Large ferroquadrupole moment induced in the octupole-ordered ${\mathrm{Ce}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{B}}_6$ revealed by high-resolution x-ray diffraction

We carried out a high-resolution x-ray diffraction experiment on ${\mathrm{Ce}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{B}}_6$ that exhibits staggered order of $4f$ octupole moments below $T_O=1.4$ K. Theoretically, ferroquadrupole moments that accompany the antiferro-octupole order and a resultant rhombohedral deformation of the cubic lattice were predicted. In contrast, experimentally, no direct evidence of the rhombohedral lattice has been obtained. We observe the splitting of Bragg peaks below $T_O$ and find that the unit cell is a rhombohedron being elongated along the [111] axis. The response of rhombohedral domains to magnetic fields also well agrees with theoretical calculations. A particular outcome of this experiment is that the magnitude of the induced quadrupole moments is precisely evaluated from the obtained shear strain. Using this result, the magnitude of the hidden octupole moments is also discussed.

Figure 1

(a) Magnetic phase diagram of ${\mathrm{Ce}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{B}}_6$ from Ref. [21]. (b) Schematic illustration of the experimental setup. HRM is viewed from the side, and the sample and the detector are viewed from the top. (c) and (d) Reciprocal space near (1,1,1) and (1,1,0), respectively. Solid circle and other symbols are reciprocal lattice points above and below $T_O$, respectively.

Figure 2

(a) Radial profiles of the (444) reflection measured above and below $T_O$. Solid lines are fitting curves using pseudo-Voigt function(s). Data and lines are vertically shifted for clarity. (b) and (c) The obtained planar spacings $d_{444}$ and $d_{550}$ as a function of temperature, respectively. Data are normalized by the value at 2 K and the deviation from unity is shown as solid circles. Open squares and crosses are calculated values (see text). Solid lines are guides to the eyes.

Figure 3

(a) Radial profiles of the (444) reflections measured at 0.6 K and several magnetic fields above and below $H_O$. Solid lines are fitting curves using pseudo-Voigt function(s). Data and lines are vertically shifted for clarity. (b) The obtained planar spacings $d_{444}$ as a function of magnetic field. Data are normalized by the values used in Fig. 2 and the deviation from unity is shown. Solid lines are guides to the eyes.

Figure 4

(a) Radial profiles of the (550) reflection measured at 0.6 K and several magnetic fields above and below $H_O$. Solid lines are fitting curves using pseudo-Voigt function(s). Data and lines are vertically shifted for clarity. (b) The obtained planar spacings $d_{550}$ as a function of magnetic field, respectively. Data are normalized by the values used in Fig. 2, and the deviation from unity is shown. Solid lines are guides to the eyes.