Short-range order stabilizes a cubic Fe alloy in Earth's inner core

The phase diagram and sound velocities of the Fe-Si binary alloy, crucial for understanding the Earth's core, are determined at inner core boundary pressure with \textit{ab-initio} accuracy through deep-learning-aided hybrid Monte Carlo simulations. A complex phase diagram emerges close to the melting temperature, where a re-entrance of the body-centered cubic (bcc) phase is observed. The bcc structure is stabilized by a pronounced short-range ordering of the Si atoms. The miscibility gap between the short-range ordered bcc structure and the long-range ordered cubic B2 structure shrinks with increasing temperature and the transition becomes continuous above 6000 K. We find that a bcc Fe-Si solid solution reproduces crucial geophysical data such as the low shear sound velocity and the seismic anisotropy of the inner core much better than other structures.