Negative thermal expansion near two structural quantum phase transitions

We present an inelastic X-ray scattering study of the structural phase transitions and thermal expansion (TE) behavior of the mercurous halides (Hg₂X₂ with X=Br,I). The body-centered tetragonal (BCT) to orthorhombic transition at T_c = 150K in Hg₂Br₂ is induced by the freezing of the transverse acoustic phonon at the X-point in the BCT Brillouin zone, as we confirm by the soft-mode behavior and static structure factor. For the case X = I, the X mode does not freeze but softens considerably, extrapolating to T_c = -22K which implies that mercurous iodide at low temperatures is situated very close to a structural quantum phase transition (SQPT). While Hg₂Br₂ displays normal TE, we report for the first time that low temperature Hg₂I₂ reveals significant negative TE behavior on the approach to the SQPT below T = 70K. We contextualize this result against the 3d-transition metal trifluorides, in particular ScF₃ which is another system that displays negative TE above an incipient structural transition.