Search for pressure-induced quantum criticality in YbFe${}_2$Zn${}_{20}$

Electrical transport measurements of the heavy-fermion compound YbFe${}_2$Zn${}_{20}$ were carried out under pressures up to 8.23 GPa and down to temperatures of nearly 0.3 K. The pressure dependence of the low-temperature Fermi-liquid state was assessed by fitting $\rho \left(T\right)={\rho }_0+A{T}^n$ with $n=2$ for $T<T_{\mathrm{FL}}$. Power-law analysis of the low-temperature resistivities indicates $n=2$ over a broad temperature range for $P\lesssim 5$ GPa. However, at higher pressures, the quadratic temperature dependence is only seen at the very lowest temperatures, and instead shows a wider range of $n<2$ power-law behavior in the low-temperature resistivities. As pressure was increased, $T_{\mathrm{FL}}$ diminished from $\sim$11 K at ambient pressure to $\sim$0.6 K at 8.23 GPa. Over the same pressure range, the $A$ parameter increased dramatically with a functional form of $A\propto {(P-P_{\mathrm{c}})}^{-2}$ with $P_{\mathrm{c}}\simeq 9.8$ GPa being the critical pressure for a possible quantum critical point.

Figure 1

Temperature dependent resistivity measurement of YbFe${}_2$Zn${}_{20}$ under pressure using a piston cylinder cell are shown up to 50 K for pressures up to 2.03 GPa. Inset: Full temperature range of the resistivity at ambient pressure and 2.03 GPa. The high-temperature region shows typical metallic behavior with a near-linear dependence on temperature.

Figure 2

Low temperature resistivity measurements under pressure using a modified Bridgman anvil cell with 1 : 1 n-pentane : iso-pentane as the liquid pressure medium, reaching a maximum pressure of 5.14 GPa. Inset: Resistivity curves for the full temperature range up to 300 K for pressures at 0, 2.85, and 5.14 GPa.

Figure 3

$T^2$ dependence of resistivity at low temperatures for measurements with the PPMS at 3.90 and 4.58 GPa shown as the closed squares and circles, respectively, as well as measurements with the ${}^3$He cryostat at 4.20 and 4.73 GPa denoted by the open squares and circles, respectively. The black dashed lines are linear fits to the low-temperature data taken with the PPMS. The arrows indicate the temperature limit of $T^2$ behavior, $T_{\mathrm{FL}}$, from PPMS data. Inset: ${\rho }_{\exp }-{\rho }_{\mathrm{fit}}$ for both 3.90 and 4.58 GPa versus $T^2$. The black dotted line indicates a difference of $-0.01\mu \Omega$ cm used to determine $T_{\mathrm{FL}}$.

Figure 4

Low temperature resistivity data for YbFe${}_2$Zn${}_{20}$ under pressures up to 8.23 GPa using 1 : 1 FC70 : FC770 as the liquid pressure transmitting medium. Selected curves are shown ($P=0$, 3.62, 4.95, 5.62, 7.68, and 8.23 GPa) from two separate sets of measurements. Inset: Resistivity curves up to 300 K for $P=0$, 3.62, and 8.23 GPa.

Figure 5

$T^2$ dependence of resistivity at pressures of 5.71, 6.79, 7.68, 8.01, and 8.23 GPa from measurements with the ${}^3$He cryostat. At maximum pressure, the $T^2$ region has greatly diminished. The black arrows indicate $T_{\mathrm{FL}}$ values that were determined as shown in the inset of Fig. 3.

Figure 6

The magnetic contribution, ${\rho }_{\mathrm{mag}}={(\rho -{\rho }_0)}_{\mathrm{Yb}}-{(\rho -{\rho }_0)}_{\mathrm{Lu}}$, to the total resistivity for various pressures is shown on a semilog scale. The inset shows the ambient pressure curves for YbFe${}_2$Zn${}_{20}$ and its nonmagnetic analog LuFe${}_2$Zn${}_{20}$.

Figure 7

$T_{\max }$ and $T_{\mathrm{FL}}$ as they evolve with pressure. The dashed lines are guides for the eye.

Figure 8

(a) Evolution of $T_{\mathrm{FL}}$ as pressure is applied. By 8.23 GPa, $T_{\mathrm{FL}}$ is only as high as $\sim$0.6 K. Crossed, closed, and open symbols are results from using the piston cylinder cell, the mBAC with the 1 : 1 n-pentane : iso-pentane mixture, and the mBAC with the 1 : 1 FC70 : FC770 mixture, respectively, in conjunction with the PPMS. Top half closed symbols and right half closed symbols indicate results from using the mBAC with the 1 : 1 n-pentane : iso-pentane mixture and the 1 : 1 FC70 : FC770 mixture, respectively, in conjunction with the ${}^3$He cryostat. (b) $T^2$ coefficient [$\rho \left(T\right)={\rho }_0+A{T}^2$] which diverges as pressure is increased. (c) $A^{-1/2}$ as it progresses with pressure. The dashed line is a linear fit to the data with $A^{-1/2}$ reaching zero near 9.8 GPa.

Figure 9

Power-law behavior for selected resistivity curves on a semilog scale. Data for $T<3$ K are from measurements with a ${}^3$He cryostat and data for $T>3$ K are from measurements with the PPMS. The black dotted line is a guide for the eye and indicates a power of $n=2$ for $\rho \left(T\right)={\rho }_0+A{T}^n$.