Magnetic surface anisotropy and ferromagnetic resonance in single-crystal GdAl2

Abstract

Ferromagnetic resonance in bulk single-crystal specimens of GdAl2 shows two overlapping absorption lines. The variation of this structure with the temperature of the specimen and the crystallographic orientation of the magnetisation M0 is described. The line with the lower resonance field is attributed to the normal bulk mode and that at higher field to a surface-induced mode. The latter is shifted to a higher field by magnetic surface anisotropy. At higher temperatures (T>80K) the bulk mode is more intense but as T is reduced the relative strength changes and below about 30K the surface-induced mode is entirely dominant. For specimens with (110) surfaces the mode separation is greatest when M0 is oriented between (111) and (111) directions and least when M0 is along (001) and (001). The model employed to interpret these phenomena is based upon a classical equation of motion for M0, Maxwell's equations and boundary conditions for the magnetisation at the sample surface which involve the magnetic surface anisotropy. By interpreting the separation of the resonance lines as a function of the orientation of M0 the expression for the magnetic surface anisotropy energy as a function of this orientation is deduced and values for the necessary three magnetic surface anisotropy constants are deduced as a function of temperature. The main surface anisotropy gives an easy direction of magnetisation perpendicular to the surface. The easiest directions within the surface are (001) and (001). Interpretation of the resonance linewidth and relative intensity of the two modes is not satisfactory. It is suggested that this is because the measured lines are influenced by inhomogeneous broadening which is absent from the theory.