Spin freezing in cobalt-based diluted magnetic semiconductors

We have measured the magnetic susceptibility of the cobalt-based diluted magnetic semiconductors ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Co}}_{\mathit{x}}$S, ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Co}}_{\mathit{x}}$S, and ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Co}}_{\mathit{x}}$Se in the temperature range 33 mK to 4.2 K, and for concentrations 0.03≤x≤0.103. All samples exhibit a low-temperature transition from paramagnetism, which is ascribed to a spin-freezing process. The spin-freezing temperatures are well described by a power-law function of the concentration. This implies that the spatial dependence of the exchange interaction is of the form J(R)∼(R/${\mathit{R}}_1$ ${)}^{\mathrm{-}\mathit{n}}$, for a nearest-neighbor distance ${\mathit{R}}_1$. The value n=6.3±1.2 is obtained, which is close to the result n=6.8 obtained in a previous analysis of manganese-based materials. We compare our results to the manganese-based data and discuss the properties of the long-range interaction which leads to spin freezing in both cases.