Percolation ferromagnetism and spin waves in Ge:Mn thin films

We studied magnetic properties of thin Ge:Mn films obtained by implantation of Mn⁺ ions into a single crystalline bulk germanium. In the net magnetic moment we were able to separate contributions originating from dispersed Mn²⁺ ions, ferromagnetic Mn₅Ge₃ precipitates, and regions of the germanium matrix enriched with diluted manganese---MnₘGeₙ alloys. In the subsystem of dispersed Mn²⁺ ions we observed a percolation transition into the ferromagnetic state at T≤13 K. Collective excitations, standing spin waves, were also detected below this temperature. The main parameters of the exchange interaction obtained from the analysis of the experimental spin-wave resonance data are consistent with results acquired from static magnetic measurements as well as with theoretical estimations for a percolation ferromagnet. Thus, we demonstrate that low-temperature magnetic properties of group IV magnetic semiconductor can be successfully explained within a magnetic polaron model.