Zero-field magnetic structure in ${\mathrm{CeB}}_6$ reinvestigated by neutron diffraction and muon spin relaxation

The zero-field magnetic structure of ${\mathrm{Ce}}^{11}{\mathrm{B}}_6$ has been revised from neutron powder and single-crystal diffraction including neutron spherical polarimetry. The crystal structure remains cubic in the antiferroquadrupolar (AFQ) ordered state ${(T}_Q=3.3\mathrm{}\mathrm{K},$ ${\mathbf{k}}_Q=[1/2,1/2,1/2])$ and in the antiferromagnetic (AFM) ordered state ${(T}_N=2.3\mathrm{}\mathrm{K},$ ${\mathbf{k}}_1=[1/4,1/4,0],$ ${\mathbf{k}}_2=[1/4,-1/4,0],$ ${\mathbf{k}}_1^{\prime }=[1/4,1/4,1/2],$ ${\mathbf{k}}_2^{\prime }=[1/4,-1/4,1/2])$ within the precision of the experiment. The model of Effantin et al. [J. Magn. Magn. Mater. 47-48, 145 (1985)] fits our 60-mK high-intensity neutron powder diffraction data rather poorly and therefore a model of the AFM multi-$\mathbf{k}$ structure has been developed. It is a 2 ${\mathbf{k}\mathbf{-}\mathbf{k}}^{\prime }$ transverse sine-wave structure with the Ce magnetic moments strictly along $\left[1-10\right]$ and [110] and orthogonal arrangement of the nearest moments. Ce atoms located at the $z=0\mathrm{}$ and $z=1\mathrm{}$ layers have significantly different magnetic moment values. In addition there is a modulation of the moment value in each layer. The resulting ordered magnetic Ce moments reach $0.744\left(16\right)\mathrm{}{\mu }_B,$ $0.543\left(16\right)\mathrm{}{\mu }_B$ at $z=1\mathrm{}$ and only $0.01{\mu }_B,$ $0.138\left(7\right)\mathrm{}{\mu }_B$ at $z=0\mathrm{}$ at 60 mK. This complex AFM structure is due to competition between the established AFQ order and the dipolar and octupolar AFM order developing at lower temperatures. The model is consistent with the $\mu \mathrm{SR}$ zero-field results [R. Feyerherm et al., J. Magn. Magn. Mater. 140-144, 1175 (1995)] and suggests a highly inhomogeneous conduction electron spin polarization and anisotropic RKKY interactions below $T_N.$