Phonon density of states of Fe${}_2$O${}_3$ across high-pressure structural and electronic transitions

High-pressure phonon density of states (PDOS) of Fe${}_2$O${}_3$ across structural and electronic transitions has been investigated by nuclear resonant inelastic x-ray scattering (NRIXS) and first-principles calculations together with synchrotron Mössbauer, x-ray diffraction, and x-ray emission spectroscopies. Drastic changes in elastic, thermodynamic, and vibrational properties of Fe${}_2$O${}_3$ occur across the Rh${}_2$O${}_3$(II)-type structural transition at 40–50 GPa, whereas the Mott insulator-metal transition occurring after the structural transition only causes nominal changes in the properties of the Fe${}_2$O${}_3$. The observed anomalous mode-softening behavior of the elastic constants is associated with the structural transition at 40–50 GPa, leading to substantial changes in the Debye-like part of the PDOS in the terahertz acoustic phonons. Our experimental and theoretical studies provide new insights into the effects of the structural and electronic transitions in the transition-metal oxide (TMO) compounds.

Figure 1

Representative PDOS of Fe from ${}^{57}$Fe${}_2$O${}_3$ at high pressures. The PDOS spectra are derived from the NRIXS experiments in a high-pressure DAC. Experimental error bars are shown as vertical gray bars.

Figure 2

Elastic, thermodynamic, and vibrational parameters of Fe${}_2$O${}_3$ as a function of pressure obtained from integration of the PDOS. (a) Debye sound velocity; (b) mean force constant, $D_{\mathrm{av}}$; (c) Lamb-Mössbauer factor, $f_{\mathrm{LM}}$; (d) vibrational specific heat, $C_{\mathrm{vib}}$ ($k_B$, Boltzmann constant); (e) vibrational entropy, $S_{\mathrm{vib}}$; (f) characteristic temperature or Lamb-Mössbauer temperature, $T_{\mathrm{LM}}$. We note that these values only represent the contribution of the Fe sublattice in Fe${}_2$O${}_3$. Using the theoretical densities we computed the sound velocities of Fe${}_2$O${}_3$ in the corundum structure at 40 GPa and Rh${}_2$O${}_3$(II) structure at 70 GPa to be 4.7 km/s and 3.8 km/s, respectively.

Figure 3

(Color online) Representative (a) x-ray diffraction and (b) Fe-Kβ x-ray emission patterns of Fe${}_2$O${}_3$ at high pressures. X-ray diffraction spectra confirmed the structural transition from the corundum-type to the Rh${}_2$O${}_3$(II)-type phase at high pressures. The intensity of the satellite K${}_{\beta }$′ peak can be used to understand the electronic spin pairing and metallization in Fe${}_2$O${}_3$. Its intensity remains similar across the structural transition but reduces significantly at higher pressures.

Figure 4

(Color online) (a) Representative synchrotron Mössbauer spectra of Fe${}_2$O${}_3$ at high pressures. Corresponding energy spectra calculated from the fits are shown in the right panels. Red dots: experimental SMS spectra; black lines: modeled spectra. (b) Analyzed hyperfine parameters and percentage of the magnetic phase in high-pressure Fe${}_2$O${}_3$. Up to 55 GPa the only spectral component is that of the low-pressure magnetic phase characterized by the hyperfine field of 51 T, a typical value of the hyperfine field for ionic ferric-oxide bonding. A NM quadrupole-splitting component emerges at approximately 55 GPa, which we assigned as the high-pressure component, coexisting with the low-pressure magnetic-split component. The relative abundance of the low-pressure component continues to decrease until the magnetic collapse is completed at around 75 GPa. We note that the hyperfine field of the magnetic component is slightly reduced by about 10% within the transition.

Figure 5

Projected Fe vibrational PDOS of Fe${}_2$O${}_3$ at high pressure from first-principles calculations. (a) The AFM corundum-type phase at 40 GPa. (b) The theoretical AFM corundum-type phase (black line) and the NM Rh${}_2$O${}_3$(II)-type phase (red line) at 55 GPa. Black lines: corundum-type phase; red lines: Rh${}_2$O${}_3$(II)-type phase. (c) The NM Rh${}_2$O${}_3$(II)-type phase at 75 GPa. The black and red circles in (a) and (c) represent the experimental and theoretical Fe PDOS, respectively.

Figure 6

Calculated phonon dispersive curves (top) and Fe-projected DOS (bottom) of the NM Rh${}_2$O${}_3$ (II) structure of Fe${}_2$O${}_3$ at 55 GPa using the GGA method.

Figure 7

Calculated phonon dispersive curves (top) and Fe-projected DOS (bottom) of the NM Rh${}_2$O${}_3$ (II) structure of Fe${}_2$O${}_3$ at 70 GPa using the GGA method.

Figure 8

Calculated Fe-projected DOS and total DOS of Fe${}_2$O${}_3$ in the corundum structure (top) and Rh${}_2$O${}_3$ (II) structure (bottom).