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Effects of electron correlations on transport properties of iron at Earth’s core conditions

A Retraction to this article was published on 13 April 2016

This article has been updated

Abstract

Earth’s magnetic field has been thought to arise from thermal convection of molten iron alloy in the outer core, but recent density functional theory calculations have suggested that the conductivity of iron is too high to support thermal convection1,2,3,4, resulting in the investigation of chemically driven convection5,6. These calculations for resistivity were based on electron–phonon scattering. Here we apply self-consistent density functional theory plus dynamical mean-field theory (DFT + DMFT)7 to iron and find that at high temperatures electron–electron scattering is comparable to the electron–phonon scattering, bringing theory into agreement with experiments and solving the transport problem in Earth’s core. The conventional thermal dynamo picture is safe. We find that electron–electron scattering of d electrons is important at high temperatures in transition metals, in contrast to textbook analyses since Mott8,9, and that 4s electron contributions to transport are negligible, in contrast to numerous models used for over fifty years. The DFT+DMFT method should be applicable to other high-temperature systems where electron correlations are important.

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Figure 1: Resistivity versus temperature of hcp iron at Earth’s core density.
Figure 2: Our computed resistivities of hcp iron are compared with experimental results.
Figure 3: Scattering rates, density of states and spectral function at Earth’s core density of hcp iron.

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Acknowledgements

This work is supported by National Science Foundation (NSF) grants EAR-1214807, DMS-1025392, and DMR-1405303. R.E.C. is supported by the Carnegie Institution and the European Research Council Advanced Grant ToMCaT. K.H. is supported by NSF grant DMR-1405303. This research used the NSF Extreme Science and Engineering Discovery Environment (XSEDE) supercomputer ‘Stampede’, and also used the resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US Department of Energy under contract number DE-AC05-00OR22725. R.E.C. and P.Z. thank I. Mazin, S. Labrosse and R. Caracas for discussions. We also acknowledge J. Robb for assistance with the manuscript preparation.

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Authors and Affiliations

Authors

Contributions

R.E.C. designed the project, P.Z. performed the computations, P.Z., R.E.C. and K.H. analysed the results and prepared the paper. The DFT + DMFT code was developed by K.H.

Corresponding author

Correspondence to R. E. Cohen.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Pressure versus temperature relationship of hcp iron at Earth’s core density and along the Hugoniot line31.

The two lines cross at P = 269.9 GPa, T = 6,658 K at Earth’s core density.

Extended Data Figure 2 Extrapolation of ImΣ(n) to zero imaginary frequency.

The self-energy is from the orbital of hcp iron at Earth’s core density and 6,000 K. Three extrapolation methods are used: linear, cubic spline and Akima spline. The imaginary part of self-energy at i0+ ranges from −0.23 eV to −0.12 eV.

Extended Data Figure 3 The imaginary part of self-energies in real frequency on the orbital of hcp iron at Earth’s core density and 6,000 K.

The self-energies are from three analytic continuation methods: MaxEnt, Padé and singular value decomposition. The inset shows the same imaginary part of self-energies in energy range [−0.01 eV, 0.01 eV] around the Fermi level. The self-energies from three analytic continuation methods agree at the low-energy region.

Extended Data Table 1 Resistivities from extrapolations and previous experiments
Extended Data Table 2 The atomic volumes, pressures, temperatures and resistivities from our study in Fig. 1 and Fig. 2

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Zhang, P., Cohen, R. & Haule, K. Effects of electron correlations on transport properties of iron at Earth’s core conditions. Nature 517, 605–607 (2015). https://doi.org/10.1038/nature14090

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