Physicists retract Nature paper on Earth’s core after findings aren’t reproducible

Physicists have retracted a highly cited paper from Nature on the behavior of electrons at the center of the Earth after other researchers could not reproduce their findings.

The 2015 paper earned coverage in Science News and Live Science, where co-author Ronald Cohen explained:

There was a big problem in how you generate a magnetic field, and now, because of our results, that problem has basically gone away.

Here are more details about what the original paper claimed, courtesy of a press release from The Carnegie Institution for Science, where co-authors Peng Zhang and Cohen work:

The center of the Earth is very hot, and the flow of heat from the planet’s center towards the surface is thought to drive most of the dynamics of the Earth, ranging from volcanoes to plate tectonics. It has long been thought that heat flow drives what is called thermal convection — the hottest liquid becomes less dense and rises, as the cooler, more-dense liquid sinks — in Earth’s liquid iron core and generates Earth’s magnetic field. But recent calculations called this theory into question, launching new quests for its explanation.

In their work, Cohen and Zhang, along with Kristjan Haule of Rutgers University, used a new computational physics method and found that the original thermal convection theory was right all along. Their conclusion hinges on discovering that the classic theory of metals developed in the 1930’s was incomplete.

The retraction note for “Effects of electron correlations on transport properties of iron at Earth’s core conditions” explains the error that felled that conclusion:

In this Letter we reported density functional theory plus dynamical mean-field theory (DFT + DMFT) computations of the resistivity from electron–electron scattering at the conditions of Earth’s core, and found that the electron–electron scattering was about the same magnitude as the conventional electron–phonon scattering, giving a total resistivity that was sufficient to allow a classical thermal-convection-driven dynamo. However, L. Pourovskii, J. Mravlje, S. Simak and I. Abrikosov could not reproduce our findings, which led us to re-examine our computations. We found an error of a factor of two that is due to our neglect of spin degeneracy (two electrons per band), which would halve the electron–electron resistivity and probably make the electron–electron scattering insignificant for the geodynamo, at least for pure iron. We therefore wish to retract this Letter.

The smaller electron–electron scattering supports the high conductivity of iron that was predicted¹from electron–phonon density functional calculations. However, preliminary calculations show that using the exact double counting² recently developed for the DFT + DMFT method increases the electron–electron scattering. It is also probable that the Wiedemann–Franz law, assumed in our previous work, is not followed or has a non-constant Lorenz number in liquid metals³ or correlated systems⁴. Whether the resulting conductivity is consistent with a geodynamo driven by thermal convection requires further detailed calculations; the results will be reported elsewhere. The results and conclusions in the Letter that refer to resistivity at low temperatures (in Fig. 2b), and scattering rate and electronic structure (in Fig. 3) remain valid.

The paper has been cited 17 times, according to Thomson Reuters Web of Science.

We always appreciate it when authors are transparent about what exactly went wrong and act promptly to fix the record, so we’re designating this an example of “doing the right thing.”

This isn’t the first time the authors have had to correct the record — we’ve found six corrections for Cohen, which note typographical errors and issues with calculations, for example:

• “Giant Electrocaloric Effect Around Tc,” published in Physical Review Letters and cited 34 times, has two corrections. One correction notes an error in the science in one of the figures; the other reports an omission in the acknowledgements.
• “Phase stability of wustite at high pressure from first-principles linearized augmented plane-wave calculations,” published in Physical Review B and cited 49 times. The correction explains that the “proposed phase diagram for FeO (Fig. 8) was confusing and should be replaced.”
• “Tight-binding computations of elastic anisotropy of Fe, Xe, and Si under compression,” published in Physical Review B and cited 78 times. The correction provides some terms from a model that “were not properly presented in our paper, though they were properly coded and all of the results are unchanged.”
• “First-principles elastic constants for the hcp transition metals Fe, Co, and Re at high pressure,” published in Physical Review B and cited 234 times. According to the correction: “In plotting the magnetic moments for the antiferromagnetic phases of hcp iron the magnetic moments were divided by two.”
• “Ab initio linear response and frozen phonons for the relaxor PbMg1/3Nb2/3O3,” published in Physical Review B and cited 36 times. The correction is for two typographical errors.

Last author Kristjan Haule has two corrections:

• “Fractional power-law behavior and its origin in iron-chalcogenide and ruthenate superconductors: Insights from first-principles calculations,” published in Physical Review B and cited 29 times. The correction notes an error in a sentence in the abstract, and in one of the references.
• “Kinetic frustration and the nature of the magnetic and paramagnetic states in iron pnictides and iron chalcogenides,” published in Nature Materials and cited 187 times — making it a highly cited paper — has a correction for a compound that was mislabeled in two figures. (The correction can be found at the end of the paper.)

We’ve reached out to Haule and Cohen, and will update this post with anything else we learn.

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