Chemical bonding and Born charge in 1T-HfS$_2$

Abstract: We combine infrared absorption and Raman scattering spectroscopies to explore the properties of the heavy transition metal dichalcogenide 1T-HfS$2$. We employ the LO-TO splitting of the $E_u$ vibrational mode along with a reevaluation of mode mass, unit cell volume, and dielectric constant to reveal the Born effective charge. We find $Z^*{\rm{B}}$ = 5.3$e$, in excellent agreement with complementary first principles calculations. In addition to resolving controversy over the nature of chemical bonding in this system, we decompose Born charge into polarizability and local charge. We find $\alpha$ = 5.07 \AA$^3$ and $Z^{*}$ = 5.2$e$, respectively. Polar displacement-induced charge transfer from sulfur $p$ to hafnium $d$ is responsible for the enhanced Born charge compared to the nominal 4+ in hafnium. 1T-HfS$_2$ is thus an ionic crystal with strong and dynamic covalent effects. Taken together, our work places the vibrational properties of 1T-HfS$_2$ on a firm foundation and opens the door to understanding the properties of tubes and sheets.