Curvature of domain walls

Abstract

An experiment was performed whereby domain walls were forced to bulge under the influence of an applied easy-axis field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> . The region where the domain wall is bent appears to be approximately circular. To relate the radius of such a curved domain wall to theory, a model was chosen that takes into account magnetostatic, anisotropy, and exchange energy. The assumption was made that anisotropy and exchange energy, as well as the magnetostatic contribution due to the local magnetization distribution of a domain wall, may be summarized in a wall energy term. The energy of the entire system has been calculated under the constraint that the domain wall should be circular and that it is inscribed tangentially into a triangle. Minimizing the total energy with respect to the radius of curvature <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</tex> , the result can be expressed approximately by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A \propto (H - H_{c})^{-1}</tex> where H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> is the coercive force. This result fits the model of a membrane under pressure.