Micromagnetics of the single-domain state of square ferromagnetic nanostructures

Using numerical micromagnetics we have studied the potential energy surface in the vicinity of the two principal remanent near single-domain states of nanoscale square-planar magnetic elements (magnetic nanostructures). We find that there is no metastability and therefore at any finite temperature the nanostructure must adopt its ground state. We have derived an analytical solution to the micromagnetic equations describing the properties of the near single-domain states by treating them as a small perturbation from the uniformly magnetized case. The analytical solution shows that the energy surface between the states can be described by a fourfold symmetric configurational anisotropy field, which can be several hundred Oersteds in strength and which changes sign at a critical width to thickness aspect ratio. The analytical model gives good physical insight into the origin of the configurational anisotropy and predicts a discontinuous transition with diverging susceptibility to occur at the critical aspect ratio.