Spin-orbit driven magnetic insulating state with $J_{\mathrm{eff}}=\frac{1}{2}$ character in a $4d$ oxide

The unusual magnetic and electronic ground states of $5d$ iridates have been shown to be driven by intrinsically enhanced spin-orbit coupling (SOC). The influence of appreciable but reduced SOC in creating the manifested magnetic insulating states in $4d$ oxides is less clear, with one hurdle being the existence of such compounds. Here, we present experimental and theoretical results on ${\mathrm{Sr}}_4{\mathrm{RhO}}_6$ that reveal SOC dominated behavior. Neutron measurements show the octahedra are both spatially separated and locally ideal, making the electronic ground state susceptible to alterations by SOC. Magnetic ordering is observed with a similar structure to an analogous $J_{\mathrm{eff}}=\frac{1}{2}$ Mott iridate. We consider the underlying role of SOC in this rhodate with density functional theory and x-ray absorption spectroscopy, and find a magnetic insulating ground state with $J_{\mathrm{eff}}=\frac{1}{2}$ character.

Figure 1

Neutron powder diffraction measurements of the crystal structure of ${\mathrm{Sr}}_4{\mathrm{RhO}}_6$. The green tick marks correspond to ${\mathrm{Sr}}_4{\mathrm{RhO}}_6$, a small impurity phase of SrO, and the Al sample can from the top down, respectively. The bond angles and distances are shown between the O (red) and Rh (blue) ions in ${\mathrm{Sr}}_4{\mathrm{RhO}}_6$, revealing near ideal and isolated octahedra. The Sr ions are shown as gray spheres.

Figure 2

(a) Difference of 15 and 3 K neutron powder diffraction measurements. The fit is to the ${\mathrm{\Gamma }}_1$ IR magnetic model. (b) The intensity of a magnetic reflection reveals long range magnetic ordering at 7.4(5) K in ${\mathrm{Sr}}_4{\mathrm{RhO}}_6$; the fit is to a power law. (c) The lowest energy ${\mathrm{\Gamma }}_1$ magnetic ordering in ${\mathrm{Sr}}_4{\mathrm{RhO}}_6$.

Figure 3

Normalized and self-absorption corrected XANES fluorescence measurements through the $L_2$ and $L_3$ edges in ${\mathrm{Sr}}_4{\mathrm{RhO}}_6$. The peak in the white line occurs at $L_2=3149.0$ eV and $L_3=3007.12$ eV. Measurements were performed at room temperature.

Figure 4

(a) DFT calculations show the ${\mathrm{\Gamma }}_1$ magnetic ordering is the lowest energy and insulating in ${\mathrm{Sr}}_4{\mathrm{RhO}}_6$. The region around the Fermi energy is shown in the inset. (b) The insulating nature was experimentally probed with resistivity measurements. The resistance increased with decreasing temperature, becoming immeasurably high below 160 K.