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Register a new userElectronic correlations in dense iron: from moderate pressure to Earths core conditions
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Leonid V. Pourovskii
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We discuss the role of dynamical many-electron effects in the physics of iron and iron-rich solid alloys under applied pressure on the basis of recent ab initio studies employing the dynamical mean-field theory (DMFT). Electronic correlations in iron in the moderate pressure range up to 60 GPa are discussed in the first section. DMFT-based methods predict an enhancement of electronic correlations at the pressure-induced transition from body-centered cubic (bcc) alpha-Fe to hexagonal close-packed (hcp) epsilon-Fe. In particular, the electronic effective mass, scattering rate and electron-electron contribution to the electrical resistivity undergo a step-wise increase at the transition point. One also finds a significant many-body correction to the epsilon-Fe equation of state, thus clarifying the origin of discrepancies between previous DFT studies and experiment. An electronic topological transition is predicted to be induced in epsilon-Fe by many-electron effects; its experimental signatures are analyzed. Next section focuses on the geophysically relevant pressure-temperature regime of the Earths inner core (EIC) corresponding to the extreme pressure of 360 GPa combined with temperatures up to 6000 K. The three iron allotropes (bcc, hcp and face-centered-cubic) previously proposed as possible stable phases at such conditions are found to exhibit qualitatively different many-electron effects as evidenced by a strongly non-Fermi-liquid metallic state of bcc-Fe and an almost perfect Fermi liquid in the case of hcp-Fe. A recent active discussion on the electronic state and transport properties of hcp-Fe at the EIC conditions is reviewed in details. We also discuss the impact of a Ni admixture, which is expected to be present in the core matter. We conclude by outlining some limitation of the present DMFT-based framework and perspective directions for further development.
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The transport properties of iron under Earths inner core conditions are essential input for the geophysical modelling but are poorly constrained experimentally. Here we show that the thermal and electrical conductivity of iron at those conditions remains high even if the electron-electron-scattering (EES) is properly taken into account. This result is obtained by ab initio simulations taking into account consistently both thermal disorder and electronic correlations. Thermal disorder suppresses the non-Fermi-liquid behavior of the body-centered cubic iron phase, hence, reducing the EES; the total calculated thermal conductivity of this phase is 220 Wm$^{-1}$K$^{-1}$ with the EES reduction not exceeding 20%. The EES and electron-lattice scattering are intertwined resulting in breaking of the Matthiessens rule with increasing EES. In the hexagonal close-packed iron the EES is also not increased by thermal disorder and remains weak. Our main finding thus holds for the both likely iron phases in the inner core.
Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d- or f-orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of little relevance to strongly correlated materials. Here we show that it represents, instead, the underlying physical mechanism in two of the most important ferromagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on the magnetism. As a result, the electron-electron scattering rate is linear in temperature, in violation of the conventional Landau theory of metals. This is true even at Earths core pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of geomagnetism may have therefore to be reconsidered.
The electronic state and transport properties of hot dense iron are of the utmost importance to geophysics. Combining the density functional and dynamical mean field theories we study the impact of electron correlations on electrical and thermal resistivity of hexagonal close-packed $epsilon$-Fe at Earths core conditions. $epsilon$-Fe is found to behave as a nearly perfect Fermi liquid. The quadratic dependence of the scattering rate in Fermi liquids leads to a modification of the Wiedemann-Franz law with suppression of the thermal conductivity as compared to the electrical one. This significantly increases the electron-electron thermal resistivity which is found to be of comparable magnitude to the electron-phonon one. The implications of this effect on the dynamics of Earths core is discussed.
We employ state-of-the-art ab initio simulations within the dynamical mean-field theory to study three likely phases of iron (hexogonal close-packed, hcp, face centered cubic, fcc, and body centered cubic, bcc) at the Earths core conditions. We demonstrate that the correction to the electronic free energy due to correlations can be significant for the relative stability of the phases. The strongest effect is observed in bcc Fe, which shows a non-Fermi liquid behaviour, and where a Curie-Weiss behaviour of the uniform susceptbility hints at a local magnetic moment still existing at 5800 K and 300 GPa. We predict that all three structures have sufficiently high magnetic susceptibility to stabilize the geodynamo.
We have studied the body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) phases of Fe alloyed with 25 at. % of Ni at Earths core conditions using an ab initio local density approximation + dynamical mean-field theory (LDA+DMFT) approach. The alloys have been modeled by ordered crystal structures based on the bcc, fcc, and hcp unit cells with minimum possible cell size allowing for the proper composition. Our calculations demonstrate that the strength of electronic correlations on the Fe 3d shell is highly sensitive to the phase and local environment. In the bcc phase the 3d electrons at the Fe site with Fe only nearest neighbors remain rather strongly correlated even at extreme pressure-temperature conditions, with the local and uniform magnetic susceptibility exhibiting a Curie-Weiss-like temperature evolution and the quasi-particle lifetime {Gamma} featuring a non-Fermi-liquid temperature dependence. In contrast, for the corresponding Fe site in the hcp phase we predict a weakly-correlated Fermi-liquid state with a temperature-independent local susceptibility and a quadratic temperature dependence of {Gamma}. The iron sites with nickel atoms in the local environment exhibit behavior in the range between those two extreme cases, with the strength of correlations gradually increasing along the hcp-fcc-bcc sequence. Further, the inter-site magnetic interactions in the bcc and hcp phases are also strongly affected by the presence of Ni nearest neighbors. The sensitivity to the local environment is related to modifications of the Fe partial density of states due to mixing with Ni 3d-states.
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