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A study of the crystallographic structure and magnetic properties of the double perovskites Ba₂MnMoO₆ and Sr₂MnMoO₆ in polycrystalline form has been carried out by means of neutron powder diffraction (NPD) and magnetization measurements. The Rietveld analysis of room temperature data shows that the Mn²⁺ and Mo⁶⁺ ions are B-site ordered, i.e. the structure is a NaCl-type ordered double perovskite. Ba₂MnMoO₆ crystallizes in the cubic space group Fm 3 m (a=8.1680(1)) and Sr₂MnMoO₆ crystallizes in the space group P4₂/n (a=7.9575(5), c=7.9583(9)). Bond valence sum (BVS) calculation revealed that these compounds have the valency pair of {Mn²⁺(3d⁵;t³_2ge²_g), Mo⁶⁺(4d⁰)}. The magnetic measurements suggest that these compounds transform to an antiferromagnetic state below 10 K.