Analytical micromagnetics of near single domain particles

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Abstract
A formalism based on the perturbation theory is described which allows for an analytical approximation to the solution of the micromagnetic equations. The approximation is valid in the limit of small deviations of the magnetization from the uniformly magnetized state. These small deviations can lead to large effective anisotropy fields in magnetic elements, which can be large enough to dominate the spin reversal behavior. We demonstrate the formalism by calculating the energy of the single domain state in nanometer scale square magnetic prisms. Good agreement is found with values calculated by conventional finite element numerical methods.