Thermal stability in exchange-spring chains of spins

Thermal stability and switching behaviour have been compared in pure-hard and soft–hard Heisenberg linear spin chains of the same total length and equal magnetic parameters (except for magnetic anisotropy) with the anisotropy axis and external magnetic field parallel to the chain direction. The zero-temperature energy barriers and finite-temperature transition rates between remanent equilibrium states have been calculated by utilizing the string method and the forward flux sampling (FFS) method, respectively. Depending on the assumed interfaces, the FFS method could in fact fail to correctly sample the characteristic transition paths at interfaces at which these paths have probabilities much lower than those associated with other non-characteristic transition paths. This can especially occur in the case of the asymmetric energy landscapes and multiple asymmetric minimum energy paths (MEPs) of soft–hard systems. Therefore, a proper interface definition is needed in order to deduce the correct transition rates. In particular, we show that the thermal switching of soft–hard chains starting in the soft or in the hard part turns out to occur with an equal rate provided that the interfaces of the FFS method are defined on the basis of the corresponding zero-temperature MEPs. The thermal stability of a soft–hard chain in the remanent equilibrium state could be to some extent lower with respect to that of a pure-hard chain, due to the shorter hard-part length crossed by the domain wall formed in the chain and also to the related slightly smaller energy barrier. However, its switching field at zero temperature is verified to be widely lower than that of the pure-hard chain. Analytical expressions of switching fields and energy barriers have been deduced in various cases.