Determination of the Orbital Moment and Crystal-Field Splitting in ${\mathrm{L}\mathrm{a}\mathrm{T}\mathrm{i}\mathrm{O}}_3$

Utilizing a sum rule in a spin-resolved photoelectron spectroscopic experiment with circularly polarized light, we show that the orbital moment in ${\mathrm{L}\mathrm{a}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ is strongly reduced from its ionic value, both below and above the Néel temperature. Using Ti $L_{2,3}$ x-ray absorption spectroscopy as a local probe, we found that the crystal-field splitting in the $t_{2g}$ subshell is about 0.12–0.30 eV. This large splitting does not facilitate the formation of an orbital liquid.

Figure 1

Spin-resolved photoemission spectra of twinned ${\mathrm{L}\mathrm{a}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ single crystal taken with circularly polarized light.

Figure 2

$⟨\sum _i{\mathbf{l}}_i·{\mathbf{s}}_i⟩$ values extracted from the spin-resolved circularly polarized photoemission data, together with theoretical predictions for various crystal-field parameters.

Figure 3

Top panel: experimental Ti $L_{2,3}$ XAS spectra taken from a twinned ${\mathrm{L}\mathrm{a}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ single crystal at 20, 100, 150, and 200 K. Left panel: simulated isotropic spectra calculated for a ${\mathrm{T}\mathrm{i}\mathrm{O}}_6$ cluster at 20, 100, 150, and 200 K for several CF parameters. Right panel: corresponding energy level diagrams for the cluster in an exchange field of $H_{\mathrm{e}\mathrm{x}}=46.5\mathrm{m}\mathrm{e}\mathrm{V}$ (from Keimer et al. [7]) at $T=0\mathrm{K}$ and vanishing at $T_N=146\mathrm{K}$. Four scenarios are presented: (a) noncubic symmetry with ${\Delta }_{\mathrm{C}\mathrm{F}}=230\mathrm{m}\mathrm{e}\mathrm{V}$ from our LDA calculation [19] and with ${\Delta }_{\mathrm{C}\mathrm{F}}=120$ and 300 meV, (b) noncubic symmetry with ${\Delta }_{\mathrm{C}\mathrm{F}}=54\mathrm{m}\mathrm{e}\mathrm{V}$ from Solovyev [11], (c) $O_h^{\prime }$, and (d) $O_h$ symmetry. The spin-orbit constant $\zeta$ is 15.2 meV for (a), (b), and (c), and 0 for (d). Note the very different energy scales.

Figure 4

Experimental temperature dependent Co $L_2$ XAS spectra of polycrystalline CoO, together with the simulated isotropic spectra and corresponding energy level diagram.