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 Co₂{Ba}₂Fe₁₂{O}₂₂$ and ${Co}₂Ba₃{Fe}₂₄O₄₁, are known as Co₂Y and Co₂Z, 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 Co₂Y an additional term K₂^'sin³θ×cosθcos3φ (where θ and φ are the polar coordinates of the magnetization) should be added to the generally accepted phenomenological hexagonal anisotropy expression. The anisotropy constant K₂^' is evaluated as 6×{}10⁵ erg/cm³ at 117^∘{}K. In the case of Co₂Z 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 Co₂Y is described and explained phenomenologically. An atomic theory assigning the origin of the trigonal anisotropy of both compounds to the cobalt ions is presented.