First-principles study of the optical properties of ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$

Thin films of ${\text{Mg}}_x{\text{Ti}}_{1-x}$ show an optical black state upon hydrogenation. We calculate the dielectric function and the optical properties of ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$, $x=0.5$, 0.75, and 0.875 using first-principles density-functional theory. We argue that the black state is an intrinsic property of these compounds, unlike similar optical phenomena observed in other metal hydride films. The structures of ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$ are represented either by simple ordered or quasirandom structures. The density of states has a broad peak at the Fermi level, composed of $\text{Ti}d$ states; hence, both interband and intraband transitions contribute to the optical response. Ordered structures have a plasma frequency of $\sim 3\text{eV}$. The plasma frequency drops below 1 eV in disordered structures, which—as a result of interband transitions—then show a low reflection and considerable absorption in the energy range of 1–6 eV, i.e., a black state.

Figure 1

(Color online) Scaled dielectric functions of a free-electron gas for $\hslash \gamma =0.1\text{eV}$ and $\hslash \gamma =1\text{eV}$, as function of the energy $\hslash \omega$. The right (left) axis refers to the real, in red (imaginary, in black), part of the dielectric functions.

Figure 2

(Color online) Imaginary parts of the interband dielectric functions of ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$ in the ordered structures.

Figure 3

(Color online) Imaginary parts of the interband dielectric functions of ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$ in the disordered structures. For $x=0.5$ the dielectric function peaks to a value of 130.

Figure 4

(Color online) Electronic densities of state of the ordered and disordered structures for the three compositions of ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$. The zero of energy is at the Fermi level.

Figure 5

(Color online) Angular-momentum-projected partial densities of states (PDOSs) [states/(atom eV)] of ${\text{Mg}}_{0.75}{\text{Ti}}_{0.25}{\text{H}}_2$ in the ordered structure. The zero of energy is at the Fermi level. The PDOS is calculated using spheres with radii of 1.3, 1.3, and $0.8\text{Å}$ for Mg, Ti, and H, respectively.

Figure 6

Band structure of ${\text{Mg}}_{0.75}{\text{Ti}}_{0.25}{\text{H}}_2$ along the $\Gamma \text{−}X$ direction in the unit cells used for the ordered (top) and the disordered (bottom) structures. The scales on the abscissa are identical.

Figure 7

(Color online) Reflectance spectra of ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$ at normal incidence in the ordered structures and disordered structures. The bulk dielectric function is used to calculate these spectra.

Figure 8

(Color online) Absorption coefficients $\alpha \left(\omega \right)=2\kappa \left(\omega \right)\omega /c$ of ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$ in the ordered and disordered structures.

Figure 9

(Color online) Transmission at normal incidence of a 10 nm palladium/200 nm ${\text{Mg}}_x{\text{Ti}}_{1-x}{\text{H}}_2$ film on a quartz substrate. The calculations are based on the disordered structures.