Theory of ferromagnetic resonance and static magnetization in ultrathin crystals

Abstract

A theory of the static magnetization orientations ${\ensuremath{\theta}}_{0}$ and of the ferromagnetic resonance fields ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{\mathrm{res}}$ in ultrathin (\ensuremath{\lesssim}50 \AA{}) monocrystalline films is presented. Both ${\ensuremath{\theta}}_{0}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{\mathrm{res}}$ are shown to depend crucially on the magnetocrystalline surface anisotropy, and a generalization of this anisotropy is proposed. The equation of motion of the magnetization is combined with the general exchange boundary condition, and realistic approximations are introduced in order to obtain closed algebraic expressions for ${\ensuremath{\theta}}_{0}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{\mathrm{res}}$. The spatial dependence of the oscillations in the presently calculated resonance modes do not represent spin waves but nondissipative exponential decays perpendicular to the film surfaces. The film thicknesses $2L$ are so small that the films are "beyond spin-wave cutoff." It is shown that the angular dependence of ${H}_{\mathrm{res}}$ differs strongly from that predicted by the uniform mode theory and that ${H}_{\mathrm{res}}$ is a linear function of $\frac{1}{L}$ rather than independent of $L$. An extension of the theory to somewhat thicker films is also presented.