Enhanced lattice-displacement effects on the crystal field and the anomalous magnetic anisotropy in cerium monopnictides

Abstract

Extremely strong $〈100〉$ magnetic anisotropy occurs in CeSb and CeBi. This contrasts with the theoretical crystal-field-only $〈111〉$ easy direction as found experimentally upon diluting the Ce with Y or La. We find that the strong $〈100〉$ anisotropy can be understood when one includes elastic and magnetoelastic effects in conjunction with magnetic ordering. Depending on the system parameter values, there are two possible types of magnetic anisotropy and distortional behavior: either (i) a small expansive trigonal distortion and magnetic ordering along $〈111〉$, or (ii) tetragonal distortion, above a significant threshold value at 0\ifmmode^\circ\else\textdegree\fi{}K, and ordering along $〈100〉$. For the tetragonal distortion, the $\frac{c}{a}$ ratio is 1 as found experimentally in CeBi. Our self-consistent calculations for CeBi use the experimental crystal-field splitting, ${T}_{N}$, and elastic constants. The occurrence of the tetragonally distorted $〈100〉$ phase is associated with the remarkable sensitivity of the crystal-field interaction to lattice spacing in the cerium monopnictides. We introduce this effect via a charge-enhancement factor $\ensuremath{\rho}$ multiplying the point-charge-model result for distortional crystal-field terms. The ${\ensuremath{\Gamma}}_{7}$ crystal-field ground state has no quadrupole moment. Because of this, distortional effects of any significance occur only with a molecular field present, as in our model calculation for CeBi, or in the absence of exchange, for $\ensuremath{\rho}$ above a threshold value necessary to give sufficiently strong ${\ensuremath{\Gamma}}_{7}\ensuremath{-}{\ensuremath{\Gamma}}_{8}$ mixing.