Magnetization curling in a disk with a uniaxial anisotropy

Abstract

To investigate the behavior of the magnetization in a single-domain disk with a uniaxial magnetocrystalline anisotropy, the assumption is made that the magnetization changes its direction by the magnetization curling mode. In this mode, the deviation θ of the spin from the z axis at (r,φ,z) in the cylindrical coordinate is given by θ=a0+a1(r/R)+a2(r/R)2+a3(r/R)3, where R is the radius of the disk and a0–a3 are coefficients. An equilibrium spin configuration is obtained for a given applied field H by finding a set of values of a0–a3 that minimize the magnetic energy of the disk. Carrying out this procedure for various H, a hysteresis loop and the coercive force are obtained. It is found that the configuration in which the spins deviate from the z axis can be stable and, therefore, the hysteresis loop is not rectangular, even though an applied field is along the z axis. The deviation is larger for the spins near the lateral surface of the disk, and the spins near the center do not incline easily. Moreover, for a large magnetocrystalline anisotropy and a large diameter, the magnetization changes its direction upward and downward alternately with r. The nucleation field calculated with the present model agrees well with that of the curling mode in an oblate spheroid.