Two Ordered Magnetic States of β-Fe ₂ SeO Characterized by Spin Exchange Analysis and by X-ray Diffraction, Torque and Magnetization Measurements

β-Fe 2 SeO, a cation-deficient antiperovskite, was found to exhibit two long-range ordered magnetic structures, one between T N1 = 104 K and T N2 = 78 K, and the other below T N2 . We explored the nature of these two ordered magnetic structures by carrying out both theoretical and experimental studies. The Fe–O–Fe spin exchanges and the magnetic anisotropies of the Fe 2+ (d 6, S = 2) ions of β-Fe 2 SeO were calculated to analyze its crystal structures from the viewpoint of these quantities. We prepared single-crystal Fe 2 SeO, determined its temperature-dependent structural parameters, and carried out its magnetic susceptibility, magnetization, and torque measurements. Specific heat measurements were also taken for crystals of Fe 2 SeO. In β-Fe 2 SeO with 18 Fe 2+ ions per unit cell, the Fe–O–Fe spin exchange paths form even-membered rings of Fe 2+ ions, and these rings are fused together. The crystal structure of β-Fe 2 SeO consists of approximately flat layers made up of fused 4-, 6-, and 14-membered rings, with 12 Fe 2+ ions per unit cell. These layers are canted away from the c -axis by ∼36° and are interconnected by the Fe 2+ ions (6 per unit cell) present between such canted layers. We show that β-Fe 2 SeO has a ferrimagnetic structure of 10↑8↓ spin configuration per unit cell in the temperature region between T N1 and T N2, that the (0.5, 0.5, 0) superstructure of β-Fe 2 SeO occurs below T N2 because adjacent unit cells of the ferrimagnetic β-Fe 2 SeO undergo an antiferromagnetic coupling along the a - and b -directions, and that β-Fe 2 SeO has an easy-axis anisotropy largely due to an antiferromagnetic spin arrangement of the Fe 2+ ions in each canted layer.