Trigonal Magnetocrystalline Anisotropy in Hexagonal Oxides

Torque measurements of the magnetocrystalline anisotropy between 77°K and 300°K are reported for single crystals of two different ferrimagnetic oxides having structures related to that of the mineral magneto-plumbite. The compounds, with chemical compositions ${\mathrm{Co}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Fe}}_{12}$ ${\mathrm{O}}_{22}$ and ${\mathrm{Co}}_2$ ${\mathrm{Ba}}_3$ ${\mathrm{Fe}}_{24}$ ${\mathrm{O}}_{41}$, are known as ${\mathrm{Co}}_{2}Y$ and ${\mathrm{Co}}_{2}Z$, respectively. Both compounds, after suitable magnetic field cooling treatment, display trigonal anisotropy in the basal plane at 77°K. The field cooling is shown to have the effect of placing the magnetization into one of two energetically equivalent orientations, each of which leads to a trigonal term of different sign. Examination of the crystal structures shows that in the case of ${\mathrm{Co}}_{2}Y$ an additional term ${K_2}^{\prime }{sin}^3\theta \times cos\theta cos3\varphi$ (where $\theta$ and $\varphi$ are the polar coordinates of the magnetization) should be added to the generally accepted phenomenological hexagonal anisotropy expression. The anisotropy constant ${K_2}^{\prime }$ is evaluated as 6×${10}^5$ erg/${\mathrm{cm}}^3$ at 117°K. In the case of ${\mathrm{Co}}_{2}Z$ this trigonal anisotropy term is not consistent with the crystal symmetry, although it is appropriate for structural subgroups of the unit cell. Its trigonal anisotropy is explained in terms of a "puckered" magnetization pattern whereby the sign of the $c$-axis component of magnetization is different for adjacent subgroups. The existence of this puckered pattern implies that the exchange coupling across the boundaries between subgroups is relatively weak. A new rotational hysteresis effect in ${\mathrm{Co}}_{2}Y$ is described and explained phenomenologically. An atomic theory assigning the origin of the trigonal anisotropy of both compounds to the cobalt ions is presented.