Quantum phase transition in the heavy-fermion compound $\mathrm{Yb}{\mathrm{Ir}}_2{\mathrm{Si}}_2$

We investigate the pressure-temperature phase diagram of $\mathrm{Yb}{\mathrm{Ir}}_2{\mathrm{Si}}_2$ by measuring the electrical resistivity $\rho \left(T\right)$. In contrast to the widely investigated $\mathrm{Yb}{\mathrm{Rh}}_2{\mathrm{Si}}_2$, $\mathrm{Yb}{\mathrm{Ir}}_2{\mathrm{Si}}_2$ is a paramagnetic metal below $p_c\simeq 8\mathrm{GPa}$. Interestingly, a first-order, presumably ferromagnetic, transition develops at $p_c$. Similar magnetic properties were also observed in $\mathrm{Yb}{\mathrm{Rh}}_2{\mathrm{Si}}_2$ and $\mathrm{Yb}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ at sufficiently high pressures, suggesting a uniform picture for these Yb compounds. The ground state of $\mathrm{Yb}{\mathrm{Ir}}_2{\mathrm{Si}}_2$ under pressure can be described by Landau Fermi-liquid theory, in agreement with the nearly ferromagnetic Fermi-liquid model. Moreover, evidence of a weak valence transition, characterized by a jump of the Kadowaki-Woods ratio as well as an enhancement of the residual resistivity ${\rho }_0$ and of the quasiparticle-quasiparticle scattering cross section, is observed around $6\mathrm{GPa}$.

Figure 1

(Color online) Schematic phase diagram for the Yb compounds other than $\mathrm{Yb}{\mathrm{Rh}}_2{\mathrm{Si}}_2$. A large-moment order, presumably FM-type, develops at a critical pressure $p_c$. The ground-state properties in both the high-$p$ phase and the paramagnetic state can be described by LFL theory. Uniquely, in $\mathrm{Yb}{\mathrm{Rh}}_2{\mathrm{Si}}_2$ (see the inset, the dot marks its location at $p=0$) AFM phase with weak magnetic moments exists below $p_c$ and vanishes at a QCP $\left(p_{c1}\right)$ where the LFL theory is violated.

Figure 2

(Color online) The electrical resistivity $\rho \left(T\right)$ $(I\Vert ab)$ for $\mathrm{Yb}{\mathrm{Ir}}_2{\mathrm{Si}}_2$ at various pressures. The downward curvature in $\rho \left(T\right)$ as marked by the arrows at $T_m$ indicates the occurrence of a magnetic transition above $8.3\mathrm{GPa}$. Inset: The resistivity $\rho \left(T\right)$ plotted as a function of $T^2$ at $p=6.4\mathrm{GPa}$.

Figure 3

(Color online) Pressure dependence of (a) $T_m$, $T_{\mathrm{FL}}$, and $T_{\max }$ and (b) the residual resistivity ${\rho }_0$ and the resistivity coefficient $A$ for $\mathrm{Yb}{\mathrm{Ir}}_2{\mathrm{Si}}_2$. The lines are used as guidance for the eyes. The inset plots $\rho \left(T\right)$ over the whole temperature range for $p=1.7\mathrm{GPa}$ and $10\mathrm{GPa}$. $T_m\left(p\right)$ of $\mathrm{Yb}{\mathrm{Rh}}_2{\mathrm{Si}}_2$ ($\times$, the high-$p$ phase, from Ref. 10) and of $\mathrm{Yb}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ (+, from Ref. 16) are included for comparison. The open symbols represent data from the sample with RRR $\simeq 350$ obtained in a clamped cell and the filled symbols are for a sample with RRR $\simeq 35$ measured in a Bridgman cell. No significant difference can be seen in either $T_{\mathrm{FL}}$ or $A$ for these two samples.

Figure 4

(Color online) The log-log plot of the coefficient $A$ and $T_{\max }$ (with $p$ as an implicit parameter), showing that $A{T}_{\max }^2=\mathrm{const}$ with distinct constants for $p>6\mathrm{GPa}$ and $p<6\mathrm{GPa}$, respectively.

Figure 5

(Color online) Pressure dependence of the resistivity isotherms $\Delta \rho \left(p\right)$ $[=\rho (T,p)-{\rho }_0\left(p\right)]$ at various temperatures.