Order Parameter Segregation in ${\mathrm{Ce}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{B}}_6$: $4f$ Octopole and $5d$ Dipole Magnetic Order

The intriguing thermophysical properties of ${\mathrm{CeB}}_6$ have been subject to investigation for more than 20 years. In particular, an exotic ground state, phase IV, emerges under doping with La. We report resonant x-ray scattering results on the order parameter symmetries in phase IV of ${\mathrm{Ce}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{B}}_6$, which condenses below $T_{\mathrm{IV}}=1.5\mathrm{K}$. The results reveal a degree of mesoscopic $5d$ dipole antiferromagnetic order, with propagation vector $Q_0=(\frac{1}{2}\frac{1}{2}\frac{1}{2})$, both below and above $T_{\mathrm{IV}}$. Below $T_{\mathrm{IV}}$, this polarization coexists with long-range $4f$ antiferro-octupole (AFO) order also at $Q_0$. The marked differences in temperature dependence and spatial correlation suggest a state of order parameter segregation at low temperature. A simple model of AFO order, consistent with the polarization dependent azimuth symmetries, the Bragg angle, and temperature dependence is given.

Figure 1

(a) Phase diagram for ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{B}}_6$ [taken from Ref. 10 ], described in the text. (b) Experimental scattering geometry: incident $\sigma$-polarized photons are scattered in either ($\sigma \sigma$) or ($\sigma \pi$) polarization. $\theta$ is the Bragg angle; $k_{i,f}$ and ${ϵ}_{i,f}$ are the incident and scattered wave vectors and polarizations, respectively. $U_{1,2,3}$ define the scattering coordinate system. The azimuth $\Phi$ corresponds to rotation of the sample around the scattering vector $\mathbf{Q}$.

Figure 2

(a) $\sigma \sigma$ (solid circles) and $\sigma \pi$ (open circles) RXS energy response at the Ce ${\mathrm{L}}_2$ absorption edge for $T=1.0\mathrm{K}$. The $\sigma \sigma$ data have been shifted slightly to match the $\sigma \pi$ background for clarity. (b) $\sigma \pi$ RXS energy response at 1.7 K. Only the E1 $\sigma \pi$ remains at this temperature. (c) The temperature response of the E2 $\sigma \sigma$ (solid circles) and $\sigma \pi$ (open circles) and E1 $\sigma \pi$ (open triangles) polarized intensities. The open squares are an independent measurement of the E2 temperature response taken without polarization analysis. The inset compares the $\sigma \pi$ longitudinal scans taken at E2 and E1 energy thresholds at $T=1.0\mathrm{K}$. All data were taken at ($\frac{3}{2}\frac{3}{2}\frac{3}{2}$) and azimuth $\Phi =0°$.

Figure 3

(a) Azimuth dependence of the E2 $\sigma \sigma$ (solid circles), E2 $\sigma \pi$ (open circles), and E1 $\sigma \pi$ (open triangles) RXS. The E2 $\sigma \sigma$ has a sixfold dependence on the azimuth while the E2 $\sigma \pi$ has a threefold. The solid line is a model fit to the data (see text). (b) RXS energy response for the $\sigma \pi$ polarized intensities at azimuth $\Phi =0°$ (open circles) and $\Phi =-60°$ (solid squares). (c) RXS energy response of the $\sigma \sigma$ (solid circles) polarized intensities at $\Phi =0°$ and $\Phi =-60°$ (open squares). All data were taken at $T=1.0\mathrm{K}$, $Q=(\frac{3}{2}\frac{3}{2}\frac{3}{2})$.

Figure 4

The configuration of the octupole symmetry elements at $\Phi =0°$. The azimuth symmetry analysis may be interpreted as a superposition of the scattering from two AFO order parameters, (a) and (b). (a) has components along the (111) direction while (b) has components in the (111) plane only. The inserts show the relative orientations of the octupoles projected on the (111) plane.