Parallel implementation of spin and spin-lattice simulations in LAMMPS

Julien Tranchida, Aidan P. Thompson

Deriving from the DFT formalism, a semi-classical methodology referred to as spin dynamics (SD) can be used as a reliable tool for the simulation of the magnetization dynamics in systems containing a large number of interacting magnetic spins 1, like spin lattices 2, or spin liquids 3. More recently, it has also been shown possible to couple spin degrees of freedom to lattice vibrations by combining the formalism of molecular dynamics to spin dynamics 4, using empirical potentials 5. The goal of our project is to construct an efficient parallel implementation of SD in Sandia's widely-used LAMMPS molecular dynamics code 6. This will allow spin-lattice simulations to use parallel computers to access length and timescales much larger than currently possible. This work will leverage LAMMPS' sophisticated integration algorithms and the highly parallel structures.

Keywords: Magnetization dynamics, Spin-lattice simulations, Molecular dynamics

1 VP Antropov, MI Katsnelson, BN Harmon, M Van Schilfgaarde, and D Kusnezov. Spin dy- namics in magnets: Equation of motion and nite temperature effects. Physical Review B, 54(2):1019, 1996.

2 Olle Eriksson, Anders Bergman, Johan Hellsvik, and Lars Bergqvist. Atomistic spin dynamics: Foundations and applications. Oxford University Press, 2017.

3 IP Omelyan, IM Mryglod, and R Folk. Algorithm for molecular dynamics simulations of spin liquids. Physical Review Letters, 86(5):898, 2001.

4 Dilina Perera, Markus Eisenbach, Don M Nicholson, G Malcolm Stocks, and David P Lan- dau. Reinventing atomistic magnetic simulations with spin-orbit coupling. Physical Review B, 93(6):060402, 2016.

5 Marek Pajda, J Kudrnovsky, Ilja Turek, Vaclav Drchal, and Patrick Bruno. Ab initio calcula- tions of exchange interactions, spin-wave stiffness constants, and curie temperatures of fe, co, and ni. Physical Review B, 64(17):174402, 2001.

6 Steve Plimpton, Paul Crozier, and Aidan Thompson. Lammps-large-scale atomic/molecular massively parallel simulator. Sandia National Laboratories, 18, 2007.