Large nonlinear magneto-optical effect in the centrosymmetric ferromagnetic semiconductor EuO

Pronounced magnetic-dipole-induced second-harmonic generation (SHG) is observed in epitaxial films of the ferromagnetic semiconductor EuO. The SHG light wave emerges background-free at the Curie temperature and couples linearly to the spontaneous magnetization. The SHG spectrum is determined by spin-allowed and spin-forbidden transitions between the $4f$ ground state and the $5d\left(t_{2g}\right)$ states of the ${\text{Eu}}^{2+}$ ion. At the coercive field, components of the spontaneous magnetization perpendicular to the applied field are observed. Spatially resolved hysteresis measurements reveal that the ferromagnetic domains possess an average extension of $<1\mu \text{m}$ although pinning effects can stabilize domains that are two orders of magnitude larger.

Figure 1

(Color online) Linear and nonlinear optical spectroscopy on epitaxial EuO(001) films. (a) Crystal structure of EuO. (b) Experimental configuration of the SHG measurements. (c) Spectrum of the optical density (OD) at 10 K of $\text{a-Si}/\text{EuO}/{\text{YAlO}}_3$ obtained with unpolarized incident light. The inset shows the temperature variation at 10, 30, 50, 60, 65, 70, 80, and 100 K. (d) Temperature dependence of the SHG intensity with assignments of SHG tensor components as in (f). (e) Thickness dependence of the SHG intensity at 10 K for ${\chi }_{xxy}$ at $2\hslash \omega =1.57$ and 2.60 eV. (f) SHG spectra for different polarization configurations of the incident fundamental and the detected component of the SHG light. The inset shows the electronic energy levels of the ${\text{Eu}}^{2+}$ ion (Ref. 22). CF and $S_T$ denote crystal field and total spin, respectively. SHG data were taken on a ferromagnetic single-domain sample $\left({\mu }_0{H}_y=0.1\text{T}\right)$.

Figure 2

Investigation of the SHG tensor components in Table by anisotropy measurements at 10 K at $2\hslash \omega =2.60\text{eV}$. Angles ${\phi }_P$ and ${\phi }_A$ denote the polarization of the incident fundamental light and the detected component of the SHG light, respectively, according to Fig. 1b. Angles $0°$ and $90°$ correspond to the $x$ and the $y$ axes, respectively. The center of each polar diagram corresponds to zero. Solid lines represent fits to the equations mentioned in the text.

Figure 3

(Color online) Hysteresis measurements in a magnetic field along $y$. (a) Magnetic-field dependence of the SHG intensity from ${\chi }_{xxy}$ and ${\chi }_{yyx}$. Data represented by closed and open symbols were taken with decreasing and increasing field, respectively. The inset shows a magnified view of the region around 0 T. The same relative scales are used in the main panels and the insets. (b) Magnetization $\left(M_y\right)$ parallel to the external magnetic field extracted from the data in (a). The vertical scale is derived from the direct magnetization measurements (Ref. 9).

Figure 4

Imaging of the topography of the crystallographic and magnetic structure of an $\text{a-Si}/\text{EuO}/{\text{YAlO}}_3$ sample. Black and white correspond to zero and maximum intensity, respectively. (a) Linear transmission image taken with white light from a flash lamp. [(b) and (c)] SHG images for ${\chi }_{xxy}$ at $2\hslash \omega =1.84\text{eV}$ in a magnetic field of (b) 0 T and (c) 0.2 T. The brightness of (b) with respect to (c) was enhanced by a factor of 4. (d) Normalized SHG image suppressing spatial inhomogeneities of the SHG yield obtained by dividing the multidomain image in (b) by the single-domain image in (c). The arrow shows a macroscopic single-domain region in the sample after zero-field cooling that is probably stabilized by pinning (see text). The same area is shown in all panels.