Publications

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Magnetization of clusters is often simulated using atomistic spin dynamics for a fixed lattice. Coupled spin-lattice dynamics simulations of the magnetization of nanoparticles have, to date, neglected the change in the size of the atomic magnetic moments near surfaces. We show that the introduction of variable magnetic moments leads to a better description of experimental data for the magnetization of small Fe nanoparticles. To this end, we divide atoms into a surface-near shell and a core with bulk properties. It is demonstrated that both the magnitude of the shell magnetic moment and the exchange interactions need to be modified to obtain a fair representation of the experimental data. This allows for a reasonable description of the average magnetic moment vs cluster size, and also the cluster magnetization vs temperature.

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We present a methodology based on the Néel model to build a classical spin-lattice Hamiltonian for cubic crystals capable of describing magnetic properties induced by the spin-orbit coupling like magnetocrystalline anisotropy and anisotropic magnetostriction, as well as exchange magnetostriction. Taking advantage of the analytical solutions of the Néel model, we derive theoretical expressions for the parametrization of the exchange integrals and Néel dipole and quadrupole terms that link them to the magnetic properties of the material. This approach allows us to build accurate spin-lattice models with the desired magnetoelastic properties. We also explore a possible way to model the volume dependence of magnetic moment based on the Landau energy. This feature allows us to consider the effects of hydrostatic pressure on the saturation magnetization. We apply this method to develop a spin-lattice model for BCC Fe and FCC Ni, and we show that it accurately reproduces the experimental elastic tensor, magnetocrystalline anisotropy under pressure, anisotropic magnetostrictive coefficients, volume magnetostriction, and saturation magnetization under pressure at zero temperature. This work could constitute a step towards large-scale modeling of magnetoelastic phenomena.

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This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.

In this paper, the magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated by means of spin dynamics simulations coupled to molecular dynamics, using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, going beyond the cluster and bulk Curie temperatures. Comparison is made with experimental data and with theoretical models based on the mean-field Ising model adapted to small clusters, and taking into account the influence of low coordinated spins at free surfaces. Our results for the temperature dependence of the average magnetization per atom M (T), including the thermalization of the transnational lattice degrees of freedom, are in very good agreement with available experimental measurements on small Fe nanoclusters. In contrast, significant discrepancies with experiment are observed if the translational degrees of freedom are artificially frozen. The finite-size effects on M (T) are found to be particularly important near the cluster Curie temperature. Simulated magnetization above the Curie temperature scales with cluster size as predicted by models assuming short-range magnetic ordering. Analytical approximations to the magnetization as a function of temperature and size are proposed.

Not long ago, it was shown that a discrete time crystal can be realized if a quantum system is periodically driven to a non-equilibrium state. Proof-of-concept experiments are reported by two groups using trapped ions and nitrogen-vacancy centers in diamond, respectively. The concept of discrete time crystals vividly demonstrates that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium. In this project, we want to test this novel concept in another canonical quantum system, the quantum Hall system in a two-dimensional electron gas (2DEG). Compared to other systems, quantum Hall magnetism (QHM) in high quality, industry-compatible GaAs/AlGaAs heterostructures allows for detailed and quantitative studies in a particularly simple and clean environment. This detailed knowledge should help achieve longer coherence times in a driven QHM system. This report will detail the results from a recent study on the stability of the quantum Hall skyrmions (QHS) state at a Landau level filling close to ν = 1 by measuring its current-voltage (I-V) breakdown characteristics under radio-frequency (RF) radiations. We observe that the critical current increases visibly when the RF frequency is right at the Larmor frequency of 75As nuclei, where the hyperfine interaction between electron and nuclear spins perturbs the QHS state most significantly. We believe that this observation is consistent with the novel concept that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium.

We present a scale-bridging approach based on a multi-fidelity (MF) machine-learning (ML) framework leveraging Gaussian processes (GP) to fuse atomistic computational model predictions across multiple levels of fidelity. Through the posterior variance of the MFGP, our framework naturally enables uncertainty quantification, providing estimates of confidence in the predictions. We used density functional theory as high-fidelity prediction, while a ML interatomic potential is used as low-fidelity prediction. Practical materials' design efficiency is demonstrated by reproducing the ternary composition dependence of a quantity of interest (bulk modulus) across the full aluminum-niobium-titanium ternary random alloy composition space. The MFGP is then coupled to a Bayesian optimization procedure, and the computational efficiency of this approach is demonstrated by performing an on-the-fly search for the global optimum of bulk modulus in the ternary composition space. The framework presented in this manuscript is the first application of MFGP to atomistic materials simulations fusing predictions between density functional theory and classical interatomic potential calculations.

Efficient algorithms for the calculation of minimum energy paths of magnetic transitions are implemented within the geodesic nudged elastic band (GNEB) approach. While an objective function is not available for GNEB and a traditional line search can, therefore, not be performed, the use of limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) and conjugate gradient algorithms in conjunction with orthogonal spin optimization (OSO) approach is shown to greatly outperform the previously used velocity projection and dissipative Landau-Lifschitz dynamics optimization methods. The implementation makes use of energy weighted springs for the distribution of the discretization points along the path and this is found to improve performance significantly. The various methods are applied to several test problems using a Heisenberg-type Hamiltonian, extended in some cases to include Dzyaloshinskii-Moriya and exchange interactions beyond nearest neighbours. Minimum energy paths are found for magnetization reversals in a nano-island, collapse of skyrmions in two-dimensional layers and annihilation of a chiral bobber near the surface of a three-dimensional magnet. The LBFGS-OSO method is found to outperform the dynamics based approaches by up to a factor of 8 in some cases.

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We propose a functional integral framework for the derivation of hierarchies of Landau-Lifshitz-Bloch (LLB) equations that describe the flow toward equilibrium of the first and second moments of the magnetization. The short-scale description is defined by the stochastic Landau-Lifshitz-Gilbert equation, under both Markovian or non-Markovian noise, and takes into account interaction terms that are of practical relevance. Depending on the interactions, different hierarchies on the moments are obtained in the corresponding LLB equations. Two closure Ansätze are discussed and tested by numerical methods that are adapted to the symmetries of the problem. Our formalism provides a rigorous bridge between the atomistic spin dynamics simulations at short scales and micromagnetic descriptions at larger scales.

This report summarizes the result of the LDRD Exploratory Express project 211666-01, titled "Coupled Magnetic Spin Dynamics and Molecular Dynamics in a Massively Parallel Framework".

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