Dipolar magnetic anisotropy energy of laterally confined ultrathin ferromagnets: multiplicative separation of discrete and continuum contributions

Very recent exact summation has indicated that the lateral confinement of ultrathin ferromagnetic islands brings about significant deviations from the usually assumed laterally infinite sample so far as the dipolar magnetic anisotropy is concerned. Here, it is demonstrated that the phenomenological rescaling of the structural detail leads to a fundamental micromagnetic (continuum theory) quantity, namely, the demagnetizing energy for the assumed shape of the mesoscopic island. The derivation of a compact analytical formula for the demagnetization factor of any right circular cylinder has been instrumental for this insight. The effects of discrete geometry (lattice and substrate orientation), thickness, and overall shape of the ultrathin structure are thus distilled into a form which exhibits a great deal of universality.