Intrinsic anomalous magnetic anisotropy of CdCr${}_2$S${}_4$

The magnetocrystalline anisotropy of the ferromagnetic spinel CdCr${}_2$S${}_4$ was investigated by ferromagnetic resonance measurements. By avoiding any contact to iron during the sample preparation we can exclude that the anisotropy is due to ferrous impurities, and by performing wavelength dispersive electron probe microanalysis as well as annealing experiments, it is demonstrated that the samples possess almost ideal stoichiometry. The resonance data suggest that compositional deviations from the stoichiometry up to ${10}^{-3}$ have no influence on our conclusion that the magnetocrystalline anisotropy is an intrinsic property of CdCr${}_2$S${}_4$, caused by trigonal distortion of the sulfur octahedra surrounding the Cr${}^{3+}$ ions. Anomalous low-temperature linewidth maxima in the $\langle 111\rangle$ directions can be understood by considering the crystal fields acting on inequivalent sites of the magnetic ions in the spinel structure and by taking into account the effect of exchange narrowing.

Figure 1

FMR spectra for a CdCr${}_2$S${}_4$ single crystal at $T=4\mathrm{K}$ with the static magnetic field $H$ applied along the principal cubic axes.

Figure 2

Angular dependencies of the resonance field (a) and of the FMR linewidth (b) in as-grown CdCr${}_2$S${}_4$. The experimental data are shown by the dots at four temperatures. The angle ${\phi }_H$ is defined as the angle between magnetic field and the [100] direction. The lines indicate fits for the range from $0^{\circ }$ to ${90}^{\circ }$ by the described uniaxial model.

Figure 3

Temperature dependence of the resonance field (a) and of the FMR linewidth (b) in as-grown CdCr${}_2$S${}_4$ for the crystallographic main directions. At high temperatures the signal is isotropic and the solid line is from a Huber law approximation to the high-temperature linewidth data.

Figure 4

Temperature dependencies of the resonance field (a) and of the FMR linewidth (b) in vacuum annealed CdCr${}_2$S${}_4$. The inset shows the corresponding angular dependencies at 20 and $40\mathrm{K}$. For comparison, the resonance field anisotropy of the as-grown CdCr${}_2$S${}_4$ crystal at $4\mathrm{K}$ is replotted in the upper frame. The line gives the fit of cubic anisotropy.

Figure 5

Temperature dependencies of the resonance field (a) and of the FMR linewidth (b) in sulfur annealed CdCr${}_2$S${}_4$. The inset shows the corresponding angular dependencies at $4\mathrm{K}$. The line reflects the fit of cubic anisotropy.

Figure 6

Comparison of the $K_1$ values (triangles) normalized to $4.4\times {10}^4\mathrm{erg}/{\mathrm{cm}}^3$ with the tenth power of the magnetization values (circles) normalized to $400\mathrm{Oe}$.