Impact of electronic correlations on the equation of state and transport in $\epsilon$-Fe

We have obtained the equilibrium volumes, bulk moduli, and equations of state of the ferromagnetic cubic $\alpha$ and paramagnetic hexagonal $\epsilon$ phases of iron in close agreement with experiment using an ab initio dynamical mean-field-theory approach. The local dynamical correlations are shown to be crucial for a successful description of the ground-state properties of paramagnetic $\epsilon$-Fe. Moreover, they enhance the effective mass of the quasiparticles and reduce their lifetimes across the $\alpha \to \epsilon$ transition, leading to a stepwise increase of the resistivity, as observed in experiment. The calculated magnitude of the jump is significantly underestimated, which points to nonlocal correlations. The implications of our results for the superconductivity and non-Fermi-liquid behavior of $\epsilon$-Fe are discussed.

Figure 1

(a) LDA+DMFT total energy vs volume per atom for bcc (ferromagnetic, solid blue line, and paramagnetic, dot-dashed black line) and hcp (dashed red line) Fe. The error bars are the CT-QMC method stochastic error. The orange long-dash-dotted straight line indicates the common tangent construction for the $\alpha \text{−}\epsilon$ transition. (b) EOS for ferromagnetic bcc (low pressure) and paramagnetic hcp (high pressure) Fe. Theoretical results are obtained by fitting the LDA+DMFT (thick line) and GGA (thin line) total energies using the Birch-Murnaghan EOS [36]. The experimental EOS of iron shown by green squares is from Dewaele et al. [37]. (c) The ratio of lattice parameters $c/a$ of $\epsilon$-Fe vs volume per atom obtained in LDA+DMFT (blue circles, dashed line) and GGA (red squares, solid line). The experimental data are from Dewaele et al. [37] (diamonds) and Glazyrin et al. [21] (pink circles).

Figure 2

The ratio of the average inverse quasiparticle lifetime $\langle \Gamma \rangle$ to temperature (left axis) and the average mass enhancement $\langle m^{*}\rangle /m_0$ (right axis) vs volume per atom. The solid lines (solid symbols) and dashed lines (hatched symbols) are $\langle \Gamma \rangle /T$ and $\langle m^{*}\rangle /m_0$, respectively. The values for bcc and hcp phases are shown by blue squares and red circles, respectively. The black stars indicate the bcc and hcp atomic volumes at the transition point.

Figure 3

The electron-electron contribution to the resistivity in bcc $\alpha$-Fe (black circles) and hcp $\epsilon$-Fe (blue squares) computed within LDA+DMFT for $T=294$ K. The experimental room-temperature resistivity divided by 10 [16] (red triangles, dashed line) is shown. The vertical dashed line indicates the theoretical transition pressure.