Monte Carlo simulations using a three-dimensional lattice model studied the Ruderman–Kittel–Kasuya–Yosida (RKKY) indirect exchange interaction of doped magnetic Co ions in ZnO films. The results of the calculations show that the RKKY interaction in Co-doped ZnO is long ranged and its magnitude is proportional to R−1 (inverse of the distance R from a central Co2+ ion). The sign oscillates with a frequency that depends on the concentration of the carrier. The long-distance sum of the RKKY indirect exchange energies is positive indicating that these materials are ferromagnetic, in direct correlation with previously reported results
Applied Physics Letters
Abraham F. Jalbout, Hanning Chen and Scott L. Whittenburg. 2002. "Monte Carlo simulation on the indirect exchange interactions of Co-doped ZnO film." Applied Physics Letters 81 (12): 2217-2219.