Magnetic Anisotropy of Tetrahedral Ferrous Ions in CdCr2S4

The magnetic anisotropy of single crystals of the ferromagnetic cubic spinel ${\mathrm{Cd}}_{1-x}{\mathrm{Fe}}_x{\mathrm{Cr}}_2{\mathrm{S}}_4$ with $x=0.005, 0.01, \mathrm{and} 0.02$ was studied by ferromagnetic resonance at 9 and 34 GHz. The anisotropy observed at 4.2 K can be explained on the basis of strongly anisotropic ${\mathrm{Fe}}^{2+}$ ions on cubic tetrahedral sites. In the crystal field model used, the cubic ${}_{}{}^5{}_{}{}^{}E$ ground state is split by exchange and spin-orbit interactions. The model provides a good description of the temperature-dependent anisotropy at temperatures below 15 K, with ${\Delta }_{\mathrm{ex}}\gtrsim 200$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $\delta =6(\frac{{\lambda }^2}{{\Delta }_c}+\rho )=13\mathrm{}\pm 1$ ${\mathrm{cm}}^{-1\mathrm{}}$.