Covalent states and spin-orbit coupling in electronic and magnetic properties of ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$

In $4d$ and $5d$ transition metal compounds, novel properties usually arise from the interplay of electron correlation and spin-orbit interaction based on isolated single-site physics. However, there are also a large number of compounds where the intersite effect plays an important role. Here, we report the electronic and magnetic properties of a hexagonal perovskite ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$, which is featured with widely spaced ${\mathrm{Rh}}_2{\mathrm{O}}_9$ spin dimers. Our calculations indicate that ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$ is a semiconductor with a small band gap of 0.2 eV, which is consistent with the experimental value of 0.16 eV. In particular, the band gap of ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$ is not due to the $J_{\mathrm{eff}}=1/2$ state from isolated single site but due to the joint effect of covalent states and spin-orbit coupling formed by Rh's $t_{2g}$ orbitals inside the ${\mathrm{Rh}}_2{\mathrm{O}}_9$ dimers. Furthermore, we find a giant magnetic anisotropy energy (MAE) of about 20 meV/Rh in ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$ with the easy axis being the $c$ axis. Model calculations show that the giant MAE is mainly due to first-order perturbation on the doubly degenerate antibonding states of $e_g^{\pi }$ orbitals. Our work not only reveals the interesting electronic and magnetic properties of ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$ but also could stimulate more studies on the materials with $4d$ and $5d$ spin dimers.

Figure 1

(a) Hexagonal crystal structure of ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$. The green, yellow, grey, blue, and red balls represent the Ba, Y, Rh, Ti, and O ions, respectively. Rh and Ti ions are at the center of ${\mathrm{RhO}}_6$ octahedron and ${\mathrm{TiO}}_4$ tetrahedron, respectively. (b) The optimized ${\mathrm{Rh}}_2{\mathrm{O}}_9$ dimer and its related structural parameters.

Figure 2

(a) Total and partial density of states. (b) Partial density of states of Rh projected in the octahedral local coordinate system of ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$ based on the nonmagnetic LDA calculation. The Fermi energy is set to zero.

Figure 3

The schematic picture of orbital occupation around Fermi level.

Figure 4

Band structures of ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$ from the (a) LDA, (b) $\text{LSDA}+U$ ($U=2$ eV), and (c) $\text{LSDA}+\text{SOC}+U$ ($U=2$ eV) calculations. The Fermi energy is set to zero. The black and red lines in panel (b) represent spin-up and spin-down bands, respectively.

Figure 5

Band structure of ${\mathrm{Ba}}_6{\mathrm{Y}}_2{\mathrm{Rh}}_2{\mathrm{Ti}}_2{\mathrm{O}}_{17}$ from $\text{LSDA}+\text{SOC}+U$ ($U=2$ eV) calculation. Spin orientations along the (a) (100) and (b) (001) direction, respectively. The Fermi energy is set to zero.