Optical third harmonic generation in the magnetic semiconductor EuSe

Third harmonic generation (THG) has been studied in europium selenide EuSe in the vicinity of the band gap at $2.1–2.6$ eV and at higher energies up to $3.7$ eV. EuSe is a magnetic semiconductor crystalizing in centrosymmetric structure of rock-salt type with the point group $m3m$. For this symmetry the crystallographic and magnetic-field-induced THG nonlinearities are allowed in the electric-dipole approximation. Using temperature, magnetic field, and rotational anisotropy measurements, the crystallographic and magnetic-field-induced contributions to THG were unambiguously separated. Strong resonant magnetic-field-induced THG signals were measured at energies in the range of $2.1–2.6$ eV and $3.1–3.6$ eV for which we assign to transitions from $4f^7$ to $4f^{6}5d^1$ bands, namely involving $5d\left(t_{2g}\right)$ and $5d\left(e_g\right)$ states.

Figure 1

THG spectra of EuSe for two experimental geometries. Solid lines give a guide for the eye and dashed lines indicate zero level. Insets show the temperature and angular dependences of the THG intensity at $E\left(3\omega \right)=3.42$ eV; the latter is measured at $T=1.6$ K. In the rotational diagram the symbol color indicates the configuration: blue closed circles located in vicinity of black solid line represent $\mathbf{E}\left(3\omega \right)\parallel \mathbf{E}\left(\omega \right)$ and red open circles in the very center represent $\mathbf{E}\left(3\omega \right)\perp \mathbf{E}\left(\omega \right)$.

Figure 2

(a) THG spectra of EuSe in the range $3.1–3.7$ eV measured in $\mathbf{E}\left(3\omega \right)\perp \mathbf{E}\left(\omega \right)\parallel \mathbf{B}\left(0\right)$ configuration in different magnetic fields. Solid lines give a guide for the eye and dashed lines indicate zero level. (b) The open circles show the magnetic-field dependence of the THG intensity integrated over the spectral range $3.1–3.7$ eV. The solid line gives normalized ${[a+bM\left(B\right)]}^2$ dependence with $a\approx 1.3b$ and $M\left(B\right)$ after Ref.27.

Figure 3

THG spectra of EuSe in the range $2.1–2.7$ eV measured in different magnetic fields. Solid lines give a guide for the eye and dashed lines indicate zero level. The inset shows the magnetic-field dependence of the THG intensity (open circles) integrated over the spectral range $2.1–2.7$ eV. Normalized dependence ${[a+bM\left(B\right)]}^2$, same as in Fig. 2b, is shown by a solid line.

Figure 4

THG rotational anisotropies for $\mathbf{E}\left(3\omega \right)\parallel \mathbf{E}\left(\omega \right)$ and $\mathbf{E}\left(3\omega \right)\perp \mathbf{E}\left(\omega \right)$ geometries. Open circles show measured data and solid lines represent best fits performed with the use of Eq. (3) and also Eqs. (10) and (11) from Ref.21.

Figure 5

THG spectra of EuSe in the range $3.1–3.7$ eV measured at different temperatures. Solid lines give a guide for the eye and dashed lines indicate zero level. The inset shows the temperature dependence of THG intensity integrated over two spectral ranges.

Figure 6

Comparison of magnetic-field-induced THG and SHG spectra of EuSe. Solid lines give a guide for the eye and dashed lines indicate zero level. SHG spectrum is multiplied by a factor of 8 for better visibility.