Possibility of ferro-octupolar order in Ba$_2$CaOsO$_6$ assessed by X-ray magnetic dichroism measurements

TL;DR

This work probes the hidden order in Ba$_2$CaOsO$_6$, a cubic double perovskite with Os$^{6+}$ ($5d^2$), to test the ferro-octupolar order hypothesis. By combining X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) at the Os $L_{2,3}$ edges with ligand-field multiplet calculations, the authors identify a ligand-field split of $Δ_{ m LF} \sim 4$ eV and a residual cubic splitting $Δ_{ m c} \approx 18$ meV that yields a non-Kramers $E_g$ ground state and a $T_{2g}$ triplet excited state. The LF multiplet analysis, including an effective molecular field of $B \approx 12$ T, reproduces the XMCD spectra and implies an exchange energy scale $J \sim 1.5$ meV necessary for ferro-octupolar order, consistent with theoretical predictions. Overall, the results support an octupolar-ground-state scenario in Ba$_2$CaOsO$_6$ and connect the hidden-order transition to octupolar exchange, while underscoring the need for single-crystal or impurity-based studies for direct confirmation.

Abstract

Localized $5d^2$ electrons in a cubic crystal field possess multipoles such as electric quadrupoles and magnetic octupoles. We studied the cubic double perovskite Ba$_2$CaOsO$_6$ containing the Os$^{6+}$ ($5d^2$) ions, which exhibits a phase transition to a `hidden order' below $T^* \sim$ 50 K, by X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) at the Os $L_{2,3}$ edge. The cubic ligand-field splitting between the $t_{2g}$ and $e_g$ levels of Os $5d$ was deduced by XAS to be $\sim$4 eV. The temperature dependence of the XMCD spectra was consistent with a $\sim$18 meV residual cubic splitting of the lowest $J_{\rm eff} =$ 2 multiplet state into the non-Kramers $E_g$ doublet ground state and the $T_{2g}$ triplet excited state. Ligand-field (LF) multiplet calculation under fictitious strong magnetic fields indicated that the exchange interaction between nearest-neighbor octupoles should be as strong as $\sim$1.5 meV if a ferro-octupole order is stabilized in the `hidden-ordered' state, consistent with the exchange interaction of $\sim$1 meV previously predicted theoretically using model and density functional theory calculations.

Figures (4)

• Figure 1: Energy levels of the Os$^{6+}$ ($5d^2$) ion in the cubic ($O_h$) crystal field. (a) The $t_{2g}^2$ part of the $5d^2$ multiplet levels. The $t_{2g}e_g$ part is located at higher energies separated by the $t_{2g}$-$e_g$ splitting of $\Delta_{\rm LF}\sim 4$ eV, see panel (b). The lowest multiplet state $J_{\rm eff}= 2$ is split by a residual cubic splitting, $\Delta_{\rm c}$, into the non-Kramers $E_g$ doublet ground state and the $T_{2g}$ triplet excited states. Under a finite magnetic field $B\parallel \langle 111\rangle$, the non-Kramers doublet is split into the two magnetic octupolar eigenstates $|\psi_{g,\pm}\rangle$ (defined in the text) separated by $\Delta E_g$ ($\propto B^3$) and the triplet is split by the Zeeman energy $\Delta E_{T_{2g}}$ ($\propto B$). (b) One-electron energy levels of the Os $5d$ orbitals. $\Delta_{\rm LF}$ is the $t_{2g}$-$e_g$ ligand-field splitting. Spin-orbit coupling (SOC) splits the $t_{2g}$ level further into the $j_{\rm eff} = \frac{1}{2}$ and $j_{\rm eff} = \frac{3}{2}$ levels separated by $\frac{3}{2}\zeta'$, and the $j_{\rm eff} = \frac{3}{2}$ level is occupied by two electrons.
• Figure 2: X-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of Ba$_2$CaOsO$_6$ at the Os $L_{2,3}$ edges measured at $T=10\ \text{K}$ and $60\ \text{K}$ under the magnetic fields of $\pm$7 T before background subtraction. (a), (b) XAS spectra at the Os $L_3$ and $L_2$ edges, respectively. (c), (d) XMCD spectra at the Os $L_3$ and $L_2$ edges, respectively.
• Figure 3: XAS and XMCD spectra of Ba$_2$CaOsO$_6$ at the Os $L_{2,3}$ edges after background subtraction compared with with ligand-field (LF) multiplet calculation. (a), (b) Experimental (blue curves with dots) and calculated (green curves) XAS spectra. The white-line background and the extended X-ray absorption fine structure (EXAFS) oscillations have been subtracted (see Appendix \ref{['xmcd']}). (c), (d) Experimental (purple and red curves with dots) and calculated (green and lilac curves) XMCD spectra. The structures around the energies of 12.40 and 12.41 keV in the experimental XMCD spectra are magnetic EXAFS oscillations. The molecular field in the multiplet calculation was adjusted to $B =$ 12 $\pm 2\ \text{T}$ so that the measured XMCD intensity at the $L_2$ edge was reproduced.
• Figure 4: Schematic drawing of the ferro-octupolar order of the Os$^{6+}$ ions in Ba$_2$CaOsO$_6$. Red and blue colors indicate the distribution of spin-up and spin-down electrons, respectively. Nearest-neighbor Os atoms are connected by blue lines.