Plasmons in Sodium under Pressure: Increasing Departure from Nearly Free-Electron Behavior

We have measured plasmon energies in Na under high pressure up to 43 GPa using inelastic x-ray scattering (IXS). The momentum-resolved results show clear deviations, growing with increasing pressure, from the predictions for a nearly free-electron metal. Plasmon energy calculations based on first-principles electronic band structures and a quasiclassical plasmon model allow us to identify a pressure-induced increase in the electron-ion interaction and associated changes in the electronic band structure as the origin of these deviations, rather than effects of exchange and correlation. Additional IXS results obtained for K and Rb are addressed briefly.

Figure 1

IXS spectra of polycrystalline sodium pressurized in a diamond anvil cell. (a) Energy transfer spectra for a momentum transfer of $q=5{\mathrm{nm}}^{-1}$ and pressures of 3.5–43 GPa. (b) Energy transfer spectra of Na at 16 GPa and momentum transfers of $2–9{\mathrm{nm}}^{-1}$. Vertical offsets are added for clarity.

Figure 2

Plasmon energies in Na, K, and Rb at $q=5{\mathrm{nm}}^{-1}$ as a function of pressure. Ambient-pressure EELS results [10] are indicated by stars. For the Na data, different symbols distinguish different sample loadings and pressure cells. Lines are guides to the eye.

Figure 3

(a) Plasmon dispersions $E(q^2)$ of polycrystalline Na as a function of pressure. Ambient-pressure electron-energy-loss spectroscopy results by vom Felde et al. [10] are indicated by small open symbols. (b) Plasmon linewidth of Na versus pressure.

Figure 4

Experimental pressure dependence of the directionally averaged plasmon energy in Na at $q=5{\mathrm{nm}}^{-1}$ (large symbols) and results of the free-electron (FE) gas model, FE model with core polarization, and the PG model (solid line). The star indicates the ambient-pressure EELS result [10].