We have measured the full temperature dependence of $M\left(H\right)$ curves for 5%, 10%, and 15% Co-doped ZnO epitaxial films with high crystalline perfection. Bulk magnetometry reveals pure paramagnetism with anisotropic $M\left(H\right)$ curves at low temperatures, whereas the x-ray magnetic circular dichroism measured at the $\text{Co}K$ edge is isotropic. Electron paramagnetic resonance shows that the $g$ factors are not significantly altered compared to ${\text{Co}}^{2+}$ impurities in ZnO. The $M\left(H\right)$ measurements are compared to simulations using either an effective spin model with zero-field splitting $D$ or Brillouin functions with an effective temperature ansatz. Whereas both models reproduce well the $H\perp c$ data, for $H\parallel c$ the effective spin model indicates that $D$ is reduced by 75% compared to ${\text{Co}}^{2+}$ impurities in ZnO. The dependence of the $M\left(H\right)$ curves and $D$ on the Co concentration is discussed in terms of magnetic interactions between the Co dopant atoms.

• Received 10 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.054420