Appearance of a field-induced phase and a quantum critical line in pressurized ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$

We report three-dimensional pressure-field-temperature phase diagrams of ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ and ${\mathrm{Yb}}_2{\left({\mathrm{Pd}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2\mathrm{Sn}$ that are constructed from electrical resistivity measurements. In ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$, which is known to be a pressure-induced antiferromagnet, we found an unexpected magnetic-field-induced phase at a higher field than the antiferromagnetic (AFM) phase under pressure. A non-Fermi-liquid (NFL) behavior characterized by $T^{3/2}$ dependence of the resistivity is observed along the AFM phase boundary, indicating the existence of the quantum critical line. As the AFM and field-induced phases approach each other with increasing pressure, the NFL behavior is more pronounced. ${\mathrm{Yb}}_2{\left({\mathrm{Pd}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2\mathrm{Sn}$ is known to be an antiferromagnet at ambient pressure. We also found a field-induced phase under pressure. Although the temperature-pressure phase diagram of ${\mathrm{Yb}}_2{\left({\mathrm{Pd}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2\mathrm{Sn}$ corresponds to that of ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ shifted by 1.7 GPa, the field-induced phase does not separate from the AFM phase. Furthermore, the NFL behavior is less pronounced than ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$. The Ni substitution for Pd not only acts as a chemical pressure but also produces other effects for the magnetism and its criticality.

Figure 1

Temperature dependence of the resistivity $\rho \left(T\right)$ in (a) ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ and (b) ${\mathrm{Yb}}_2{\left({\mathrm{Pd}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2\mathrm{Sn}$ under several pressures. The straight arrow indicates the antiferromagnetic phase transition temperature $T_{\mathrm{N}}$. The inset shows the resistivity of ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ at 0.16 GPa on the logarithmic temperature scale. The upward arrow indicates the maximum temperature $T_{\max }$ of $\rho \left(T\right)$.

Figure 2

Magnetoresistivity $\rho \left(H\right)$ at 0.2 K and its field derivative $d\rho /dH$ under several pressures. The white, gray, and black triangles indicate peak fields of $d\rho /dH$ named $H_{\mathrm{N}}$, $H_{\mathrm{XL}}$, and $H_{\mathrm{X}}$, respectively. The zero value of $d\rho /dH$ for each plot is drawn as a dotted line.

Figure 3

Second derivative of the resistivity $d^2\rho /d{T}^2$ as a function of temperature in ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ at several pressures and fields. The arrow indicates a peak temperature $T_{\mathrm{X}}$. Each plot is vertically shifted by an amount proportional to the measured field, where the field is indexed in the right axis. The horizontal-zero line is drawn as a dotted line.

Figure 4

Resistivity and its squared-temperature coefficient $A$ of ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ at 3.07 GPa. (a) and (b) The field and temperature dependence of the resistivity, respectively. The inset of the panel (a) shows the magnetoresistivity of ${\mathrm{Yb}}_2{\left({\mathrm{Pd}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2\mathrm{Sn}$ at 3.07 GPa. (c) Field dependence of $A$. Vertical lines correspond to $H_{\mathrm{N}}$, $H_{\mathrm{XL}}$, and $H_{\mathrm{X}}$ on $d\rho /dH$ at 0.2 K. (d) Squared-temperature dependence of the resistivity of ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ at 3.07 GPa.

Figure 5

Pressure dependence of (a) $T_{\mathrm{N}}$, (b) $T_{\max }$, and (c) ${\rho }_0$. The pressure scales for ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ and ${\mathrm{Yb}}_2{\left({\mathrm{Pd}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2\mathrm{Sn}$ are drawn on the bottom and top axes, respectively. The origin of the scale for ${\mathrm{Yb}}_2{\left({\mathrm{Pd}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2\mathrm{Sn}$ is shifted by $+1.7$ GPa from the scale for ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$.

Figure 6

Three-dimensional pressure-field-temperature phase diagrams of (a) ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ and (b) ${\mathrm{Yb}}_2{\left({\mathrm{Pd}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2\mathrm{Sn}$. The right-hand back plane corresponds to the field-temperature phase diagram at 3.07 GPa. The contour map on the bottom plane represents the $T^2$ coefficient $A$ of the resistivity obtained from a fit for $\rho \left(T\right)={\rho }_0+A{T}^2$. The cross mark indicates the position of the magnetic field and pressure at which the data in Fig. 7 were taken.

Figure 7

Temperature dependence of the resistivity of ${\mathrm{Yb}}_2{\mathrm{Pd}}_2\mathrm{Sn}$ for the selected fields at which the $A$ coefficient becomes the maximum in each pressure. The temperature scaling in each panel is (a) linear, (b) $T^{3/2}$, and (c) squared. Solid lines are guide for eyes.