Analysis of switching in uniformly magnetized bodies

Abstract

Summary form only given. When defining standard problems for verifying micromagnetic calculations, one important limiting case is uniform magnetization. Exchange energy vanishes and the total energy can be simplified to the expression, E=(/spl mu//sub 0//2)M/sup T/DM-/spl mu//sub 0/H/sup T/M, where H=Hh is the applied field and by choice of coordinates the diagonal matrix D=diag(D/sub x/,D/sub y/,D/sub z/) accounts for self-magnetostatic and uniaxial anisotropy energy. This is the 3D analog to the familiar 2D Stoner-Wohlfarth model. Lagrange multiplier analysis defines M/sub /spl nu//= h/sub /spl nu///(D/sub /spl nu//-/spl lambda/) for /spl nu/= x, y, z and the constraint |M|= M/sub s/ leads to an equation to be solved for the n stationary points of total energy. Depending on the value of H, n may vary between 2 and 6. With the solutions /spl lambda//sub 1/ to /spl lambda//sub n/, in increasing order, our complete analysis shows that /spl lambda//sub 1/ corresponds to the global energy minimum and /spl lambda//sub n/ the global energy maximum. Examination of the solutions leads to an iterative calculation for the critical switching fields and a closed form calculation for the coercive field when it differs from the switching field.