Van Vleck paramagnetism of chromium- and iron-doped II-VI semiconductors

We present a study of the Van Vleck paramagnets ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Cr}}_{\mathit{x}}$B and ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$B, where AB is a II-VI semiconductor having the zinc-blende or the wurtzite structure. In cubic zinc-blende hosts the nonlinear magnetization M depends on the orientation of the external magnetic field B with respect to the cubic axes of the crystal. We show that, while for iron M is largest when B is along a cubic axis and a minimum for B\ensuremath{\parallel}[111], for chromium the anisotropy is reversed and the largest value of M occurs for B\ensuremath{\parallel}[111]. Expansions of the angular variation of the magnetization in terms of combinations of spherical harmonics invariant under the operations of the symmetry group (${\mathit{T}}_{\mathit{d}}$ or ${\mathit{C}}_{3\mathit{v}}$) of the site of the impurity are used to analyze the anisotropy. The magnetic-field dependence of the coefficients in the expansion is investigated. The magnetic susceptibility of ${\mathrm{Cr}}^{2+}$ in wurtzite-structure hosts is expected to be particularly large.