Unusual Anisotropy Mechanism in Ce-pnictides Due to Virtual Valence Fluctuation

--Unusual strong magnetic anisotropies in CeBi and CeSb are explained based on the anisotropic mixing mechanism between the 4f states and the valence electrons, This is consistent with the fact that no such strong anisotropy isfbund in other Ce-pnictides. Ce-pnictides are interesting materials showing various unusual anomalous properties. In CeN, Ce is believed to be tetravalency and thus non-magnetic /l/, while in CeP, Ce Cs trivalency and thus the real valence fluctuation is expected to occur in their alloys /2/. They are also interesting in the sense of narrow gap semiconductor. The gap between the conduction bands, which are made mostly by the 5d t atomic states with the 29 minimums at the three X-points / 3 / , and the valence bands,which are made mostly by the p states of pnictogens with a maximum at the r-point /3/, seems to disappear in between CeP and CeAs. In actual materials, however, because of the difficulty to make perfact crystals without vacancies, sharp change for the metal-non metal transition is not observed in their transport properties. On the other hand, the magnetic properties show a lot of variety /4/. In particular, the magnetic properties of CeSb and CeBi are very unusual, with many phases depending on temperature and magnetic field, however, in all ofwhich the sublattice moments are kept in the [lo0 1 direction. Even the strong field up to 150 kOe in the 1 111 1 direction can not change the direction of the sublattice moments /5/. This is not understood from the usual crystal field effect because the ground state for the crystal field splitting is the doublet, which is spherical and in CeBi the crystal field splitting is believedto be very small. Cooper tried to explain this unusual anisotropy by the strong magnetoelastic effect / 6 / , but it is difficult to give such a large anisotropy. Here, we explain this anisotropy on the stand point of the anisotropic f-p virtual mixing mechanism, or the anisotropic virtual valence fluc-