Intersite Coulomb Repulsion Driven Quadrupole Instability and Magnetic Ordering in the Orbital Frustrated Ba₂MgReO₆

Abstract In order to calculate the multipoles in real materials with considerable intersite Coulomb interaction V, we develop a self-consistent program which starts from the first-principles calculations to solve the tight-binding Hamiltonian including onsite Coulomb repulsion U, V, and spin-orbital coupling λ. The program is applied to Ba₂MgReO₆ to figure out the mechanism of structural instability and magnetic ordering. A comprehensive quadrupole phase diagram versus U and V with λ = 0.28 eV is calculated. Our results demonstrate that the easy-plane anisotropy and the intersite Coulomb repulsion V must be considered to remove the orbital frustration. The increase of V to > 20 meV would arrange quadrupole Q_x²–y² antiparallelly, accompanied by small parallel Q_3z²–r², and stabilize Ba₂MgReO₆ into the body-centered tetragonal structure. Such antiparallel Q_x²–y² provides a new mechanism for the Dzyaloshinskii–Moriya interaction and gives rise to the canted antiferromagnetic (CAF) state along the 110 axis. Moreover, sizable octupoles such as $O_{21}^{31}$, $O_{21}^{33}$, $O_{21}^{34}$ and $O_{21}^{36}$ are discovered for the first time in the CAF state. Our study not only provides a comprehensive understanding of the experimental results in Ba₂MgReO₆, but also serves as a general and useful tool for the study of multipole physics in 5d compounds.