SPILADY: A parallel CPU and GPU code for spin–lattice magnetic molecular dynamics simulations

Spin–lattice dynamics generalizes molecular dynamics to magnetic materials, where dynamic variables describing an evolving atomic system include not only coordinates and velocities of atoms but also directions and magnitudes of atomic magnetic moments (spins). Spin–lattice dynamics simulates the collective time evolution of spins and atoms, taking into account the effect of non-collinear magnetism on interatomic forces. Applications of the method include atomistic models for defects, dislocations and surfaces in magnetic materials, thermally activated diffusion of defects, magnetic phase transitions, and various magnetic and lattice relaxation phenomena. Spin–lattice dynamics retains all the capabilities of molecular dynamics, adding to them the treatment of non-collinear magnetic degrees of freedom. The spin–lattice dynamics time integration algorithm uses symplectic Suzuki–Trotter decomposition of atomic coordinate, velocity and spin evolution operators, and delivers highly accurate numerical solutions of dynamic evolution equations over extended intervals of time. The code is parallelized in coordinate and spin spaces, and is written in OpenMP C/C++ for CPU and in CUDA C/C++ for Nvidia GPU implementations. Temperatures of atoms and spins are controlled by Langevin thermostats. Conduction electrons are treated by coupling the discrete spin–lattice dynamics equations for atoms and spins to the heat transfer equation for the electrons. Worked examples include simulations of thermalization of ferromagnetic bcc iron, the dynamics of laser pulse demagnetization, and collision cascades. Program summary Program title: SPILADY, version 1.0 Catalogue identifier: AFAN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Apache License, Version 2.0 No. of lines in distributed program, including test data, etc.: 1611165 No. of bytes in distributed program, including test data, etc.: 367246683 Distribution format: tar.gz Programming language: OpenMP C/C++, CUDA C/C++. Computer: Any computer with an OpenMP capable C/C++ compiler or computer with CUDA capable GPU card and an nvcc compiler. Operating system: Linux, Unix, Windows. RAM: At least 500 MB, depending on the number of atoms or atomic spins, and on the simulation type. Classification: 7.7. Nature of problem: Excitation of magnetic degrees of freedom affects a broad range of properties of magnetic materials, including their equilibrium crystal structure and response to mechanical deformation. Existing atomistic simulation methods, for example molecular dynamics, do not treat magnetic degrees of freedom and do not describe the effect of magnetism on interatomic forces. This is addressed by the spin–lattice dynamics approach. The integration algorithm satisfies the requirement of phase volume conservation in the multi- dimensional space of atomic coordinates, velocities, and atomic spins, which is achieved through the application of the symplectic Suzuki–Trotter decomposition. Numerical solutions of spin–lattice dynamics equations retain high accuracy over extended intervals of time. Solution method: An atomic scale simulation technique for modelling the coupled dynamics of atomic coordinates and spins. The method generalizes molecular dynamics to the case of magnetic materials, and uses a parallel Suzuki–Trotter decomposition-based time integration algorithm. Restrictions: The current version assumes a single chemical element material composition. The spin Hamiltonian and equations of motion assume isotropic magnetic interactions. Evolution equations assume the validity of localized magnetic moment approximation. Unusual features: An open source spin–lattice dynamics code. The time integration algorithm uses the Suzuki–Trotter decomposition, which is a symplectic integration method retaining high accuracy over extended intervals of time. The code can be executed in parallel on multiple CPUs using OpenMP directives, or on an Nvidia GPU card. Additional comments: Further information available on website: http://spilady.ccfe.ac.uk Running time: Similar to molecular dynamics, from several minutes to several weeks or months, depending on the number of atoms or spins involved in a simulation, and on the type of the simulation.