Phonon dispersion throughout the iron spin crossover in ferropericlase

Ferropericlase (Fp), $\left({\mathrm{Mg}}_{1-x}{\mathrm{Fe}}_x\right)\mathrm{O}$, is the second most abundant phase in the Earth's lower mantle. At relevant pressure-temperature conditions, iron in Fp undergoes a high spin (HS), S = 2, to low spin (LS), S = 0, state change. The nature of this phenomenon is quite well understood now, but there are still basic questions regarding the structural stability and the existence of soft phonon modes during this iron state change. General theories exist to explain the volume reduction, the significant thermoelastic anomalies, and the broad nature of this HS-LS crossover. These theories make extensive use of the quasiharmonic approximation. Therefore, dynamical and structural stability is essential to their validity. Here, we investigate the vibrational spectrum of Fp throughout this spin crossover using ab initio density-functional theory $+U_{\mathrm{sc}}$ calculations. We address vibrational modes associated with isolated and (second-)nearest-neighbor iron ions undergoing the HS-LS state change. As expected, acoustic modes of this solid solution are resilient, while optical modes are the most affected. We show that there are no soft phonon modes across this HS-LS crossover, and Fp is dynamically stable at all relevant pressures.

Figure 1

Supercell structures used in the calculations of phonon dispersions. Red, orange, and blue spheres represent oxygen, magnesium, and iron, respectively.

Figure 2

Predominant $d$ level splitting diagrams for $\mathrm{F}{\mathrm{e}}^{2+}$ in an octahedral site (a) in the high spin (HS) state and (b) in the low spin (LS) state.

Figure 3

Electron density isosurfaces for the (a) majority and (b) minority electrons in the HS and in the (c) LS states in iron in the $3d^6$ electronic configuration.

Figure 4

Enthalpy difference between HS and LS states for ${\mathrm{Mg}}_x{\mathrm{Fe}}_{1-x}\mathrm{O}$. The transition pressure is ∼70 ($\pm 3$) GPa in this calculation.

Figure 5

Total energy vs Fe-O bond-length change in Fp with $X_{Fe}=3\%$ showing a highly quadratic behavior. The HS state at 0 GPa is used as a reference.

Figure 6

Phonon dispersions in 3Fp for the atomic configuration shown in Fig. 1 (64 atoms supercell) unfolded in the first Brillouin zone of the face-centered primitive cell of MgO. These dispersions are compared with the phonon dispersion of MgO (dashed black lines). There are no phonon instabilities in the low-pressure HS state up to 135 GPa or in the high-pressure LS state down to 0 GPa.

Figure 7

6Fp phonon dispersion for HS, LS, and MS (HS-LS) states in the 2nn [Fig. 1] and 11nn [Fig. 1] configurations unfolded into the BZ of the B1-type structure.

Figure 8

Total and partial vibrational density of states of 6Fp for all configurations investigated compared to that of pristine MgO at 60 GPa.