Importance of Correlation Effects in hcp Iron Revealed by a Pressure-Induced Electronic Topological Transition

We discover that hcp phases of Fe and ${\mathrm{Fe}}_{0.9}{\mathrm{Ni}}_{0.1}$ undergo an electronic topological transition at pressures of about 40 GPa. This topological change of the Fermi surface manifests itself through anomalous behavior of the Debye sound velocity, $c/a$ lattice parameter ratio, and Mössbauer center shift observed in our experiments. First-principles simulations within the dynamic mean field approach demonstrate that the transition is induced by many-electron effects. It is absent in one-electron calculations and represents a clear signature of correlation effects in hcp Fe.

Figure 1

Debye sound velocity $V_D$ as a function of pressure for pure iron (closed black squares) and ${\mathrm{Fe}}_{0.9}{\mathrm{Ni}}_{0.1}$ alloy (open triangles). The upper axis shows the density scale. Also shown are literature data on sound velocities obtained with NIS (open circles [20] and half-filled circles [21]), and impulsive stimulated light scattering measurements [22] (circles with crosses) for pure $\epsilon$-Fe, as well as NIS data [23] for $\epsilon \mathrm{\text{−}}{\mathrm{Fe}}_{0.92}{\mathrm{Ni}}_{0.08}$ (blue open squares). Experimental data presented in the figure show the softening of $V_D$ in a pressure region of 42–52 GPa.

Figure 2

Experimental pressure dependence of (a) the hcp phase lattice parameter $c/a$ ratio and (b) the Mössbauer center shift based on several experimental data sets for pure iron (red circles) and for ${\mathrm{Fe}}_{0.9}{\mathrm{Ni}}_{0.1}$ alloy (blue circles). The center shift values are given relative to pure bcc iron. Straight gray lines in (a) are guides for the eye.

Figure 3

The $\mathrm{LDA}+\mathrm{DMFT}$ $\mathit{k}$-resolved spectral function $A(\mathit{k},E)$ (in $V_{\mathrm{at}}/\mathrm{eV}$, where $V_{\mathrm{at}}$ is the volume per atom) of hcp Fe at volumes of $8.9{\AA }^3/\mathrm{at}$ (a) and $10.4{\AA }^3/\mathrm{at}$ (b) corresponding to pressures of 69 and 15.4 GPa, respectively. The energy zero is taken at the Fermi level. The holelike bands at the $\mathbf{\Gamma }$ and $\mathbf{L}$ points at volume $8.9{\AA }^3/\mathrm{at}$. (indicated by the white arrows) are below $E_F$ at $V=10.4{\AA }^3/\mathrm{at}$. The corresponding LDA band structures are shown in (c) and (d), respectively. In (e) and (f) the corresponding $\mathrm{LDA}+\mathrm{DMFT}$ Fermi surfaces are shown for the same volumes. The full Fermi surface is plotted on the left-hand side and its cut along the $\mathbf{\Gamma }\mathrm{\text{−}}\mathbf{M}$ direction is displayed in the right-hand side. Changes of the FS topology around the $\mathbf{L}$ and $\mathbf{\Gamma }$ points are clearly seen.