Intersite Coulomb repulsion driven quadrupole instability and magnetic ordering in the orbital frustrated Ba₂MgReO₆

In order to calculate the multipoles in real materials with considerable intersite Coulomb interaction V, we develop a self-consistent program which start from the first-principles calculations to solve the tight-binding Hamiltonian including 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=0.28eV 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 increasing of V to >20meV would arrange quadrupole Q_x²-y² antiparallelly, accompanied with small parallel Q_3z²-r², and stabilize Ba₂MgReO₆ into the body-centered tetragonal structure. Such antiparallel Q_x²-y² provides a new mechanism of the Dzyaloshinskii-Moriya interaction, and gives rise to the canted antiferromagnetic (CAF) state along the 110 axis. Moreover, sizable octupoles such as O₂₁³¹, O₂₁³³, O₂₁³⁴ and O₂₁³⁶ are discovered for the first time in CAF state. Our study not only provides a comprehensive understanding of the experiment results in Ba₂MgReO₆, but also serves as a general and useful tool for the study of the multipole physics in 5d compounds.