Magnetic behavior of partially filled finite Ising surfaces

Abstract

We study the onset of spontaneous magnetization and the hysteresis properties of finite size two-dimensional Ising spin configurations which are assumed to lie on a smooth nonmagnetic surface. We model the dynamics of the spin system with and without a time-periodic magnetic field using a Monte Carlo simulation. For dilute spin lattices, we find that spontaneous magnetization occurs for spin densities well below thermodynamic predictions; this regime is identified as superparamagnetism. Based on numerical evidence and theoretical arguments we find that for a range of lattice sizes the density is proportional to $\sqrt{T}$ along the line between the paramagnetic regime and the regime in which spontaneous magnetization can occur. We also study hysteresis on four different spin structures for a piece-wise-linear magnetic driving field. We find that the hysteresis loop area depends on the effective exchange coupling as well as the detailed structure of the surface. We define a nearest-neighbor structure constant and study the dependence of the hysteresis loop area on the effective exchange coupling for each of the four different spin structures.