Theoretical prediction of a surface-induced spin-reorientation phase transition in BaFe12O19 nanocrystals

The equation of the magnetization of a hexagonal crystal is derived for the first time for an arbitrary orientation of the external magnetic field relative to the crystallographic c axis. In order to clarify the magnetization mechanism for a real ensemble of small particles in the framework of the given problem, surface anisotropy (which is significant for nanosize objects) was taken into account along with crystalline magnetic anisotropy and anisotropy in the particle shape. Model computer experiments prove that the magnetization curves for nanocrystals oriented in a polar angle range of 65–90° exhibit an anomaly in the form of a jump, indicating a first-order spin-reorientation phase transition. This explains a larger steepness of the experimental curve reconstructed taking into account the interaction between particles as compared to the theoretical dependence obtained by Stoner and Wohlfarth [IEEE Trans. Magn. MAG 27 (4), 3469 (1991)]. An analysis of variation of the characteristic anisotropy surface and its cross section with increasing ratio |K₂|/K₁ of the crystalline magnetic anisotropy constants upon a transition from a macroscopic to a nanoscopic crystal shows that surface anisotropy leads to a change in the magnetic structure. As a result, an additional easy magnetization direction emerges in the basal plane apart from the easiest magnetization direction (along the c axis). The direction of hard magnetization emerges from the basal plane, the angle of its orientation relative to the c axis being a function of the ratio | K₂|/K₁.