Electronic structure and exchange interactions of insulating double perovskiteLa2CuRuO6

We have performed first-principles calculations of the electronic and magnetic properties of insulating double perovskite compound ${\mathrm{La}}_{2}{\mathrm{CuRuO}}_{6}$ (LCRO) which has recently been reported to exhibit intriguing magnetic properties. We derived a tight-binding Hamiltonian for LCRO based on the $N\mathrm{th}$-order muffin-tin orbital (NMTO) downfolding technique. The computed on-site energies and hopping integrals are used to estimate the dominant exchange interactions employing an extended Kugel-Khomskii model. This way the dominant exchange paths were identified and a low-energy spin model was proposed. The Green function method based on the magnetic force theorem has also been used to extract the exchange interactions to provide a more accurate estimation and to justify the model calculations. Our results show that the nearest neighbor (NN) Cu-Ru magnetic interactions are very much direction dependent and a strong antiferromagnetic next nearest neighbor Ru-Ru interaction along the crystallographic $b$ axis is responsible for the magnetic frustration observed experimentally in this system. We argue that due to the broken symmetry, NN Cu-Ru interaction becomes stronger along one direction than the other, which essentially reduces the amount of frustration and helps the system to achieve an antiferromagnetic ground state at low temperature. A detailed microscopic explanation of the exchange mechanism is discussed. We also find that spin-orbit coupling effect is significant and causes a canting of the Ru spin with respect to the Cu moments.