We have measured the element specific $M\left(H\right)$ curves for 5$\%$, 10$\%$, and 15$\%$ Co-doped ZnO epitaxial films with high crystalline perfection using x-ray magnetic circular dichroism (XMCD). The XMCD$\left(H\right)$ curves do not saturate up to 17 T directly evidencing antiferromagnetic exchange between neighboring Co dopant atoms. Angular-dependent XMCD$\left(H\right)$ measurements in combination with theoretical calculations based on a well-established model Hamiltonian allow to determine both the next-neighbor exchange $J$ as well as the single ion anisotropy $D$ quantitatively. While for 5$\%$ and 10$\%$ Co doping, $J=15$ K and $D=3$ K, for 15$\%$ Co doping, they are reduced to 10 and 2 K, respectively. High-field, element selective magnetometry based on XMCD is thus shown to be a suitable technique to determine microscopic magnetic parameters even in thin epitaxial films of dilute magnetic systems.

• Received 11 October 2011

DOI:https://doi.org/10.1103/PhysRevB.85.245202