Field-Induced Quantum Critical Point in ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}}_5$

The resistivity of the heavy-fermion superconductor ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}}_5$ was measured as a function of temperature, down to 25 mK and in magnetic fields of up to 16 T applied perpendicular to the basal plane. With increasing field, we observe a suppression of the non-Fermi liquid behavior, $\rho \sim T$, and the development of a Fermi liquid state, with its characteristic $\rho ={\rho }_0+A{T}^2$ dependence. The field dependence of the $T^2$ coefficient shows critical behavior with an exponent of 1.37. This is evidence for a field-induced quantum critical point (QCP), occurring at a critical field which coincides, within experimental accuracy, with the superconducting critical field $H_{c2}$. We discuss the relation of this field-tuned QCP to a change in the magnetic state, seen as a change in magnetoresistance from positive to negative, at a crossover line that has a common border with the superconducting region below $\sim 1\mathrm{K}$.

Figure 1

Resistivity of ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}}_5$ under various fields, shown (a) for $H=0$, 6, and 16 T, (b) as magnetoresistance versus temperature, normalized to zero field resistivity, and (c) versus applied field, as isotherms for $T=16$, 14.5, 13, 11.5, 10, 8.5, 7, 5.5, 4, 2.5, 2.25, 2, 1.5, 1, 0.5, 0.3, and 0.1 K from top to bottom (lines are guides to the eye and are not offset). The arrows in (c) indicate the position of the crossover from positive to negative MR with increasing field for each temperature.

Figure 2

Low temperature resistivity of ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}}_5$ plotted vs $T^2$ for several magnetic fields, with an inset showing low temperature data (data sets are offset for clarity in both figures). The solid lines are linear fits to the data, showing the behavior of the quadratic-term coefficient (slope) under applied field, with arrows indicating the upper limit of the temperature range of $T^2$ behavior.

Figure 3

$H\mathrm{\text{−}}T$ phase diagram of ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}}_5$ determined from resistivity measurements, including the upper bound of $T^2$ resistivity (■), the position of the MR maximum (●), and $H_{c2}$ determined by resistivity $H$ and $T$ sweeps (▲), which agrees with specific heat (○) and resistivity (△) measurements from Ref. 2. The hatched lines indicate the crossover boundaries between FL and NFL (negative and positive MR) regimes, as explained in the text. The inset shows the field dependence of the quadratic coefficient $A$ of $\rho (T)$ [the solid line is a fit of the data points ($\mathbf{+}$) to the displayed formula].