Transport properties of iron at Earth's core conditions: The effect of spin disorder

The electronic and thermal transport properties of the Earth's core are crucial for many geophysical models such as the geodynamo model of the Earth's magnetic field and of its reversals. Here we show, by considering bcc iron and an iron-rich iron-silicon alloy as a representative of the Earth's core composition and applying first-principles modeling, that the spin disorder at the Earth's core conditions not considered previously provides an essential contribution, of order 20 $\mu \mathrm{\Omega }$ cm, to the electrical resistivity. This value is comparable in magnitude with the electron-phonon and with the recently estimated electron-electron scattering contributions. The origin of the spin-disorder resistivity (SDR) consists of the existence of fluctuating local moments that are stabilized at high temperatures by the magnetic entropy even at pressures at which the ground state of iron is nonmagnetic. We find that electron-phonon and SDR contributions are not additive at high temperatures. We thus observe a large violation of the Matthiessen rule, not common in conventional metallic alloys at ambient conditions.

Figure 1

Fluctuating values of the local Fe moment $|m_{\mathrm{Fe}}|$ in bcc iron as a function of the temperature for the Earth's core atomic volume (Wigner-Seitz radius is 2.25 bohrs): (i) the LSF model [13] (empty circles) and (ii) the present DLM-FSM model (full circles).

Figure 2

Calculated SDR in bcc Fe as a function of the temperature for the same atomic volume as in Fig. 1 with fluctuating local moments obtained from the DLM-FSM model.

Figure 3

The resistivity due to phonons as a function of the rms displacement $\sqrt{\langle u^2\rangle }$ calculated for a model based on the multicomponent CPA [20, 31] for the Earth's core conditions. (a) Ideal bcc Fe with phonons only (filled circles), with phonons and the SDR contribution for $T=5500$ K calculated including both effects together on equal footing (filled triangles), and assuming the validity of the Matthiessen rule (empty circles). (b) Disordered bcc ${\mathrm{Fe}}_{0.92}{\mathrm{Si}}_{0.08}$ alloy with phonons only (filled circles), with phonons and the SDR contribution for $T=5500$ K including both effects together with alloy disorder on equal footing (filled triangles).