin-flop transition. These results suggest that the role of an antiferromagnetic Nd6Fe13Cu grain boundary phase in the coercivity enhancement of Nd–Fe–B–Cu magnets is more complex than previously thought, mainly due to the competition between its antiferro- and ferromagnetic exchange interactions.

Correlation of Interface Interdiffusion and Skyrmionic Phases.

Magnetic skyrmions are prime candidates for the next generation of spintronic devices. Skyrmions and other topological magnetic structures are known to be stabilized by the Dzyaloshinskii-Moriya interaction (DMI) that occurs when the inversion symmetry is broken in thin films. Here, we show by first-principles calculations and atomistic spin dynamics simulations that metastable skyrmionic states can also be found in nominally symmetric multilayered systems. We demonstrate that this is correlated with the large enhancement of the DMI strength due to the presence of local defects. In particular, we find that metastable skyrmions can occur in Pd/Co/Pd multilayers without external magnetic fields and can be stable even near room temperature conditions. Our theoretical findings corroborate with magnetic force microscopy images and X-ray magnetic circular dichroism measurements and highlight the possibility of tuning the intensity of DMI by using interdiffusion at thin film interfaces.

Quantized movement of magnetic skyrmions in moiré multiferroic heterostructures

Moir\'e superlattices made with van der Waals layers are an excellent platform for exploring a wide range of exotic and important physical phenomena. In this study, we used first-principles calculations and atomistic spin dynamics simulations to design a two-dimensional van der Waals $\mathrm{Mn}{\mathrm{S}}_{2}/\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ multiferroic moir\'e heterosuperlattice with tunable skyrmions through magnetoelectric coupling. The inherent lattice mismatch between the two monolayers of $\mathrm{Mn}{\mathrm{S}}_{2}$ and $\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ creates incommensurate moir\'e patterns, along with modulated magnetic anisotropy and emerging magnetic skyrmions in $\mathrm{Mn}{\mathrm{S}}_{2}$. The magnetic skyrmion in $\mathrm{Mn}{\mathrm{S}}_{2}$ is strongly influenced by magnetoelectric coupling and can be tuned by the ferroelectric polarization of $\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$. Furthermore, these magnetic skyrmions can be controlled by a pulsed current to move or freeze within the moir\'e period under different ferroelectric polarization states of the $\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ layer. Our work showcases a two-dimensional van der Waals moir\'e heterosuperlattice with magnetoelectrically tuned magnetic skyrmions, which establishes a foundation for designing future spintronic devices.

Magnetic properties of hematite revealed by an ab initio parameterized spin model

Hematite is a canted antiferromagnetic insulator, promising for applications in spintronics. Here we present ab initio calculations of the tensorial exchange interactions of hematite and use them to understand its magnetic properties by parametrizing a semiclassical Heisenberg spin model. Using atomistic spin dynamics simulations, we calculate the equilibrium properties and phase transitions of hematite, most notably the Morin transition. The computed isotropic and Dzyaloshinskii--Moriya interactions result in a N\'eel temperature and weak ferromagnetic canting angle that are in good agreement with experimental measurements. Our simulations show how dipole-dipole interactions act in a delicate balance with first and higher-order on-site anisotropies to determine the material's magnetic phase. Comparison with spin-Hall magnetoresistance measurements on a hematite single crystal reveals deviations of the critical behavior at low temperatures. Based on a mean-field model, we argue that these differences result from the quantum nature of the fluctuations that drive the phase transitions.

Heliknoton in a film of cubic chiral magnet

Cubic chiral magnets exhibit a remarkable diversity of two-dimensional topological magnetic textures, including skyrmions. However, the experimental confirmation of topological states localized in all three spatial dimensions remains challenging. In this paper, we investigate a three-dimensional topological state called a heliknoton, which is a hopfion embedded into a helix or conic background. We explore the range of parameters at which the heliknoton can be stabilized under realistic conditions using micromagnetic modeling, harmonic transition state theory, and stochastic spin dynamics simulations. We present theoretical Lorentz TEM images of the heliknoton, which can be used for experimental comparison. Additionally, we discuss the stability of the heliknoton at finite temperatures and the mechanism of its collapse. Our study offers a pathway for future experimental investigations of three-dimensional topological solitons in magnetic crystals.