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 Ba 2 MgReO 6 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 &gt; 20 meV would arrange quadrupole Q x 2 – y 2 antiparallelly, accompanied by small parallel Q 3 z 2 – r 2 , and stabilize Ba 2 MgReO 6 into the body-centered tetragonal structure. Such antiparallel Q x 2 – y 2 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mrow> <mml:mn>21</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>31</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mrow> <mml:mn>21</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>33</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mrow> <mml:mn>21</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>34</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mrow> <mml:mn>21</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>36</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> are discovered for the first time in the CAF state. Our study not only provides a comprehensive understanding of the experimental results in Ba 2 MgReO 6 , but also serves as a general and useful tool for the study of multipole physics in 5d compounds.