Magnetic domain wall dislocation analogy and intrinsic coercivity

Abstract

A close analogy is shown to exist between a discrete crystal model of a magnetic domain wall and the Frenkel-Kontorowa model for crystal dislocations. It is used here for a simple calculation of the intrinsic coercivity (that due solely to the discrete character of the crystal lattice) of a 180° wall in an otherwise perfect crystal. On a purely continuum level, the analogy between dislocations and domain walls as two types of mobile crystal defects has been stressed by Akulov [1]. As will be seen in the present paper, the analogy extends to the atomistic level and a simple discrete model of a domain wall leads to difference equations which are similar to those of the Frenkel-Kontorowa model [2] for a dislocation. Some of the analytical experience and physical insight gained in the treatment of the latter problem, therefore, can be transferred to the magnetic case. As an example we reexamine in the light of this analogy the concept recently introduced by van den Broek and Zijlstra [3] of intrinsic coercivity due to the discrete nature of the crystal lattice. To understand the nature of this concept consider the following idealized situation: an infinite crystal contains a single planar 180° magnetic domain wall and no other defects. From a continuum quasi-static viewpoint this wall would be perfectly mobile, moving freely (even in the absence of thermal or zero-point motion) under an arbitrarily small applied magnetic field. However, if one adopts a discrete, atomistic viewpoint, then two equivalent equilibrium domain wall configurations which differ only by the displacement through one lattice parameter will be separated by a small energy barrier and a nonzero applied magnetic field H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> will be required to move it. This situation is completely analogous in crystal dislocation theory to the concept of the Peierls stress, which is defined as the stress required to move a straight dislocation, quasi-statically, from one equilibrium position to an adjacent equilibrium position in the absence of other defects and without the aid of thermal or zero-point motion. Its calculation also requires a model which includes the discrete character of the crystal; a purely continuum calculation leads to a zero Peierls stress. In fact, because of the close analogy, it might be desirable to use the term Peierls field for the critical applied field strength H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> since this term so clearly conveys the concept, at least to those familiar with dislocation theory. The general nature of the model of a 180° domain wall is similar to that employed by van den Broek and Zijlstra [3].