Surface anisotropy effects in the spontaneous magnetization of a semi-infinite ferromagnet (abstract)

An early theory1 of the temperature and position dependence of the spontaneous magnetization near the surface of a semi-infinite ferromagnet is generalized by including the effects of surface anisotropy. Using the surface anisotropy constants Ks and Kss defined [G. T. Rado, Phys. Rev. B 26, 295 (1982)] for a {110} surface of a bcc crystal, we find that for Ks≠0, Kss≠0 the excitations at low temperatures are combined volume and surface spin waves and that at the ferromagnetic surface the deviation M0−MT of the spontaneous magnetization at temperature T from its value at 0 °K is proportional to T3/2. Such a T dependence was obtained previously1 for Ks=Kss =0 on the basis of the pure volume waves. Next we refine the conditions2 under which the entire early theory1 remains valid when Ks≠0 and Kss≠0. Finally, we consider the special case Ks =0, Kss>0 and predict that here volume and surface spin waves (both are thermally excited) can exist independently and that at the ferromagnetic surface the T dependence of M0−MT has a T3/2 component due to volume waves but a quasilinear component due to surface waves. No quasilinear component of the T dependence at the surface of a semi-infinite ferromagnet at low T has been predicted previously. Because of the lack of existing evidence for the (effective) surface anisotropy determining the type of T dependence of M0−MT at a ferromagnetic surface, the present theory may help explain why the experimentally observed3 T dependence at a {110} Fe surface is proportional T3/2 when the Fe is covered with Ag but quasilinear when it is covered with MnF2. A full account of this work will be published elsewhere.