First-order phase transitions in intermediate-valence solids—a theory based on metallic hydrogen

Abstract

We have developed a theory of the first-order phase transition in intermediate-valence (IV) solids at zero temperature. Inputs into the theory are ${m}^{*}$, the effective mass of the $5d$ electrons, $\ensuremath{\kappa}$, the electronic dielectric constant at low frequencies, ${I}_{0}$, a formation energy of an electron-hole pair ${(4f)}^{\ensuremath{\alpha}}\ensuremath{\rightarrow}{(4f)}^{\ensuremath{\alpha}\ensuremath{-}1}$ ($5d$ or $6s$) in the metallic state, and the repulsive energy between positive [both ${(4f)}^{\ensuremath{\alpha}}$ and ${(4f)}^{\ensuremath{\alpha}\ensuremath{-}1}5d$] and negative ions. All these quantities, except ${I}_{0}$, can be obtained from independent measurements. The many-body properties of the $5d$ electrons, including the important screening effects, are obtained by suitable scaling from density-functional calculations of metallic hydrogen. Depending on the values of ${m}^{*}$, $\ensuremath{\kappa}$, ${I}_{0}$, the lattice parameter $a$, and the ionic repulsive energies, the system is in conventional insulating, Mott insulating, integral, or nonintegral valence (IV) metallic states. We have applied the theory to SmS, where ${m}^{*}\ensuremath{\simeq}1$ and $\ensuremath{\kappa}\ensuremath{\sim}4.5$. We have treated ${I}_{0}$ as a free parameter. With the choice of ${I}_{0}=2.5$ eV, the experimental first-order phase transition between insulating and IV metallic states was well reproduced: $P\ensuremath{\sim}6.5$ kbar, $\frac{\ensuremath{\Delta}V}{V}\ensuremath{\simeq}13%$, and a valence change of about 0.6.