Magnetization of two-dimensional square arrays of nanomagnets

The interplay between dipole-dipole interaction, magnetocrystalline anisotropy, and disorder on the magnetic hysteresis in two-dimensional square arrays of nanomagnets is studied by numerically solving the Landau-Lifshitz equation. The interaction-induced frustration gives rise to even-odd oscillations in the magnetic properties when the system size is varied. The oscillations persist to remarkably large arrays with fluctuating amplitudes, evidencing the significance of the boundary effects and the competition among a number of quasistable orders of the magnetic moments. The hysteresis is strongly affected by the magnetocrystalline anisotropy and disorder. While both of them broaden the hysteresis loop, the remanence in the disordered system bears a universal value: almost half of the saturation magnetization.