Hexagonal ferrites: a unified model of the (TS) n T series in superspace

Abstract

Hexagonal ferrites represent an extensive family of mixed-layer magnetic materials with periods up to 1500 Å along the stacking direction, probably constituting the largest unit cells in the inorganic realm. The (TS) n T subfamily includes P\bar{3}m1 and R\bar{3}m structures that can be derived from Y ferrite Ba2 M 2Fe12O22 (M = Zn, Fe, Co, Mg, Mn) by introducing stacking faults. A unified (3 + 1)-dimensional superspace model is proposed for all members of the (TS) n T family. The model belongs to the superspace group X\bar{3}m1(00\gamma) with \textstyle X = \{\left({{1}\over{3}},{{2}\over{3}},0,{{1}\over{3}}\right), \textstyle\left({{2}\over{3}},{{1}\over{3}},0,{{2}\over{3}}\right)\}, has a unit cell of the basic structure with a = 5.88, c = 4.84 Å and modulation vector {\bf q} = {{4n+3}\over{9n+6}}{\bf c}^*, where n is rational for periodic structures and irrational for the aperiodic ones. The model was tested on calculated data of one of the principal members of the (TS) n T family, the Y ferrite (n = \infty). The fit obtained with the superspace model was excellent. The model allowed a reduction of refinable parameters by 19% with respect to the ordinary refinement without a significant increase of the refinement R values.