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

β-Fe2SeO, a cation-deficient antiperovskite, was found to exhibit two long-range ordered magnetic structures, one between TN1 = 104 K and TN2 = 78 K, and the other below TN2. 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 Fe2+ (d6, S = 2) ions of β-Fe2SeO were calculated to analyze its crystal structures from the viewpoint of these quantities. We prepared single-crystal Fe2SeO, 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 Fe2SeO. In β-Fe2SeO with 18 Fe2+ ions per unit cell, the Fe–O–Fe spin exchange paths form even-membered rings of Fe2+ ions, and these rings are fused together. The crystal structure of β-Fe2SeO consists of approximately flat layers made up of fused 4-, 6-, and 14-membered rings, with 12 Fe2+ ions per unit cell. These layers are canted away from the c-axis by ∼36° and are interconnected by the Fe2+ ions (6 per unit cell) present between such canted layers. We show that β-Fe2SeO has a ferrimagnetic structure of 10↑8↓ spin configuration per unit cell in the temperature region between TN1 and TN2, that the (0.5, 0.5, 0) superstructure of β-Fe2SeO occurs below TN2 because adjacent unit cells of the ferrimagnetic β-Fe2SeO undergo an antiferromagnetic coupling along the a- and b-directions, and that β-Fe2SeO has an easy-axis anisotropy largely due to an antiferromagnetic spin arrangement of the Fe2+ ions in each canted layer.