Magnetic structure and origin of insulating behavior in the ba₂ cuoso₆ system, and the role of a-site ionic size in its bandgap opening: Density functional theory approaches

The magnetic structure and the origin of band gap opening for Ba₂ CuOsO₆ were investigated by exploring the spin exchange interactions and employing the spin–orbit coupling effect. It revealed that the double-perovskite Ba₂ CuOsO₆, composed of the 3d (Cu²⁺ ) and 5d (Os⁶⁺ ) transition metal magnetic ions is magnetic insulator. The magnetic susceptibilities of Ba₂ CuOsO₆ obey the Curie–Weiss law, with an estimated Weiss temperature of −13.3 K, indicating AFM ordering. From the density functional theory approach, it is demonstrated that the spin exchange interaction between Cu ions plays a major role in exhibiting an antiferromagnetic behavior in the Ba₂ CuOsO₆ system. An important factor to understand regarding the insulating behavior on Ba₂ CuOsO₆ is the structural distortion shape of OsO₆ octahedron, which should be closely connected with the ionic size of the A-site ion. Since the d-block of Os⁶⁺ (d² ) ions of Ba₂ CuOsO₆ is split into four states (xy < xz, yz < x² –y² < z² ), the crucial key is separation of doubly degenerated xz and yz levels to describe the magnetic insulating states of Ba₂ CuOsO₆. By orbital symmetry breaking, caused by the spin–orbit coupling, the t_2g level of Os⁶⁺ (d² ) ions is separated into three sublevels. Two electrons of Os⁶⁺ (d² ) ions occupy two levels of the three spin–orbit-coupled levels. Since Ba₂ CuOsO₆ is a strongly correlated system, and the Os atom belongs to the heavy element group, one speculates that it is necessary to take into account both electron correlation and the spin–orbit coupling effect in describing the magnetic insulating states of Ba₂ CuOsO₆.