Evidence for a Non-Fermi-Liquid Phase in Ge-Substituted ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$

The canonical view of heavy fermion quantum criticality assumes a single quantum critical point separating the paramagnet from the antiferromagnet. However, recent experiments on Yb-based heavy fermion compounds suggest the presence of non-Fermi liquid behavior over a finite zero-temperature region. Using detailed susceptibility and transport measurements we show that the classic quantum critical system, Ge-substituted ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, also displays such behavior. We advance arguments that this is not due to a disorder-smeared quantum critical point, but represents a new class of metallic phase.

Figure 1

Electrical resistivity of ${\mathrm{YbRh}}_2({\mathrm{Si}}_{0.95}{\mathrm{Ge}}_{0.05}{)}_2$. (a) Low-$T$ resistivity for various $B\parallel c$. For clarity, curves at $B>0$ are shifted by $0.2\mu \Omega \mathrm{cm}$ with respect to each other. Below $T_{\mathrm{LFL}}$, LFL behavior is recovered. Inset: Shaded area depicts region of LFL behavior determined from $\rho (T)$. The $T_{\mathrm{LFL}}$ line is a polynomial fit and serves as guide-to-the-eye. (b) Scaled isothermal magnetoresistance for $B\perp c$ (${\rho }_0=4.51\mu \Omega \mathrm{cm}$). Data for pure ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ (open symbols, ${\rho }_0=1.81\mu \Omega \mathrm{cm}$) are shown for comparison. (c) Isothermal magnetoresistance for $B\parallel c$. The arrows denoted by $B_{\mathrm{infl}}$ mark the inflection points [16] of the fits to the data [dashed lines in (b) and (c)] using the crossover function introduced in Ref. 15.

Figure 2

Ac susceptibility of ${\mathrm{YbRh}}_2({\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x{)}_2$ for $x=0.05$ (●) and, for comparison, for $x=0$ (○). Inset: Positions of the maxima in iso-$B$ ${\chi }_{\mathrm{ac}}(T)$ curves (circles) and of the inflection points [16] $B_{\mathrm{infl}}$ of $\rho (B)$ isotherms (diamonds) of both samples. The power law $(B-B_c{)}^{0.75}$ (solid line) with $B_c=0.06\mathrm{T}$ is a good description of all data points.

Figure 3

Phase diagram of ${\mathrm{YbRh}}_2({\mathrm{Si}}_{0.95}{\mathrm{Ge}}_{0.05}{)}_2$ for $B\parallel c$. Symbols represent $B_{\mathrm{infl}}$ (◆) and the upper boundary of LFL behavior (▼). The dashed $T_{\mathrm{LFL}}$ line is the polynomial fit shown in the inset of Fig. 1a. Data points from measurements with $B\perp c$ are included by multiplying $B$ with the factor 11: ⋄ symbolizes $B_{\mathrm{infl}}$, ○ displays $T_{\max }$ from ${\chi }_{\mathrm{ac}}(T)$. The solid $T^{*}$ line is taken from the inset of Fig. 2. Hexagons represent $T^{*}$ [16] (or $T_{\mathrm{Hall}}$ [15]) of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$. ■ marks $T_N$ observed by specific heat. The dotted $T_N$ line indicates the typical evolution of $T_N$ for ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, $T_N(B)=T_N(0)(1-B/B_c{)}^{0.36}$ [9], using the respective parameters for ${\mathrm{YbRh}}_2({\mathrm{Si}}_{0.95}{\mathrm{Ge}}_{0.05}{)}_2$ ($T_N(0)=18\mathrm{mK}$, $B_c=11\times B_c^{\perp c}\approx 0.3\mathrm{T}$) [12]. The hatched area $0.3\mathrm{T}\le B\le 0.66\mathrm{T}$ marks the zero $T$ NFL phase characterized by $\Delta \rho \sim T$. The inset compares the evolution of the resistivity exponent $\epsilon$, derived from the dependence $(\rho -{\rho }_0)\sim T^{\epsilon }$ (see also Ref. 12), for ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ (top) and ${\mathrm{YbRh}}_2({\mathrm{Si}}_{0.95}{\mathrm{Ge}}_{0.05}{)}_2$ (bottom) in the same $B$ and $T$ range.

Figure 4

Generic phase diagram displaying the combined effects of Kondo coupling ($K$) and magnetic frustration, or quantum zero-point motion ($Q$). For the location of compounds in the phase diagram (red crosses), see text.