The electronic and thermal transport properties of the Earths core are crucial for many geophysical models such as the geodynamo model of the Earths magnetic field and of its reversals. Here we show, by considering bcc-iron and iron-rich iron-silicon alloy as a representative of the Earths core composition and applying the first-principles modeling that the spin disorder at the Earths core conditions provides an essential contribution, of order 20~$muOmega$,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 in 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 non-magnetic. 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.
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