Spin-flip scattering of critical quasiparticles and the phase diagram of ${\text{YbRh}}_2{\text{Si}}_2$

Several observed transport and thermodynamic properties of the heavy-fermion compound ${\text{YbRh}}_2{\text{Si}}_2$ in the quantum critical regime are unusual and suggest that the fermionic quasiparticles are critical, characterized by a scale-dependent diverging effective mass. A theory based on the concept of critical quasiparticles scattering off antiferromagnetic spin fluctuations in a strong-coupling regime has been shown to successfully explain the unusual existing data and to predict a number of so far unobserved properties. In this paper, we point out a new feature of a magnetic field-tuned quantum critical point of a heavy-fermion metal: anomalies in the transport and thermodynamic properties caused by the freezing out of spin-flip scattering of critical quasiparticles and the scattering off collective spin excitations. We show a steplike behavior as a function of magnetic field of, e.g., the Hall coefficient and magnetoresistivity results, which accounts quantitatively for the observed behavior of these quantities. That behavior has been described as a crossover line $T^{*}\left(H\right)$ in the $T-H$ phase diagram of ${\text{YbRh}}_2{\text{Si}}_2$. Whereas some authors have interpreted this observation as signaling the breakdown of Kondo screening and an associated abrupt change of the Fermi surface, our results suggest that the $T^{*}$ line may be quantitatively understood within the picture of robust critical quasiparticles.

Figure 1

Renormalized Zeeman splitting $h(T,H)$ at various $T$, in degrees K. The unrenormalized Zeeman splitting $h_0$ is also shown. The magnetic field unit is Tesla and the temperatures are in Kelvin.

Figure 2

Magnetoresistivity $\rho (T,H)$ at various $T$. Clockwise from upper left, $T=18,38,65$, and 100 mK. $H$ is in Tesla and $\rho$ is in $\mu \mathrm{\Omega }\text{cm}$. Dots are theory, Eq. (17); triangles are from the data, Ref. [24].

Figure 3

Hall constant $R_H$ at various $T$. Clockwise from upper left, $T=18,38,65$, and 100 mK. $H$ is in Tesla and $R_H$ is in ${10}^{-10}{\mathrm{m}}^3/\mathrm{C}$. Dots are theory, Eq. (22); triangles are from the data, Ref. [24].

Figure 4

Experimental phase diagram of YRS [28]. In the FL region (blue) the resistivity is $\propto T^2$. NFL denotes the non-Fermi-liquid region where the resistivity varies with $T$ as $T^{\alpha }$ with $\alpha \le 1$. The purple region is where several experimental probes exhibit a crossover behavior, called the $T^{*}$ line. The dots are the theoretical positions of the onset of spin-flip scattering—from quantum fluctuations (yellow) and at higher $(T,H)$, from the spin resonance (red). The red dots at $H<0.1T$ are calculated using unpublished data [27].