Trigonal crystal field effect in spin-orbit Mott insulating Sr$_3$NiIrO$_6$

Sr$_3$NiIrO$_6$ is a member of $5d$ transition-metal Ir oxides with a long chain alternating Ni$^{2+}$ in trigonal prismatic coordination and Ir$^{4+}$ in octahedral coordination along $c$ axis. Sr$_3$NiIrO$_6$ is considered to be a spin-orbit Mott insulator like Sr$_2$IrO$_4$. Since the Ir $5d$ spin-orbit coupling (SOC) and crystal field (CF) effect in $t_{2g}$ orbitals from trigonal distortion are comparable, however, competition between the SOC and CF effect makes the Ir $5d$ electronic structures different from the so-called $j_{eff}$ = 1/2 ground state. The modified Ir $5d$ electronic structures under the trigonal crystal field effect are still unclear. We have studied the Ir $5d$ electronic structures of Sr$_3$NiIrO$_6$ by using Ir $L_3$-edge resonant inelastic x-ray scattering and O $K$-edge x-ray absorption spectroscopy measurements. Through the analyses of the low-energy $d$-$d$ excitations and the unoccupied Ir $5d$ states, we discuss the influence of the competition of SOC and CF effects on the Ir $5d$ electronic structures of Sr$_3$NiIrO$_6$.