Influence of Mn Distribution on Ferromagnetism in Magnetic Semiconductor Mn$_x$Ge$_{1-x}$

The ferromagnetism of Mn-doped Ge, grown with molecular beam epitaxy, is studied by controlling Mn distributions in the films via post-annealing and digital doping techniques. Randomly doped Mn$_{x}$Ge$_{1-x }$films exhibit a high concentration of Mn trapped at interstitial sites in Ge, and reveal two ferromagnetic transitions at $T_{C}$* and \textit{Tc}, respectively. A strong correlation between magnetic and transport properties is observed both at $T_{C}$* and $T_{C}$. Upon annealing as-grown films at a low-temperature, some interstitial Mn atoms are driven toward the surface of the film and even to the substitutional sites of Ge, as predicted by a theory and revealed by ion channeling and x-ray photoemission spectroscopy. This Mn redistribution leads to a large increase in ferromagnetism with both $T_{C}$* and $T_{C}$ shifting toward higher temperatures. Spatial control of Mn atoms along the growth direction is achieved in a Mn$_{x}$Ge$_{1-x}$/Ge digital heterostructure. Ferromagnetism enhancement is also observed in digital structures as compared to randomly doped material with same nominal $x$. The ferromagnetism variation is studied by changing undoped Ge spacer layer thickness and $x$ in doped Mn$_{x}$Ge$_{1-x}$ layer.