Spin-Orbit Coupling Controlled $J=3/2$ Electronic Ground State in $5d^3$ Oxides

Entanglement of spin and orbital degrees of freedom drives the formation of novel quantum and topological physical states. Here we report resonant inelastic x-ray scattering measurements of the transition metal oxides ${\mathrm{Ca}}_3{\mathrm{LiOsO}}_6$ and ${\mathrm{Ba}}_2{\mathrm{YOsO}}_6$, which reveals a dramatic spitting of the $t_{2g}$ manifold. We invoke an intermediate coupling approach that incorporates both spin-orbit coupling and electron-electron interactions on an even footing and reveal that the ground state of $5d^3$-based compounds, which has remained elusive in previously applied models, is a novel spin-orbit entangled $J=3/2$ electronic ground state. This work reveals the hidden diversity of spin-orbit controlled ground states in $5d$ systems and introduces a new arena in the search for spin-orbit controlled phases of matter.

Figure 1

Incident energy dependence of electronic excitations in ${\mathrm{Ca}}_3{\mathrm{LiOsO}}_6$. Measurements were performed at 300 K.

Figure 2

RIXS excitation spectra measured in ${\mathrm{Ca}}_3{\mathrm{LiOsO}}_6$ and ${\mathrm{Ba}}_2{\mathrm{YOsO}}_6$. Panels (a) and (b) show the data for ${\mathrm{Ca}}_3{\mathrm{LiOsO}}_6$ and ${\mathrm{Ba}}_2{\mathrm{YOsO}}_6$, respectively. Black lines indicate the FWHM of the elastic line. Panels (c) and (d) show the energy range 0.4–2 eV, i.e. the $t_{2g}$ manifold, with the results of Gaussian peak fitting to the data shown as solid lines.

Figure 3

Structure of $t_{2g}^3$ levels for ${\mathrm{Os}}^{5+}$ ions in octahedral environment with strong spin-orbit interaction. The irreducible representations for the states without SOC, i.e., ${\zeta }_{\mathrm{SO}}=0$, are labeled by the appropriate Mulliken symbols; full spatial forms are tabulated in many textbooks, e.g., Ref. [4]. Here, ${{}^{2}E}_g$ and ${{}^{2}T}_{1g}$ appear degenerate as we determine $B=0.00(4)\mathrm{eV}$ within resolution; see main text. The irreducible representations describing the SOC-induced states are fourfold degenerate, ${\mathrm{\Gamma }}_8$, and twofold degenerate, ${\mathrm{\Gamma }}_6$ and ${\mathrm{\Gamma }}_7$. Dashed lines link the final states with the ${\zeta }_{\mathrm{SO}}=0$ states that provide the greatest contribution to them; however, each final state is an intermixing of all ${\zeta }_{\mathrm{SO}}=0$ states, which allows SOC to enter the ground state ${\mathrm{\Gamma }}_8$. The labels a, b, c, and d indicate the excited-state energies that are observed in the RIXS spectra of ${\mathrm{Ba}}_2{\mathrm{YOsO}}_6$ and ${\mathrm{Ca}}_3{\mathrm{LiOsO}}_6$.