Octupolar versus Néel Order in Cubic $5d^2$ Double Perovskites

We report time-of-flight neutron spectroscopy and neutron and x-ray diffraction studies of the $5d^2$ double perovskite magnets, ${\mathrm{Ba}}_{2}M{\mathrm{OsO}}_6$ ($M=\text{Zn},\text{Mg},\text{Ca}$). These materials host antiferromagnetically coupled $5d^2$ ${\mathrm{Os}}^{6+}$ ions decorating a face-centered cubic (fcc) lattice and are found to remain cubic down to the lowest temperatures. They all exhibit thermodynamic anomalies consistent with a single phase transition at a temperature $T^{*}$, and a gapped magnetic excitation spectrum with spectral weight concentrated at wave vectors typical of type-I antiferromagnetic orders. However, while muon spin resonance experiments show clear evidence for time-reversal symmetry breaking below $T^{*}$, we observe no corresponding magnetic Bragg scattering signal. These results are shown to be consistent with ferro-octupolar symmetry breaking below $T^{*}$, and are discussed in the context of other $5d$ double perovskite magnets and theories of exotic orders driven by multipolar interactions.

Figure 1

(a)–(c) Neutron scattering intensity contour plots for BZO, BMO, and BCO shown as a function of energy transfer $E$ and momentum transfer $|Q|$ at base temperature (top) and at $T>T^{*}$ (bottom), respectively. Below $T^{*}$, clear gapped magnetic inelastic spectral weight develops around (100) and (110) wave vectors ($\sim 0.78{\AA }^{-1}$) and 110 ($1.1{\AA }^{-1}$) in each case. (d),(e) Low $|Q|$ integrated cuts of the neutron scattering intensity as a function of energy transfer $E$ as a function of temperature for BZO, BMO, and BCO, respectively. A gap in the magnetic excitation spectrum is clearly revealed for each compound for $T<T^{*}$.

Figure 2

(a) Neutron powder diffraction measurements on BZO for $T=10\mathrm{K}$ with the experimental dataset in black and the fit to the refined $Fm\overline{3}m$ structure in red. (b) Subtraction of the 50 K dataset from the 10 K dataset. The red line shows the calculated magnetic diffraction pattern for BZO with an ${\mathrm{Os}}^{6+}$ ordered moment of $0.06{\mu }_B$, which we establish as the upper limit for an ordered dipole moment in BZO. Green fiducial lines indicate the locations of the magnetic peaks expected for type-I antiferromagnetic order. Panels (c) and (d) show the same comparison for BMO and BCO. These establish upper limits on an ordered ${\mathrm{Os}}^{6+}$ dipole moment of 0.11 and $0.13{\mu }_B$, respectively.

Figure 3

(a) The neutron powder diffraction profile for BCO is shown at $T=1.5\mathrm{K}$ in the main panel, while the inset shows a comparison of neutron powder diffraction versus synchrotron x-ray diffraction data taken on BCO at 20 K. Panels (b) and (c) show synchrotron x-ray diffraction data on BCO at $\mathrm{T}=20\mathrm{K}$ (b) and $\mathrm{T}=250\mathrm{K}$ (c), along with corresponding cubic structural refinements, in red.

Figure 4

Schematic level diagram showing single-particle $t_{2g}$ orbitals split by spin-orbit coupling ($\lambda$) and interactions (Hund’s coupling) leading to a $J=2$ ground state. Residual crystal field $H_{{\text{CEF}}^{\prime }}$ splits this $J=2$ manifold into a non-Kramers doublet ground state and an excited magnetic triplet (see text for details).