Suppression of magnetism in ${\mathrm{Ba}}_5{\mathrm{AlIr}}_2{\mathrm{O}}_{11}$: Interplay of Hund's coupling, molecular orbitals, and spin-orbit interaction

The electronic and magnetic properties of ${\mathrm{Ba}}_5{\mathrm{AlIr}}_2{\mathrm{O}}_{11}$ containing Ir-Ir dimers are investigated using the generalized gradient approximation (GGA) and GGA + spin-orbit coupling (SOC) calculations. We found that the strong suppression of the magnetic moment in this compound recently found by Terzic et al. [Phys. Rev. B 91, 235147 (2015)] is not due to charge ordering but is related to the joint effect of the spin-orbit interaction and strong covalency, resulting in the formation of metal-metal bonds. They conspire and act against the intraatomic Hund's rule exchange interaction to reduce total magnetic moment of the dimer. We argue that the same mechanism could be relevant for other $4d$ and $5d$ dimerized transition metal compounds.

Figure 1

Crystal structure of ${\mathrm{Ba}}_5{\mathrm{AlIr}}_2{\mathrm{O}}_{11}$. Ir ions (violet balls) are in the oxygen (small blue balls) octahedra. Two nearest ${\mathrm{IrO}}_6$ octahedra form dimer, sharing their faces. Al (large blue balls) ions are in the oxygen tetrahedra and Ba (green balls) sits in the voids.

Figure 2

The sketch, which shows (a) the level splitting in the dimer constructed out of face-sharing octahedra: the largest bonding-antibonding splitting corresponds to $a_{1g}$ orbitals, directed to each other in this geometry. Panels (b) and (c) illustrates two possible states in such a system with different values of total spin.

Figure 3

Upper panel: total DOS in the nonmagnetic GGA and GGA + SOC calculations. Lower panel: partial DOS in the nonmagnetic GGA in the local coordinate system (LCS), when the $z$ axis looks along the vector connecting two Ir in the dimer. This choice of LCS is not ideal, since the symmetry is very low and octahedra are strongly distorted, but one may see that the rightmost peak mostly corresponds to the antibonding $a_{1g}$ orbital, while the one centered at $\approx -0.16$ eV corresponds to the antibonding $e_g^{\pi }$ states. Fermi energy is set to zero.

Figure 4

Results of the ferromagnetic GGA + SOC calculations. Positive (negative) values correspond to spin majority (minority). Fermi energy is set to zero.