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 frst-principles calculations to solve the tight-bindi...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 frst-principles calculations to solve the tight-binding Hamiltonian including onsite Coulomb repulsion U,V,and spin-orbital couplingλ.The program is applied to Ba_(2)MgReO_(6)to fgure out the mechanism of structural instability and magnetic ordering.A comprehensive quadrupole phase diagram versus U and V withλ=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_(x^(2)-y^(2))antiparallelly,accompanied by small parallel Q_(3z)^(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 O_(21)^(31),O_(21)^(33),O_(21)^(34)and O_(21)^(36)are discovered for the frst 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.展开更多
基金was supported by the National Key Research and Development Program of China(Grant Nos.2024YFA1611200 and 2018YFA0307000)the National Natural Science Foundation of China(Grant Nos.12274154 and 12404182)。
文摘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 frst-principles calculations to solve the tight-binding Hamiltonian including onsite Coulomb repulsion U,V,and spin-orbital couplingλ.The program is applied to Ba_(2)MgReO_(6)to fgure out the mechanism of structural instability and magnetic ordering.A comprehensive quadrupole phase diagram versus U and V withλ=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_(x^(2)-y^(2))antiparallelly,accompanied by small parallel Q_(3z)^(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 O_(21)^(31),O_(21)^(33),O_(21)^(34)and O_(21)^(36)are discovered for the frst 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.
