Minimum energy paths in spin chain systems

Minimum energy paths (MEPs) link two given stable magnetic configurations and reveal the energy barrier between states. Analysing reaction pathways is especially relevant in the context of magnetic recording where one is concerned with the thermal stability of written data. The storage industry is currently migrating to Heat Assisted Magnetic Recording enabling the writing process of highly coercive grains. However, thermal stability remains a problem, especially when the bit patterns are subjected to high temperatures during the writing or rewriting of neighbouring tracks. Concerning ourselves with the long-term and controlled stability of the recorded information, we developed an atomistic 1-dimensional model which allows us to analyse MEPs of reversal and extract the corresponding energy barriers. Our work is based on the Lagrange multiplier method of finding points of extremum for functions subject to equality constraints. Here, we integrate the Lagrange optimisation strategy in a direct minimisation tool based on the gradient descent algorithm. We first apply our model to a generic single-phase spin chain, demonstrating its ability to track energy surfaces for coherent or domain-wall based reversal. Energy barriers are investigated varying the height of the grain, achieving good agreement with the Stoner-Wohlfarth model or the 180◦ Bloch wall description. Additionally, our results are shown to overlap with the dynamic calculations obtained using the Landau-Lifshitz-Gilbert equation. An analysis of field-dependent MEPs, revealed identical coercivities irrespective of the grain height, in the case of an applied field parallel with respect to the easy-axis. Finally, we qualitatively describe MEPs of reversal in exchange coupled hard/soft systems emphasising the role of the interfacial exchange in lowering the switching field. Presently, the model can successfully be applied in monolayer structures; in bi-layer systems, the Lagrange multiplier method is limited due to the form of the constraint field acting upon the spin chain.