Computational Modeling of the Phase Diagram of Magnetic Skyrmions

Magnetic skyrmions are vortex-like spin structures that appear in magnetic materials with Dzyaloshinskii-Moriya(DM) interactions and exchange interactions. Their small size and inherent stability suggest the potential application in magnetic memory systems. A well-defined phase diagram of skyrmions is important for investigating their stability. This is a complicated task due to the topological nature of magnetic skyrmions, whose phase transitions are not obviously illustrated by general parameters such as total energy and magnetization. In this thesis, we have developed a methodology in determining the phase diagram of the skyrmion lattice model by performing the atomistic spin simulation. We investigate the spin states of the lattice in the magnetic fields at zero temperature first, then apply finite temperatures in studying the phase transition between the skyrmion state and other states. At 0 K we find five spin states in varying magnetic fields. In the skyrmion state, the ratio between DM interaction and exchange interaction, together with the magnetic anisotropy affect the size and shape of skyrmions. At finite temperatures, the thermal stability of the skyrmion lattice is shown by a contour plot of the skyrmion number as a function of external field and temperature. The loss of lattice symmetry with a growing temperature is demonstrated by the spin configurations of the lattice in the real and reciprocal space. We then characterize the phase transition of the skyrmion state by several specific parameters, such as the specific heat capacity, the static magnetic susceptibility and the skyrmion life time. The parameters show similar critical temperature of the skyrmion state. Specifically, the skyrmion life time of the applied model follows the Arrhenius law as a function of temperature. We also discuss the effect of the femtosecond heat and magnetic pulse on the nucleation of the skyrmion state