Elasticity of Antiferromagnetic hcp Iron

The thermodynamic properties of the high pressure polymorph of iron (hcp, ǎrepsilon) under compression are an essential component of our understanding of Earth's core, with particular importance of compression behavior and elasticity. While at core pressure the equation of state and bulk moduli from experiment and computational mineral physics agree well, there is considerable discrepancy in compressional and shear elasticity below 100 GPa [1,2]. Using accurate first principles theory we previously [2] found an orthorhombic magnetic ground state for hcp iron (afmII, stable up to ~ 50 GPa) that considerably improves the agreement of the equation of state between experiment and theory. By computing the full elastic constant tensor of the magnetic superstructure (nine independent elastic constants) we evaluate the influence of magnetic correlations on the elasticity of hcp iron. We apply state of the art all electron density functional theory (implemented in the Linearized Augmented Plane Wave method) with a GGA exchange correlation potential, and compute elastic constants from strain energy, relaxing the positions of the atoms in the hcp cell. We find that for afmII both the longitudinal and shear moduli are reduced considerably, resulting in a lower shear modulus over the compression range where afmII is predicted to be stable. This yields overall better agreement in aggregate acoustic properties with experimental studies, although there remains some disagreement in the shear wave velocity. We further find enhanced single crystal anisotropy for the afmII structure over non-magnetic hcp iron. [1] H. K. Mao et al., Nature 396, 741 (1998); ibid. 399, 280 (1999); Science 292, 914 (2001); [2] G. Steinle-Neumann et al., Phys. Rev. B 60, 791 (1999)