Magnetic-Field Induced Quantum Critical Point in $\mathrm{Y}\mathrm{b}\mathrm{R}{\mathrm{h}}_{\mathrm{2}}\mathrm{S}{\mathrm{i}}_{\mathrm{2}}$

We report low-temperature calorimetric, magnetic, and resistivity measurements on the antiferromagnetic (AF) heavy-fermion metal ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2{\mathrm{S}\mathrm{i}}_2$ ($T_N=70\mathrm{m}\mathrm{K}$) as a function of magnetic field $B$. While for fields exceeding the critical value $B_{c0}$ at which $T_N\to 0$ the low-temperature resistivity shows an $A{T}^2$ dependence, a $1/(B-B_{c0})$ divergence of $A\left(B\right)$ upon reducing $B$ to $B_{c0}$ suggests singular scattering at the whole Fermi surface and a divergence of the heavy quasiparticle mass. The observations are interpreted in terms of a new type of quantum critical point separating a weakly AF ordered from a weakly polarized heavy Landau-Fermi liquid state.

Figure 1

Low-temperature ac susceptibility ${\chi }_{\mathrm{a}\mathrm{c}}$ of ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2{\mathrm{S}\mathrm{i}}_2$ at varying fields applied perpendicular to the $c$ axis (a) and isothermal dc magnetization $M_{\mathrm{d}\mathrm{c}}$ at varying temperatures in magnetic fields applied along and perpendicular to the $c$ axis. Arrows indicate critical fields $B_{c0}$.

Figure 2

Low-temperature electrical resistivity of ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2{\mathrm{S}\mathrm{i}}_2$ at varying magnetic fields applied along the $a$ axis (a) and the $c$ axis (b). For clarity the different curves in $B>0$ were shifted subsequently by $0.1\mu \Omega \mathrm{c}\mathrm{m}$. Up- and downraising arrows indicate $T_N$ and the upper limit of $T^2$ behavior, respectively. Dotted and solid lines represent $\Delta \rho \sim T^{\epsilon }$ with $\epsilon =1$ and $2$, respectively.

Figure 3

Specific heat as $\Delta C/T=(C-C_Q)/T$ vs $T$ (on a logarithmic scale) for ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2{\mathrm{S}\mathrm{i}}_2$ at varying fields applied parallel to the $c$ axis. $C_Q\sim T^{-2}$ is the nuclear quadrupole contribution calculated from recent Mössbauer results [15].

Figure 4

$T\text{−}B$ phase diagram for ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2{\mathrm{S}\mathrm{i}}_2$ with $T_N$ as derived from $d\rho /dT$ vs $T$ and $T^{*}$, the upper limit of the $\Delta \rho =A{T}^2$ behavior, as a function of magnetic field, applied both along and perpendicular to the $c$ axis. For the latter ones the $B$ values have been multiplied by a factor of 11. Lines separating the antiferromagnetic (AF), non-Fermi liquid (NFL), and Landau Fermi liquid (LFL) phase are guides to the eye. Note that the AF phase transition as a function of field is a continuous one cf. $M_{\mathrm{d}\mathrm{c}}\left(B\right)$ curves in Fig. 1b.

Figure 5

Coefficient $A=\Delta \rho /T^2$ vs field $B$. Data for $B$ perpendicular to the $c$ direction have been multiplied by 11. Dashed line marks $B_{c0}$, and solid line represents $(B-B_{c0}{)}^{-1}$. Inset shows double-$\log \text{\hspace{0.17em}︀}$ plot of $A$ vs ${\gamma }_0$ and $A$ vs ${\chi }_0$ for different magnetic fields. Solid lines represent $A/{\gamma }_0^2=5.8\times {10}^{-6}\mu \Omega \mathrm{c}\mathrm{m}(\mathrm{K}\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}/\mathrm{m}\mathrm{J}{)}^2$ and $A/{\chi }_0^2=1.25\times {10}^{12}\mu \Omega \mathrm{c}\mathrm{m}{\mathrm{K}}^{-2}/({\mathrm{m}}^3/\mathrm{m}\mathrm{o}\mathrm{l}{)}^2$.