Theory of near-gap second harmonic generation in centrosymmetric magnetic semiconductors: Europium chalcogenides

Abstract

Second harmonic generation is strictly forbidden in centrosymmetric materials, within the electric dipole approximation. Recently, it was found that the centrosymmetric magnetic semiconductors EuTe and EuSe can generate near-gap second harmonics, if the system is submitted to an external magnetic field. Here, a theoretical model is presented, which well describes the observed phenomena. The model shows that second harmonic generation becomes efficient when the magnetic dipole oscillations between the band-edge excited states of the system, induced by the excitation light, enter the in-phase regime, which can be achieved by applying a magnetic field to the material.

Optical third-harmonic spectroscopy of the magnetic semiconductor EuTe

“…We have shown that particular features of the crystallographic structure and the electronic band structure of the centrosymmetric EuTe allow crystallographic and magnetic-field-induced THG. In contrast to the SHG studies, 6,7,60 THG of electric dipole type was observed in zero magnetic field. The contained resonances were assigned to specific electronic transitions between the ground 4f 7 state at the top of the valence band and excited 4f 6 5d 1 states of the Eu 2+ ions, which form the lowest energy conduction band.…”

“…60 We also assume T = 0 K, meaning that the unperturbed electronic system is in the ground state 4f 7 ͑ 8 S 7/2 ͒. We shall use two characteristics of the above described electronic energy level scheme: ͑i͒ the energy spread of the excited states is much smaller than the band gap, i.e., E G ӷ 4f and E G is much larger than the energy width of ⑀ X ͑k͒; ͑ii͒ all excited states have the same parity, which is opposite to the parity of the ground state.…”

“…60 The main purpose is to verify the adequateness of the level scheme to describe the main features of the THG spectrum, and, in particular, to gain an understanding why the THG efficiency is nonzero in zero magnetic field. This is in contrast to the SHG efficiency, which is zero if no magnetic field is applied to the EuTe crystal.…”

“…12͑a͒, for zero magnetic field, the order in EuTe is antiferromagnetic. SHG is due to the magnetic dipole coupling between excited states, 6,7,60 and the polarization waves arising from both magnetic sublattice, containing Eu 2+ spins pointing in opposite directions, are in opposite phase to each other, and their interference leads to a zero net second-order polarization. Thus SHG vanishes in zero field.…”

“…Then, calculation of all matrix elements, such as ͗4fm͉x͉ ͘, can be done as described in detail in Ref. 60.…”