The newly developed technique of generalized polarization analysis has been used to re-examine the triangular magnetic structure of Mn3Sn. The magnitude and direction of the polarization of neutrons scattered by some mixed magnetic and nuclear Bragg reflections at 200 K have been measured for a range of different incident polarization directions using a zero-field polarimeter. The results have been used to discriminate between different models which have been proposed for the magnetic structure. The analysis shows unambiguously that a structure allowing three trigonal domains is necessary to account for the scattered polarizations. Of the models suggested up to now only the 'inverse triangle' structure satisfies this criterion. The manganese moment was determined to be 3.00(1) mu B much larger than the value (1.78 mu B) given by earlier measurements of the flipping ratios in an applied field. On cooling below 50 K the polarization analysis gave evidence for a transition to a magnetic structure with a significant ferromagnetically aligned moment parallel to (001).
The magnetization distribution due to the Cr3+ ion in
Cr2O3 has been determined using spherical neutron
polarimetry. The magnetic structure factors of h 0 l
reflections have been measured out to sin θ/λ = 0.75 Å-1. The results show that the Cr3+ magnetic
moment is reduced by the zero-point spin deviation and by
covalent mixing to 2.48 µB. They are consistent
with the Cr d electrons being in the trigonally symmetric a1
and e orbitals derived from the cubic orbitals with t2g
symmetry. There is a small but significant magnetization which
is not accounted for by these orbitals, which is attributed to
covalent overlap. Its symmetry is consistent with the
magneto-electric susceptibility.
The zero-field magnetic structure of Ce 11 B 6 has been revised from neutron powder and single-crystal diffraction including neutron spherical polarimetry. The crystal structure remains cubic in the antiferroquadrupolar ͑AFQ͒ ordered state (T Q ϭ3.3 K, k Q ϭ͓1/2,1/2,1/2͔) and in the antiferromagnetic ͑AFM͒ ordered state (T N ϭ2.3 K, k 1 ϭ͓1/4,1/4,0͔, k 2 ϭ͓1/4,Ϫ1/4,0͔, k 1 Јϭ͓1/4,1/4,1/2͔, k 2 Јϭ͓1/4,Ϫ1/4,1/2͔) within the precision of the experiment. The model of Effantin et al. ͓J. Magn. Magn. Mater. 47-48, 145 ͑1985͔͒ fits our 60-mK high-intensity neutron powder diffraction data rather poorly and therefore a model of the AFM multi-k structure has been developed. It is a 2 kÀkЈ transverse sine-wave structure with the Ce magnetic moments strictly along ͓1Ϫ10͔ and ͓110͔ and orthogonal arrangement of the nearest moments. Ce atoms located at the zϭ0 and zϭ1 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) B , 0.543(16) B at zϭ1 and only 0.01 B , 0.138(7) B at zϭ0 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 SR zero-field results ͓R. Feyerherm et al., J. Magn. Magn. Mater. 140-144, 1175 ͑1995͔͒ and suggests a highly inhomogeneous conduction electron spin polarization and anisotropic RKKY interactions below T N .
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