The effect of temperature and external field on transitions in elements of kagome spin ice

Abstract

Transitions between magnetic states of one and two ring kagome spin ice elements consisting of 6 and 11 prolate magnetic islands are calculated and the lifetime of the ground states evaluated using harmonic transition state theory and the stationary state approximation. The calculated values are in close agreement with experimental lifetime measurements made by Farhan and co-workers (Farhan et al 2013 Nat. Phys. 9 375) when values of the parameters in the Hamiltonian are chosen to be best estimates for a single island, obtained from measurements and micromagnetic modeling. The effective pre-exponential factor in the Arrhenius rate law for the elementary steps turns out to be quite small, on the order of 109 s−1, three orders of magnitude smaller than has been assumed in previous analysis of the experimental data, while the effective activation energy is correspondingly lower than the previous estimate. The application of an external magnetic field is found to strongly affect the energy landscape of the system. Even a field of $4\,{\rm{mT}}$ can eliminate states that correspond to ground states in the absence of a field. The theoretical approach presented here and the close agreement found with experimental data demonstrates that the properties of spin ice systems can be calculated using the tools of rate theory and a Hamiltonian parametrized only from the properties of a single island.