Zero-field magnetic structure inCeB6reinvestigated by neutron diffraction and muon spin relaxation

Abstract

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 ${(T}_{Q}=3.3\mathrm{K},$ ${\mathbf{k}}_{Q}=[1/2,1/2,1/2])$ and in the antiferromagnetic (AFM) ordered state ${(T}_{N}=2.3\mathrm{K},$ ${\mathbf{k}}_{1}=[1/4,1/4,0],$ ${\mathbf{k}}_{2}=[1/4,\ensuremath{-}1/4,0],$ ${\mathbf{k}}_{1}^{\ensuremath{'}}=[1/4,1/4,1/2],$ ${\mathbf{k}}_{2}^{\ensuremath{'}}=[1/4,\ensuremath{-}1/4,1/2])$ 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 ${\mathbf{k}\mathbf{\ensuremath{-}}\mathbf{k}}^{\ensuremath{'}}$ transverse sine-wave structure with the Ce magnetic moments strictly along $[1\ensuremath{-}10]$ and [110] and orthogonal arrangement of the nearest moments. Ce atoms located at the $z=0$ and $z=1$ 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 $0.744(16){\ensuremath{\mu}}_{B},$ $0.543(16){\ensuremath{\mu}}_{B}$ at $z=1$ and only $0.01{\ensuremath{\mu}}_{B},$ $0.138(7){\ensuremath{\mu}}_{B}$ at $z=0$ 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 $\ensuremath{\mu}\mathrm{SR}$ 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 ${T}_{N}.$