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PDC Center for High Performance Computing

UppASD for Simulating Atomistic Spin Dynamics

The Uppsala Atomistic Spin Dynamics (UppASD) project is one of the ongoing code development projects being run by the Division of Materials Theory at Uppsala University and the Dept. of Applied Physics at the KTH Royal Institute of Technology. The researchers have developed a program, known as UppASD ( github.com/UppASD/UppASD ), for simulating atomistic spin dynamics at finite temperatures, which makes it possible to describe magnetization dynamics on an atomic level. For example, the cover image (by Anders Bergman from Uppsala University) shows the dynamics of interacting spins in a paramagnetic phase where the system is not long range ordered. 

Using UppASD for Simulations

Simulations with UppASD are often performed as part of multiscale modelling of magnetic materials. Modern implementations of first principles density functional theory (DFT) can be used to calculate ground state properties of a crystalline or nanoscale magnetic material, but do not by themselves give access to the dynamics of the spin polarization over extended time and length scales. Atomic magnetic moments can be defined for each lattice site as the integral of the magnetization density over atomic volumes, and thereby constitute a coarse grained representation of the magnetization. Over nanometer length scales, the interactions between magnetic moments are mainly of quantum mechanical origin. The strength of these interactions can be calculated from the DFT ground state solution of the material. The magnetic moments and their interactions are the required ingredients for constructing materials-specific effective magnetic Hamiltonians.

The magnetic phase diagram and thermodynamical properties of a magnetic Hamiltonian can be investigated with techniques for Monte Carlo simulations. Alternatively, the equations of motion of the Hamiltonian can be investigated. In the atomistic spin-dynamics method, the dynamics of the Hamiltonian are treated in the semiclassical limit. This enables simulations that readily can consist of hundreds of thousands of spins evolved over hundreds of picoseconds. An important capability of atomistic approaches is that short-ranged local interactions and correlations, and the spin texture over longer distances, can be studied simultaneously. This is of importance, for instance, in simulations of domain wall motions and for topological excitations [1].

In condensed matter physics, a key knob for tuning the properties of materials is to change their chemical composition. For magnetic materials, doping can be used to alter the interactions between magnetic moments, as well as the magnetocrystalline anisotropy. Modelling of chemically disordered materials is, in general, more demanding than modelling pristine material with perfect crystalline structure. The UppASD code supports the modelling of disordered material, as was done for instance in modelling of ultrafast magnetization dynamics in amorphous Gd-Fe alloys [2], and the multiferroic phase of the insulating magnet CuO [3]. When chemical disorder is treated on atomic length scales, the computational effort can drastically increase given that averaging needs to be done over simulations of different realizations of the disorder. In methods for simulating coupled spin-lattice dynamics the atomistic spin-dynamics method is augmented to include also the ionic motion degrees of freedom. Support for spin-lattice dynamics simulations has been implemented in UppASD, with modelling having been done for few body systems, as well as for ferromagnetic iron [4].

UppASD Autumn School 2022

A three-day course on modelling atomistic spin dynamics with UppASD was held at the KTH Royal Institute of Technology in Stockholm in October. The school included lectures on the background physics concepts relating to atomistic spin-dynamics, plus tutorials where attendees practised using the UppASD program with assistance from mentors. Amongst the thirty-eight participants at the school, there were early pioneers of the field of atomistic spin dynamics and the lead developers of UppASD, as well as new and more experienced users of the program. The hands-on exercises were run on the CPU partition of the new Dardel supercomputer system at PDC.

UppASD can be built and run on desktop and laptop computers, as well as on supercomputers. The dynamics and characteristics of toy models can sometimes be explored in short and small simulations on, for example, a laptop, whereas more careful investigations of more refined models require extensive computing resources. Consequently it was beneficial for the participants to gain practical experience running UppASD on Dardel during the school’s hands-on sessions.

The school was partially sponsored by the Swedish e-Science Research Centre (SeRC) and was organised by PDC (Johan Hellsvik) together with researchers from Uppsala University (Anders Bergman, Manuel Pereiro and Olle Eriksson), KTH (Banasree Sadhukhan, Zhiwei Lu and Anna Delin) and Örebro University (Danny Thonig). Some important parts of the preparations for the school included upstreaming recently developed functionality to the main branch of the UppASD code repository, revising the code documentation and example directories, and writing UppASD tutorial material ( uppasd.github.io/UppASD-tutorial ). This general overhaul of the program resulted in a new release of the code, incrementing the lead version number to six and constituting a good stepping stone for future work on porting selected kernels to GPUs.

References

  1. M. Pereiro, D. Yudin, J. Chico, C. Etz, O. Eriksson, and A. Bergman, “Topological excitations in a kagome magnet”, Nature Comm. 5, 4815 (2014). doi.org/10.1038/ncomms5815
  2. R. Chimata, L. Isaeva, K. Kádas, A. Bergman, B. Sanyal, J. H. Mentink, M. I. Katsnelson, Th. Rasing, A. Kirilyuk, A. Kimel, O. Eriksson, and M. Pereiro, “All-thermal switching of amorphous Gd-Fe alloys: Analysis of structural properties and magnetization dynamics”, Phys. Rev. B 92, 094411 (2015). doi.org/10.1103/PhysRevB.92.094411
  3. J. Hellsvik, M. Balestieri, T. Usui, A. Stroppa, A. Bergman, L. Bergqvist, D. Prabhakaran, O. Eriksson, S. Picozzi, T. Kimura, and J. Lorenzana, “Tuning order-by-disorder multiferroicity in CuO by doping”, Phys. Rev. B 90, 014437 (2014). doi.org/10.1103/PhysRevB.90.014437
  4. J. Hellsvik, D. Thonig, K. Modin, D. Iuşan, A. Bergman, O. Eriksson, L. Bergqvist, and A. Delin. “General method for atomistic spin-lattice dynamics with first-principles accuracy”, Phys. Rev. B 99, 104302 (2019). doi.org/10.1103/PhysRevB.99.104302