The energetics of thin elongated ferromagnetic nano-islands is considered
for some different shapes, aspect ratios, and applied magnetic field directions.
These nano-island particles are important for artificial spin-ice materials. For low
temperature, the magnetic internal energy of an individual particle is evaluated
numerically as a function of the direction of a particle’s net magnetization. This
leads to estimations of effective anisotropy constants for (1) the easy axis along the
particle’s long direction, and (2) the hard axis along the particle’s thin direction. A
spin relaxation algorithm together with fast Fourier transform for the demagnetization
field is used to solve the micromagnetics problem for a thin system. The magnetic
hysteresis is also found. The results indicate some possibilities for controlling the equilibrium and dynamics in spin-ice materials by using different island geometries.