Noncollinear alignment of the surface and bulk magnetic moment in localized ferromagnets

A model for noncollinear alignment between the surface-atomic-layer magnetic moment and bulk magnetic moment is proposed. It takes place due to the competition between ferromagnetic and antiferromagnetic exchange interactions of atomic layer with the nearest atomic layer and next-nearest atomic layer in the surface region. The criterion of the stability of surface state with collinear surface to bulk alignment is derived. On the basis of this criterion the phase diagram of surface magnetic states corresponding to a range of surface to bulk alignments at zero temperature is presented. We show that within this model the noncollinear surface to bulk alignment leads to a spiral magnetic structure in the surface region of a bulk ferromagnet. In the framework of this model a temperature-induced surface spin-reorientation transition takes place due to the change in the balance between exchange energies in the surface region with temperature. A self-consistent solution of the magnetization profile determination problem for any number of subsurface layers considered to be perturbed by the surface is used. In contrast to previous theoretical results we show that the increase in effective magnetic moment of a surface with temperature observed in experiments with Gd(0001), Tb(0001), and FeN3 surfaces does not necessarily imply antiparallel alignment of surface and bulk magnetic moment at zero temperature. We demonstrate that this phenomenon is consistent with parallel surface to bulk alignment at low temperature as demonstrated in recent experiments on the Gd(0001) surface.