Angular dependence of perpendicular magnetic surface anisotropy and the spin-reorientation transition

For a complete description of out-of-plane magnetic surface anisotropy and its angular dependence, higher-order terms are needed beyond the quadratic N\'eel-type approximation. The spin-reorientation transition between perpendicular and in-plane magnetization is influenced by these higher-order terms in an elementary manner. Second- and fourth-order terms of the magnetic surface anisotropy were determined by torsion-oscillation magnetometry for uncovered Fe(110) films prepared on Cr(110), and for Pd-covered Co films prepared on Pd(111). These samples show different types of the spin-reorientation transition.