Ferromagnetism and two magnetic phases in rutile (TiO$_2$) implanted by cobalt ions

Single crystalline (100)- and (001)-plates of rutile were implanted by Со$^+$ ions with energy of 40 keV in a wide range of doses, 0.1–1.5$\cdot10^{17}$ ion/cm$^2$, with the aim to investigate formation of the ferromagnetic phase response in the samples. With increasing the ion dose, the rutile plates reveal consecutively paramagnetic, then superparamagnetic, and at last anisotropic ferromagnetic properties at room temperature. Analysis of the temperature dependence of saturation magnetization has shown that two ferromagnetic phases develop in the implanted rutile with magnetic ordering temperatures $T_{C1}\sim 850$ К and $T_{C2}\sim 700$ К respectively. Annealing of the samples in air substantially suppresses the ferromagnetic phases if the annealing temperature exceeds the corresponding magnetic transition temperature. Formation of the two ferromagnetic phases in a model of two layers having different concentration and valence state of the cobalt dopant is discussed.