Clarification of the different roles of surface anisotropy for thermal spin waves and FMR modes

Abstract

Measurements by Mössbauer spectroscopy of the position dependence of the hyperfine field in monocrystalline iron films show that the fractional deviation of the spontaneous magnetization at temperature T from its value at T=0 K is larger by a factor of about two at a film surface than in the film’s interior. This result agrees with an early theoretical prediction of a factor of exactly two which is based on the assumption that the surface anisotropy is zero. In contrast, the results of recent ferromagnetic resonance experiments on ultra-thin films of monocrystalline iron were shown to be dominated by a surface anistropy which is nonzero. This discrepancy is reconciled for measurements at T=300 K by making use of the general boundary condition which contains the exchange stiffness A and some component(s) of the surface anisotropy Ksurf. The crucial argument is that at 300 K the thermally excited spin wavelengths are so short that at the film surfaces the normal derivative 2A∂m↘/∂n of the oscillating magnetization m↘ is very much larger than Ksurfm↘. Thus Ksurfm↘ is neglible for thermal spin waves even though it is comparable to 2A∂m↘/∂n for the long decay distances (or wavelengths) occurring in ferromagnetic resonance.