Far-infrared investigation of band-structure parameters and exchange interaction in ${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Eu}}_{\mathit{x}}$Te films

Far-infrared (FIR) magnetotransmission has been investigated in molecular-beam-epitaxy-grown ${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Eu}}_{\mathit{x}}$Te films with Eu concentration x=0.02. The experiments were carried out at fixed FIR photon energies between 2.5 and 21.4 meV, in the temperature range 1.8≤T≤60 K, and in magnetic fields up to 6 T. From the magnetic-field dependence of the cyclotron-resonance energies the momentum matrix elements have been determined within the framework of the Mitchell-Wallis k⋅p model: 2${\mathit{P}}_{\mathit{t}}^2$/${\mathit{m}}_0$=8.23±0.02 eV and 2${\mathit{P}}_{\mathit{l}}^2$/${\mathit{m}}_0$=0.55±0.02 eV. The results signal a strong increase of band anisotropy due to the presence of Eu, from ${\mathit{P}}_{\mathit{t}}^2$/${\mathit{P}}_{\mathit{l}}^2$=10.3 for pure PbTe to ${\mathit{P}}_{\mathit{t}}^2$/${\mathit{P}}_{\mathit{l}}^2$=14.9 for ${\mathrm{Pb}}_{0.98}$${\mathrm{Eu}}_{0.02}$Te. The low-field approximation of the model yields the following components of the effective-mass tensors: ${\mathit{m}}_{\mathit{t}}^{\mathit{v}}$/${\mathit{m}}_0$=0.023, ${\mathit{m}}_{\mathit{l}}^{\mathit{v}}$/${\mathit{m}}_0$=0.287, ${\mathit{m}}_{\mathit{t}}^{\mathit{c}}$/${\mathit{m}}_0$=0.020, and ${\mathit{m}}_{\mathit{l}}^{\mathit{c}}$/${\mathit{m}}_0$=0.218. A resonant transition from shallow acceptor states to valence band has also been observed. The analysis of these transitions in finite magnetic fields provided the value of the valence-band g factor, ${\mathit{g}}_{\mathit{t}}^{\mathit{v}}$=15.9. This in turn served to place an upper limit on the valence-band exchange integral α, α=-7.5±5.5 meV. The small value of α indicates that the hole-Eu exchange interaction in the ${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Eu}}_{\mathit{x}}$Te system is at least one order of magnitude weaker than the hole-Mn interaction in ${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te, and two orders of magnitude below exchange parameters in ${\mathrm{II}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$VI systems.