Spectroscopic ellipsometry study of optical anisotropy in ${\mathrm{Gd}}_5{\mathrm{Si}}_2{\mathrm{Ge}}_2$ and comparison with reflectance difference spectra

The complex dielectric functions of single crystals of ${\mathrm{Gd}}_5{\mathrm{Si}}_2{\mathrm{Ge}}_2$ were obtained using spectroscopic ellipsometry (SE) in the photon energy range of $1.5–5.0\mathrm{eV}$ at room temperature. Reflectance difference (RD) spectra for the $a\text{‐}b$ and $b\text{‐}c$ planes of single crystals of ${\mathrm{Gd}}_5{\mathrm{Si}}_2{\mathrm{Ge}}_2$ were derived from these dielectric functions and compared to those obtained from reflectance difference spectroscopy (RDS) at near-normal incidence. The two experimental RD spectra from SE and RDS agreed well. The in-plane optical anisotropy of the sample is mainly due to intrinsic bulk properties because of its larger magnitude $(4\times {10}^{-2})$ compared to surface-induced optical anisotropies, with a magnitude of only about ${10}^{-3}$ for a typical cubic material.

Figure 1

(Color online) Experimental configuration for $a$-axis ${\mathrm{Gd}}_5{\mathrm{Si}}_2{\mathrm{Ge}}_2$ with the $b$ axis pointing in the $y$ direction. The plane of incidence is the $x\text{‐}z$ plane, and the $z$ direction is normal to the sample surface. Large spheres are Gd atoms, and small ones are Si or Ge atoms.

Figure 2

The real part of the complex dielectric functions of the $a\text{‐}b$ and $b\text{‐}c$ planes of ${\mathrm{Gd}}_5{\mathrm{Si}}_2{\mathrm{Ge}}_2$ measured with ellipsometry.

Figure 3

The imaginary part of the complex dielectric functions of the $a\text{‐}b$ and $b\text{‐}c$ planes of ${\mathrm{Gd}}_5{\mathrm{Si}}_2{\mathrm{Ge}}_2$ measured with ellipsometry.

Figure 4

RD spectra of the $b\text{‐}c$ plane and $a\text{‐}b$ plane ${\mathrm{Gd}}_5{\mathrm{Si}}_2{\mathrm{Ge}}_2$. The spectra from the ellipsometry were scaled with 45% for the $a$ axis ($b\text{‐}c$ plane) and 50% for the $c$ axis ($a\text{‐}b$ plane) sample.

Figure 5

Comparison of measured imaginary parts of the dielectric functions with angle-averaged spectrum from Ref. 10. The average values of the $b\text{‐}c$ and $a\text{‐}b$ planes were used for ${\epsilon }_{2b}$.