Static magnetization direction under perpendicular surface anisotropy

The problem of depth dependence of the magnetization tilt angle {θ}(z) is solved analytically for an exchange-coupled ferromagnet with dipole energy, applied field, and surface anisotropy Kₛ. For Kₛ{≤}({π}M²A)1/2=Kc, the surface magnetization direction remains in the plane, θₛ={θ}(0)={π}/2. For Kₛ{≥}Kc, the magnetization vector moves out of the surface, initially with dθₛ/dKₛ=-{∞}, then slowly approaches θₛ=0 as Kₛ approaches infinity. For Fe, Kc is of order 4 erg/cm². The results indicate that a perpendicular component of magnetization at the surface relaxes to its bulk in-plane orientation over a distance that is generally much shorter than the bulk domain-wall width. The surface remanence and initial susceptibility of the surface magnetization for in-plane applied field are calculated and provide useful expressions for interpreting experimental results. The experimentally measured surface magnetization increases linearly with probe sensitivity depth.