Quasiuniform in-plane magnetization state of thin cylindrical dots in a square array and related anisotropy

The energy (magnetostatic, exchange, and Zeeman terms) of a square array of cylindrical submicron dots made of soft ferromagnetic material is calculated analytically and minimized, taking into account the quasiuniformity of dot magnetization. The dependence of the equilibrium energy of the array on the direction of the externally applied magnetic field in the array plane is recovered, exhibiting the fourfold anisotropy. The anisotropy constant is calculated. Its values for different array geometries are in excellent agreement with the recent independent experiments. A new eightfold anisotropy effect is predicted. The theory involves no adjustable parameters.