Site-Specific Phonon Density of States Discerned using Electronic States

We have performed the measurement of the site-specific phonon densities of states (PDOS) discerned using electronic states. As far as we know, no general method could give the site-specific PDOS, although oscillating properties of the individual atoms in nonequivalent positions are not necessarily equivalent. However, the combination of the energy and time domain measurements of the nuclear resonant scattering of synchrotron radiation allows the identification of site-specific PDOS. We measured the site-specific PDOS of iron atoms in magnetite, which is a mixed valent compound, and the difference between partial phonon densities of the iron sites was clearly observed.

Figure 1

Energy spectrum of nuclear resonant scattering of synchrotron radiation of all ${}^{57}\mathrm{F}\mathrm{e}$ atoms in ${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4$. Inset is the same spectrum except that it was measured with Al foil placed between the sample and the APD detectors.

Figure 2

Time spectra measured by one of the four APD elements at different incident photon energies (deviations from nuclear resonant energy; closed diamonds, 16 meV; open circles, 22 meV; open diamonds, 35 meV). Lines are least-square fitted spectra with two exponential functions accompanied by sinusoidal quantum beats [23].

Figure 3

Phonon densities of states of ${}^{57}\mathrm{F}\mathrm{e}$ in the ${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4$ sample. The phonon density of states of all Fe is shown in closed circles. The partial phonon densities of states of the $A$ and $B$ sites obtained experimentally are shown as downward and upward triangles, respectively. Lines are guides for the eye.

Figure 4

Phonon densities of states of Fe in the ideal ${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4$ obtained by ab initio band calculations [27]. The phonon density of states of all Fe is shown as a solid line. The partial phonon densities of states of the $A$ and $B$ sites obtained by the calculations are shown as dashed and dash-dotted lines, respectively.