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The archetypal $3d$ Mott insulator hematite, Fe$_2$O$_3$, is one of the basicoxide components playing an important role in mineralogy of Earth's lowermantle. Its high pressure-temperature behavior, such as the electronicproperties, equation of state, and phase stability is of fundamental importancefor understanding the properties and evolution of the Earth's interior. Here,we study the electronic structure, magnetic state, and lattice stability ofFe$_2$O$_3$ at ultra-high pressures using the density functional plus dynamicalmean-field theory (DFT+DMFT) approach. In the vicinity of a Mott transition,Fe$_2$O$_3$ is found to exhibit a series of complex electronic, magnetic, andstructural transformations. In particular, it makes a phase transition to ametal with a post-perovskite crystal structure and site-selective local momentsupon compression above 75 GPa. We show that the site-selective phase transitionis accompanied by a charge disproportionation of Fe ions, with Fe$^{3\pm\delta}$ and $\delta \sim 0.05$-$0.09$, implying a complex interplay betweenelectronic correlations and the lattice. Our results suggest thatsite-selective local moments in Fe$_2$O$_3$ persist up to ultra-high pressuresof $\sim$200-250 GPa, i.e., sufficiently above the core-mantle boundary. Thelatter can have important consequences for understanding of the velocity anddensity anomalies in the Earth's lower mantle.

Charge disproportionation and site-selective local magnetic moments in the post-perovskite-type Fe$_2$O$_3$ under ultra-high pressures