Numerical integration methods for spin-lattice dynamics

SNIC 2018/7-7


SNAC Small

Principal Investigator:

Johan Hellsvik


Kungliga Tekniska högskolan

Start Date:


End Date:


Primary Classification:

10105: Computational Mathematics



The present application is done in connection to a master thesis project on the topic of numerical integration methods for spin-lattice dynamics Student: Kristoffer Aronsen, KTH. Supervisors: Johan Hellsvik, KTH, and Klas Modin, Chalmers. Examiner: Jack Lidmar, KTH. Computer simulations have emerged as a vital tool for investigations of magnetism in materials. A state-of-the-art approach for the modelling of magnetization dynamics is to combine density functional theory (DFT) calculations with numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equation that describes the dynamics of the system [1]. In order to obtain qualitatively correct dynamics, it is important to avoid un-physical features in the numerical discretization, for example numerical damping that can result in drift of the total energy and the total angular momentum. For dynamical systems originating from molecular dynamics it is well-known that one should use symplectic integrators. In spin dynamics, however, the phase space structure is more complicated than in molecular dynamics. For long symplectic integration was therefore out-of- reach, until very recently with the development of the spherical midpoint method - the first generic symplectic integrator for spin dynamics [2]. Recently the coupling of spin and lattice degrees of freedom has emerged as a central theme in experimental and theoretical condensed matter physics, relevant to phenomena such as the transfer of angular momentum on sub-picosecond time-scales, magnetocaloric refrigeration, and magnetoelectric materials. The project at hand aims at extending the spherical midpoint method to spin-lattice dynamics, and implement it in the software package UppASD for large-scale atomistic spin and spin-lattice dynamics simulations. The methods to be developed in the project are at the forefront of current research - the outcome of the project may result in new tools for the numerical integration of spin- lattice coupled systems, of high relevance for computational materials science. [1] O. Eriksson, A. Bergman, L. Bergqvist, and J. Hellsvik. Atomistic Spin Dynamics: Foundations and Applications. Oxford University Press (2017). [2] R. I. McLachlan, K. Modin, and O. Verdier. A minimal-variable symplectic integrator on spheres. Math. Comp. 86, 2325 (2017).