Metallic State in Cubic FeGe Beyond Its Quantum Phase Transition

We report on results of electrical resistivity and structural investigations on the cubic modification of FeGe under high pressure. The long-wavelength helical order ($T_C=280\mathrm{K}$) is suppressed at a critical pressure $p_c\approx 19\mathrm{GPa}$. An anomaly at $T_X(p)$ and strong deviations from a Fermi-liquid behavior in a wide pressure range above $p_c$ suggest that the suppression of $T_C$ disagrees with the standard notion of a quantum critical phase transition. The metallic ground state persisting at high pressure can be described by band-structure calculations if zero-point motion is included. The shortest FeGe interatomic distance display discontinuous changes in the pressure dependence close to the $T_C(p)$ phase line.

Figure 1

Nonphononic contribution to the electrical resistivity in cubic FeGe, $\rho -{\rho }_{\mathrm{ph}}$. The onset of different spiral magnetic ordering at $T_C$ and $T_2$ leads to anomalies in $\rho (T)$, indicated by the symbols. The nature of the anomaly at $T_X$ is not known. Inset: ($T$, $p$) phase diagram of cubic FeGe.

Figure 2

Pressure-dependence of the resistivity parameters $A^{*}$, $n$, and ${\rho }_0$ in cubic FeGe. For comparison, MnSi data for $A^{*}$ and $n$ taken from Ref. 12 are included but shifted by $\Delta p=17.3\mathrm{GPa}$ to match $p_c$ of FeGe.

Figure 3

Pressure dependence of the Fe-Ge distance $d_1$ at 82 K (left scale) and 230 K (right scale) in cubic FeGe. Lines are fits to the data and error bars represent 3 times the standard deviation. The vertical arrows indicate the onset of the anomaly in $d_1(p)$. Inset: $V(p)$ data and fit for $T=82\mathrm{K}$.

Figure 4

(a) ($T$, $V$) phase diagram of cubic FeGe obtained from $\rho (T)$ and structural data (triangles). The $T_2$ data point (circle) at zero compression is taken from Ref. 15. $T_C[V(x)]$ data on ${\mathrm{FeSi}}_{1-x}{\mathrm{Ge}}_x$ (diamonds) are taken from Ref. 3, 27. (b) Calculated magnetization $m_{\mathrm{calc}}$ with and without zero-point motion (bold and open symbols, respectively).