Electronic and crystal structures of osmium under high pressure

The equation of states, electronic and phonon band structure, Fermi surface, and transport properties of Os under high pressure have been studied with first-principles calculations. The theoretical results reproduced the experimentally observed anomaly in the $c∕a$ ratio around $25\mathrm{GPa}$. Analysis of the electronic band structure and Fermi surface does not support an electronic topological transition. Moreover, no phonon softening was observed in the lattice dynamics calculations. However, calculations of the Hall coefficient reveal subtle changes in the electron band dispersions at the Fermi surface which may account for the observed anomaly in the $c∕a$ ratio.

Figure 1

(Color online) Comparisons of the calculated equation of states (solid curve) in hcp Os with the experimental measurements from Ref. 1 (red solid circles), Ref. 19 (black solid down triangles), and Ref. 20 (blue solid up triangles).

Figure 2

(Color online) Optimized cell parameters $a$ and $c$ with pressure below $80\mathrm{GPa}$ for hcp Os are shown in (a) and (b), respectively. Dashed lines are linear fits to the calculated data in the pressure ranges of below and above the transition pressure at $27\mathrm{GPa}$. (c) A comparison of the optimized c/a (black solid squares) versus pressure with experimental measurements from Ref. 1 (blue solid up triangles) and Ref. 19 (red solid down triangles), respectively. Dashed curves are the linear fits over two pressure ranges. (d) A comparison of optimized $c∕a$ (black solid circles) versus volume with the experimental measurements taken from Ref. 1 (red solid up squares). The dashed curves are the linear fits to c/a versus volume.

Figure 3

(Color online) (a) Calculated two-dimensional Fermi surface along several high symmetry directions in the BZ at zero pressure. (b) The calculated three-dimensional Fermi surface at 2.88, 21.35, and $38.42\mathrm{GPa}$, respectively.

Figure 4

(Color online) (a) Calculated phonon dispersion curves for hcp Os at zero pressure. (b) The theoretical phonon density of states at 0, 20, and $40\mathrm{GPa}$. (c) The solid symbols are the theoretical longitudinal optical mode (LO) (red squares) and transverse optical mode (TO) (blue squares) with pressure at zone center, together with the experimental Raman measurement (pink open circles) for TO mode with laser excitation at $542\mathrm{nm}$ from Ref. 34. Dashed lines are second-order polynomial fit through the data points.

Figure 5

(Color online) Theoretically predicted variation of the Hall coefficients with unit cell volume in hcp Os.