Thermally Activated Transitions in Confined Terromagnets with Perpendicular Magnetic Anisotropy as Function of the Interfacial Dzialoshinskii-Moriya Interaction Strength.

Abstract

The topological number of micromagnetic textures (Q) is a useful quantity for information encoding and transport [1,2], and determines the dynamics of magnetic objects such as skyrmions, merons and domain walls. Recent developments allow us to tune the strength of the interfacial Dzyaloshinskii-Moriya interaction, thereby inducing the formation of different states and generating a rich energy landscape for a given physical device, leading to new and potentially useful applications [3].This energy landscape determines the thermal stability of a given state which is strongly dependent on the barrier that separates neighboring minima [4-6]. In this work we use the String Method for the Study of Rare Events to determine transition states and thermal barriers of a circular nanodisk at different magnitudes of the Dzialoshinskii-Moriya constant (D).Low values of D are associated with high energies of domain wall formation; in this regime mostly uniform magnetizations with isolated skyrmions correspond to the lowest energy states. The transition between these states occurs by the motion of entire skyrmions across the material's edge. At intermediate values of D, domain walls require less energy, skyrmions have large radii and leave the nanodisk via an intermediate minima in which a meron is expelled from the film (Figures 1 and 2). Very large D values cause complex textures to form but transtions are still mediated by meron motion across the device's edge.This work emphasizes the importance of considering meron-mediated-transitions to appropriately create the initial path used in methods that use chain-of-states to estimate transition barriers.  String Method results showing energy and skyrmion number along the transition path. The images above correspond to points indicated in the images. The disk diameter is 80nm and its thickness is 0.4nm.  Skyrmion Number vs Energy for the same transition path of Fig.1. The skyrmion numbers of energy minima differ by roughly 1/2, highlighting the importance of meron motion across the edges as a mechanism for switching between energy minima. The values are not half-integer due to magnetization tilting at the sample's edge.