O)

Ferropericlase (Fp), (Mg_1-xFe_x)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 large elastic anomalies, and the broad nature of this HS-LS crossover. These theories make extensive use of the quasi-harmonic approximation (QHA), therefore, dynamical and structural stability are essential to the validity of these theories. Here, we investigate the vibrational spectrum of Fp throughout this spin crossover using ab initio DFT+Usc calculations. We address vibrational modes associated with isolated and (2nd) nearest neighbor Fe atoms undergoing the HS-LS state change. As expected, acoustic modes of this solid solution reproduce the well-known elastic anomalies, but optical modes display unusual features. We show that there are no soft phonon modes across this HS-LS crossover and Fp is dynamically stable at all mantle pressures and relevant iron concentrations.