Deep fractionation of Hf in a solidifying magma ocean and its implications for tungsten isotopic heterogeneities in the mantle

Recent geochemical studies document a wide range of ¹⁸²W anomalies in mantle-derived rocks, the origin of which is unknown. Here we explore the consequences of basal magma ocean crystallization while ¹⁸²Hf was extant. We determine the partition coefficient of Hf between bridgmanite and silicate melt D_Hf throughout the pressure-temperature regime of Earth's lower mantle from first principles molecular dynamics coupled with thermodynamic integration. The calculations are based on Hf⁴⁺ entering the Mg-site, which we show is energetically preferable to the Si-site. We find that D_Hf increases by more than an order of magnitude from 25 GPa to 140 GPa, making Hf much more compatible with increasing pressure. The larger D_Hf at greater depths produces a strong fractionation of ¹⁸²Hf between crystallized bridgmanite and silicate melt. We use a simple geochemical model to show that heterogeneous tungsten anomalies are a natural outcome of the formation and crystallization of a basal magma ocean, with the crystallized products enriched in ¹⁸²W, while the remaining liquid is depleted by a similar amount. Our results show that the observed large variability of ¹⁸²W/¹⁸⁴W in terrestrial samples may be due to the solidification of a basal magma ocean.