Magnetism and band structure of the semimagnetic semiconductor Pb-Sn-Mn-Te

Measurements of magnetization, magnetic susceptibility, specific heat, and Hall effect of the ${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}\mathrm{-}\mathit{y}}$ ${\mathrm{Sn}}_{\mathit{x}}$ ${\mathrm{Mn}}_{\mathit{y}}$Te semimagnetic semiconductor (x=0.72, y=0.03 and x=0.64, y=0.03) were performed in samples with different concentration of carriers (p=8×${10}^{19}$ to 1.4×${10}^{21}$ ${\mathrm{cm}}^{\mathrm{-}3}$). A low-temperature ferromagnetic phase was established in the samples with carrier concentration larger than a threshold value ${\mathit{p}}_{\mathit{t}}$=3×${10}^{20}$ ${\mathrm{cm}}^{\mathrm{-}3}$. Samples with lower carrier concentrations are paramagnetic in the whole temperature range studied (T=1.5–300 K). The carrier-concentration dependence of the Curie temperature has an unusual thresholdlike character. The explanation of this effect is based on the Ruderman-Kittel-Kasuya-Yosida (RKKY) indirect exchange interaction between Mn spins and a two-valence-band model of the band structure of ${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}\mathrm{-}\mathit{y}}$ ${\mathrm{Sn}}_{\mathit{x}}$ ${\mathrm{Mn}}_{\mathit{y}}$Te. Theoretical calculations based on the experimentally determined parameters of the band structure are presented. The results show that the most important role in the RKKY interaction is played by heavy holes from the Σ band located 185 meV below the top of the L band of light holes.