Measure of Self-Consistency in 180° Domain Wall Models

Abstract

Two expressions are given for the energy of an interdomain wall, and it is shown that these expressions are identical for wall configurations which represent an energy minimum. In any Ritz method calculation, in which the magnetization distribution inside the wall is approximated by a certain functional form with adjustable parameters, the ratio between these two energy expressions is defined as the self-consistency parameter S. This parameter should, thus, be close to one, if the assumed wall structure is close to some minimum-energy configuration. Although having S ≈ 1 is only necessary, and not sufficient, condition for the structure to be a good approximation to some physical situation, calculating this parameter can serve as a convenient method for eliminating inadequate theories. The self-consistency parameter S is calculated for the wall models of Middlehoek, Dietze. and Thomas, and Aharoni. It is found that for the Bloch wall, although these theories leave a lot to be desired, they at least yield an S which is of the order of one. Even this is not true for the Néel wall, where S is of the order of ten for Permalloy films, 100 to 200 Å thick.