Low-temperature properties of CeAu${}_2$Ge${}_2$ single crystals grown from Au-Ge and Sn flux

The specific heat of CeAu${}_2$Ge${}_2$ single crystals grown from Au-Ge (AGF) or Sn flux (SF) was measured at temperatures $T$ between 1.8 and 200 K. Two magnetic transitions are observed in the zero-field specific heat at 12.1 and 14.5 K in the AGF sample, while only a single sharp transition at 9.2 K is seen in the SF sample, confirming our recent susceptibility results [Fritsch et al., Phys. Rev. B 84, 104446 (2011)]. We observe several field-induced transitions in the magnetoresistance of the AGF sample measured at 1.6 and 2.3 K in accordance with the $B-T$ phase diagram constructed from isothermal magnetization curves $M\left(B\right)$. In addition, we have measured $M\left(B\right)$ under hydrostatic pressure $P$ up to 10.5 kbar. The Néel temperature $T_{\mathrm{N}}$ increases linearly with $P$ at a small rate of 0.049 K/kbar, which suggests that, if $T_{\mathrm{N}}\left(P\right)$ is attributed to a pure volume effect, this compound is close to the maximum transition temperature of the Doniach diagram. The transition fields $B_{\mathrm{M}}$ between the field-induced phases increase linearly with $P$ as well. The comparable Grüneisen parameters of $T_{\mathrm{N}}$ and $B_{\mathrm{M}}$ indicate that the energy scale depending on the sample's volume is given by the antiferromagnetic correlations and not by the Kondo effect. We discuss possible reasons for the different magnetic behavior of AGF and SF samples.

Figure 1

Electrical resistivity $\rho \left(T\right)$ of (a) AGF-CeAu${}_2$Ge${}_2$ and (b) SF-CeAu${}_2$Ge${}_2$ normalized to their values ${\rho }_{300}$ at 300 K in magnetic fields between 1.6 and 25 K. The data $\ge$1 T are shifted consecutively downward by 0.01 in (a) and 0.04 in (b) for clarity. Arrows indicate the $T_{\mathrm{N}}{}^{\prime }s$ which are determined at the slope change of $\rho \left(T\right)$. Insets show $\rho \left(T\right)$ in zero field from 300 to 1.6 K ($B$ $=$ 0.05 T is applied when $T<$ 5 K in SF-CeAu${}_2$Ge${}_2$ to suppress the superconductivity of Sn).

Figure 2

Electrical resistivity $\rho \left(T\right)$ vs $T^2$ of (a) AGF-CeAu${}_2$Ge${}_2$ and (b) SF-CeAu${}_2$Ge${}_2$. The data of $B=$ 1 and 2 T in (a) are omitted for clarity. Solid lines represent the best fit of $\rho \left(T\right)$ $=$ ${\rho }_0$+$A{T}^2$ [the fit of $B=$ 3 T in (a) is omitted for clarity], and the coefficient $A$ as a function of magnetic fields is plotted in insets.

Figure 3

(a) and (b) show magnetoresistance $\delta \rho \left(B\right)/\rho \left(0\right)$ $=$ $\left[\rho \right(B)-\rho (B=0\left)\right]/\rho (B=0)$ of AGF- and SF-CeAu${}_2$Ge${}_2$ at different fixed temperatures. The data $>$1.6 K are shifted consecutively downward by 0.01 in (b) for clarity. (c), (d), and (e) show differential plots of (a) and (b) as $-d$[$\delta \rho \left(B\right)/\rho \left(0\right)$]/$d$$B$ vs $B$. The data for $T>1.6$ K are shifted consecutively downward by 5 units in (c) and (d) and 0.05 units in (e) for clarity. Arrows indicate the transitions in addition to sharp antiferromagnetic transitions in AGF CeAu${}_2$Ge${}_2$.

Figure 4

Specific heat $C$ of SF- and AGF-CeAu${}_2$Ge${}_2$ in zero magnetic field plotted as $C/T$ vs $T$.

Figure 5

Magnetic contribution to the specific heat $C_{4f}$ vs temperature $T$ of (a) AGF- and (b) SF-CeAu${}_2$Ge${}_2$ together with Schottky fits (see text for details). Error bars indicate $\pm$0.5$\%$ of the total specific heat. Insets show the Ce 4$f$ entropy $S_{4f}$ vs $T$ in the same temperature region. The arrow in (b) indicates the weak shoulder (see text).

Figure 6

Ce 4$f$ contribution $C_{4f}$ to the specific heat of (a) AGF- and (b) SF-CeAu${}_2$Ge${}_2$ vs temperature $T$. In (a) the data of 3, 1, and 0 T are consecutively upward shifted by 3 J/mol K for clarity. (c) and (d) show the magnetization $M\left(T\right)$ of AGF- and SF-CeAu${}_2$Ge${}_2$ samples measured in $B=$ 0.1 T (from Ref. 14). The inset of (c) shows $M\left(T\right)$ with expanded horizontal and vertical scales to highlight the transition at $T_{\mathrm{N}2}$. Vertical dashed lines indicate the antiferromagnetic transition temperatures $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2}$ in zero field.

Figure 7

$B-T$ phase diagram of (a) AGF-CeAu${}_2$Ge${}_2$ and (b) SF-CeAu${}_2$Ge${}_2$. The $dM/dT$, $dM/dB$, and $M\left(T\right)$ data are from Ref. 14.

Figure 8

(a) Temperature dependence of the magnetization $M$ from 5 to 40 K at different pressures for AGF-CeAu${}_2$Ge${}_2$ with the magnetic field $B=0.1$ T parallel to the $c$ axis. (b) Pressure dependence of the antiferromagnetic ordering temperature $T_{\mathrm{N}1}$. Vertical error bars denote the temperature width of 90$\%$ of the magnetization maximum. Horizontal bars denote the 10$\%$–90$\%$ width of the superconducting transition temperature of Sn serving as a pressure gauge.

Figure 9

Isothermal field dependence of normalized magnetizations up to 8 T at $T=1.6$ K under different pressures; the inset shows the $dM/dB$ vs $B$ at 7.87 kbar. Arrows indicate transition fields.

Figure 10

Pressure dependence of the metamagnetic transition fields $B_{\mathrm{M}1}$ (circles), $B_{\mathrm{M}2}$ (triangles), and the critical field $B_{\mathrm{C}}$ (inverted triangles) in AGF-CeAu${}_2$Ge${}_2$. Around ambient pressure, solid symbols are the data taken when the sample is just mounted in the pressure cell; open symbols are the data taken after the sample is depressurized; half-filled symbols are the data taken when the sample is removed from the pressure cell.