Optical third-harmonic spectroscopy of the magnetic semiconductor EuTe

EuTe possesses the centrosymmetric crystal structure $m3m$ of rocksalt type in which the second-harmonic generation is forbidden in electric dipole approximation but the third-harmonic generation (THG) is allowed. We studied the THG spectra of this material and observed several resonances in the vicinity of the band gap at 2.2--2.5 eV and at higher energies up to 4 eV, which are related to four-photon THG processes. The observed resonances are assigned to specific combinations of electronic transitions between the ground 4f⁷ state at the top of the valence band and excited 4f⁶5d¹ states of Eu²⁺ ions, which form the lowest energy conduction band. Temperature, magnetic field, and rotational anisotropy studies allowed us to distinguish crystallographic and magnetic-field-induced contributions to the THG. A strong modification of THG intensity for the 2.4 eV band and suppression of the THG for the 3.15 eV band was observed in applied magnetic field. Two main features of the THG spectra were assigned to 5d(t2g) and 5d(eg) subbands at 2.4 eV and 3.15 eV, respectively. A microscopic quantum-mechanical model of the THG response was developed and its conclusions are in qualitative agreement with the experimental results.