Carrier-induced ferromagnetism in $p-{\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$

We present a systematic study of the ferromagnetic transition induced by the holes in nitrogen doped ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ epitaxial layers, with particular emphasis on the values of the Curie-Weiss temperature as a function of the carrier and spin concentrations. The data are obtained from thorough analyses of the results of magnetization, magnetoresistance, and spin-dependent Hall effect measurements. The experimental findings compare favorably, without adjustable parameters, with the prediction of the Rudermann-Kittel-Kasuya-Yosida (RKKY) model or its continuous-medium limit, that is, the Zener model, provided that the presence of the competing antiferromagnetic spin-spin superexchange interaction is taken into account, and the complex structure of the valence band is properly incorporated into the calculation of the spin susceptibility of the hole liquid. In general terms, the findings demonstrate how the interplay between the ferromagnetic RKKY interaction, carrier localization, and intrinsic antiferromagnetic superexchange affects the ordering temperature and the saturation value of magnetization in magnetically and electrostatically disordered systems.