Magnetic Anisotropy of Tetrahedral Ferrous Ions in CdCr2S4

Abstract

The magnetic anisotropy of single crystals of the ferromagnetic cubic spinel ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Cr}}_{2}{\mathrm{S}}_{4}$ 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 ${\ensuremath{\Delta}}_{\mathrm{ex}}\ensuremath{\gtrsim}200$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and $\ensuremath{\delta}=6(\frac{{\ensuremath{\lambda}}^{2}}{{\ensuremath{\Delta}}_{c}}+\ensuremath{\rho})=13\ifmmode\pm\else\textpm\fi{}1$ ${\mathrm{cm}}^{\ensuremath{-}1}$.