Power-law relaxation decay in two-dimensional arrays of magnetic dots interacting by long-range dipole-dipole interactions

Abstract

The magnetic relaxation of two-dimensional arrays of dipolar coupled magnetic dots has been measured and simulated. Arrays $(50\ifmmode\times\else\texttimes\fi{}50)$ with perpendicular magnetized Co dots $(2 \ensuremath{\mu}\mathrm{m}\ifmmode\times\else\texttimes\fi{}2 \ensuremath{\mu}\mathrm{m})$ were patterned using a high resolution ${\mathrm{Ga}}^{+}$ focused ion beam irradiation. Magnetic domain pattern and time relaxation of the dot arrays were investigated using Faraday magneto-optical microscopy. For arrays designed with high irradiation doses $(>~0.5 \mathrm{n}\mathrm{C}/\mathrm{c}\mathrm{m}),$ the magnetic relaxation of the array proceeds by the magnetization reversal of individual dots and follows a power-law time decay. The long-range character of the dipolar interaction is found to be responsible for magnetic relaxation with a power-law decay. Monte Carlo simulations, based on a modified Ising Hamiltonian, reproduce this time dependence, and show that the power law is not a consequence of either the finite size or the boundary of the arrays, and it is independent of the shape of dots as well.