Covalent states and spin-orbit coupling in electronic and magnetic properties of Ba6Y2Rh2Ti2O17

Abstract

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 ${e}_{g}^{\ensuremath{\pi}}$ 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.