Minimal model of the magnetically induced metal-insulator transition: Finite-temperature properties

An unconventional type of metal-insulator transition is realized in the FeSi${}_{1-x}$Ge${}_x$ alloys which is driven by the magnetic instability of the paramagnetic insulator. Recently, a minimal model for this type of transition has been introduced and studied in the limit of vanishing temperature. Here we explore the finite-temperature properties of the minimal model in the mean-field approximation. We show that the predictions of the model are in qualitative agreement with experimental data on FeSi${}_{1-x}$Ge${}_x$ and on FeGe under pressure.

Figure 1

fcc lattice with two inequivalent types of sites. Black and white sites correspond to $\lambda =1$ and $\lambda =2,3,4$, respectively. The on-site lattice potential on the black sites is lower than on the white sites.

Figure 2

Finite-temperature phase diagram of the minimal model along the line defined by Eq. (2). The dotted line shows the locations of the maxima in the temperature dependence of the uniform susceptibility $\chi$ in the paramagnetic state.

Figure 3

Magnetic susceptibility $\chi$ (top panel), electronic compressibility $\kappa$ (middle panel), and specific heat $c$ (bottom panel) as functions of temperature for several values of $U$. Note that for $U/t=3.5$ the system is already ferromagnetic and its susceptibility $\chi$ diverges as $T\to 0$.

Figure 4

A detailed view of the same observables as in Fig. 3 for $U\sim U_c$ in the limit of low temperatures.

Figure 5

Optical conductivity $\sigma \left(\omega \right)$ of the minimal model for $U/t=3.4$ at several temperatures. The inset shows the restricted sum-rule function $\mathcal{N}\left(\omega \right)$ for the same parameters. Both $\sigma \left(\omega \right)$ and $\mathcal{N}\left(\omega \right)$ are plotted in arbitrary units.

Figure 6

Magnetization $m$ as a function of temperature for several values of $U/t$.

Figure 7

Fluctuating moment $S$ and the low-temperature ordered moment $m\left(0\right)$ as functions of $U/t$. The inset shows the fit of ${\chi }^{-1}\left(T\right)$ for $U/t=7.5$ making use of Eq. (12).

Figure 8

Fermi volume $\Omega$ (see text), electronic compressibility $\kappa \left(0\right)$, density of states at the Fermi level $N\left(0\right)$, the Landau compressibility parameter $F_0^s$, and the Drude weight $D$ measured in units of $\frac{3t{e}^2}{{\hslash }^{2}a}$ in the metallic state as functions of $U/t$ for $T/t=0.002$.