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 10 9 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 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.

Thermal stability of magnetic states in submicron magnetic islands

“…Experimental estimates for islands falling within a more limited range in shape and size are in close agreement with the calculated values [16]. An HTST estimate for larger permalloy islands used in kagome spin ice systems [17] gave a smaller value, 9.9×10 8 sec −1 [18] while analysis of the experimental data had assumed a value of 10 12 sec −1 [17].…”

“…The approach presented here has already been shown to be accurate in calculations of the lifetime of single and double kagome rings [18].…”

“…The dimensionality of the energy surface used for those calculations ranged from several hundreds up to tens of thousands. Good agreement has been found between HTST calculations and experimental measurements of lifetimes of both single and double kagome rings when the parameters in the calculations were determined from basic properties of a single island and no adjustment made to fit the data [18].…”

Advances in artificial spin ice

“…This observation indicates that two vertices with opposite charge prefer to order simultaneously so that charge neutrality is maintained, thus creating restrictions on how the domains grow 87 . Another challenge associated with achieving the ground state through thermal relaxation in highly frustrated systems is that such systems are susceptible to residual magnetic fields, which can dramatically change the energy landscape 104 .…”

Calculations of switching field and energy barrier for magnetic islands with perpendicular anisotropy

“…This model was recently used to analyze remagnetization in elements of kagome spin ice [17]. In order to mimic the islands measured by de Vries et al, the easy axis is taken to be perpendicular to the surface plane, and the applied magnetic field is directed parallel to the easy axis and opposite to the initial direction of the magnetization.…”