Electronic structure and exchange interactions of insulating double perovskite ${\mathrm{La}}_2{\mathrm{CuRuO}}_6$

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.

Figure 1

(a) Schematic crystal structure of the unit cell (side view) of ${\mathrm{La}}_2{\mathrm{CuRuO}}_6$. The main exchange paths in the $a\text{−}b$ plane are shown for (b) $z=0$ and (c) $z=\frac{1}{2}$. All the Cu, Ru, and O ions are marked to explain the detailed crystal geometry in the text.

Figure 2

Non-spin-polarized (a) band dispersion along various high symmetry directions and (b) partial density of states, computed within LDA.

Figure 3

Schematic diagram to show the crystal field splitting of Cu-$d$ and Ru-$d$ states, based on on-site energies, obtained from our NMTO calculations.

Figure 4

The effective (a) Cu $z^2$, (b) Ru $yz$, (c) Ru $xz$, and (d) Ru $x^2-y^2$ orbitals with lobes of opposite signs colored as red and blue. The orbitals are defined in the global frame as described in the text.

Figure 5

A schematic to show the superexchange processes due to the virtual hopping between half-filled Cu-$z^2$ and Ru orbitals when (a) an antiferromagnetic and (b) ferromagnetic order between Cu and Ru ions are assumed. The allowed hoppings are marked by red dotted arrows in both cases.