Probing the phase diagram of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$ by thermopower at high pressure

The temperature dependence of the thermoelectric power, $S\left(T\right)$, and the electrical resistivity of the magnetically ordered $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$ ($T_N=8.55\mathrm{K}$ and $T_C=7.40\mathrm{K}$) were measured for pressures $p<16\mathrm{GPa}$ in the temperature range $1.2\mathrm{K}<T<300\mathrm{K}$. Long-range magnetic order is suppressed at $p_c\approx 7.8\mathrm{GPa}$. Pressure drives $S\left(T\right)$ through a sequence of temperature dependences, ranging from a behavior characteristic for magnetically ordered heavy fermion compounds to a typical behavior of intermediate-valent systems. At intermediate pressures a large positive maximum develops above $10\mathrm{K}$ in $S\left(T\right)$. Its origin is attributed to the Kondo effect and its position is assumed to reflect the Kondo temperature $T_K$. The pressure dependence of $T_K$ is discussed in a revised and extended $(T,p)$ phase diagram of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$.

Figure 1

Top view of the inner part of the pressure chamber before closing. Close to the heater two thermocouples ($\underset{̱}{\mathrm{Au}}\mathrm{Fe}$ and Chromel) are located on top of the sample. The Au wire connected at the opposite edge of the sample is chosen as a reference point for the two thermovoltages $V_{\underset{̱}{\mathrm{A}}\mathrm{u}\mathrm{Fe}}$ and $V_{\text{Chromel}}$. Lead is used as pressure gauge. Au wires establish the connection through the pyrophyllite gasket. Steatite serves as pressure transmitting medium.

Figure 2

Magnetic contribution ${\rho }_{\mathit{mag}}\left(T\right)$ to the electrical resistivity of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$ at different pressures. Two different antiferromagnetic phases occur below $T_N$ and $T_L$. A ferromagnetic ground state is present below $T_C$ and low pressure. No traces of magnetic order are observed for $p>7\mathrm{GPa}$ above $1.2\mathrm{K}$. Inset: raw data of $\rho \left(T\right)$ in a linear plot. Incoherent Kondo scattering is apparent for $p=5.7\mathrm{GPa}$.

Figure 3

Temperature dependence of the thermoelectric power $S\left(T\right)$ of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$ at selected pressures. The entrance into the magnetically ordered states is indicated by $T_N$, $T_C$, and $T_L$, as deduced from the $\rho \left(T\right)$ data. $T_K$ and $T_S$ label the center of broad, pressure-induced maxima. The inset shows the low-temperature part of $S\left(T\right)$ at low pressure.

Figure 4

Thermoelectric power $S\left(T\right)$ of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$ above the critical pressure. $S\left(T\right)$ is dominated by a high-temperature maximum. The inset shows the ambient pressure $S\left(T\right)$ data of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$ (Ref. 17) and its nonmagnetic counterpart $\mathrm{La}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$.

Figure 5

$(T,p)$ phase diagram of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$ obtained from electrical resistivity (half open symbols) (Refs. 16, 17) calorimetric open symbols (Ref. 18), and the combined $\rho \left(T\right)$ and $S\left(T\right)$ (bold symbols) measurements. At low pressure a paramagnetic (PM) to antiferromagnetic (AFM I) phase transition occurs at $T_N$ and a subsequent transition into a ferromagnetic phase (FM) takes place at $T_C$. The FM ground state is suppressed at $2.3\left(2\right)\mathrm{GPa}$ and a second antiferromagnetically ordered phase (AFM II) occurs below $T_L$. Long-range magnetic order is suppressed at $p_c\approx 7.8\mathrm{GPa}$. $T_{\rho }$ is the position of a maximum in $\rho \left(T\right)$ whereas $T_S$ and $T_K$ represent the center of peaks in $S\left(T\right)$. The half-filled diamonds indicate $T_K\left(p\right)\propto 1∕{\sqrt{A}}^{17}$. They are shifted by $1.4\mathrm{GPa}$ towards lower pressure (see text).

Figure 6

Comparison of $S\left(T\right)$ of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Ge}}_2$ at $7.0\mathrm{GPa}$ and $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Si}}_2$ at ambient pressure (Ref. 37). Both curves reveal a pronounced high-temperature maximum and a moderate positive contribution to $S\left(T\right)$ at about $25\mathrm{K}$. Inset: The low temperature part of $S\left(T\right)$ of $\mathrm{Ce}{\mathrm{Ru}}_2{\mathrm{Si}}_2$ contains an additional positive peak below $1\mathrm{K}$.