Thermoelectric power investigations of YbAgGe across the quantum critical point

The magnetic field and temperature dependences of the thermoelectric power (TEP) of the antiferromagnetically ordered heavy fermion compound YbAgGe are measured across the field-induced quantum critical point. These TEP measurements reproduce the earlier $H\text{−}T$ phase diagram and identify an additional domelike phase between $\sim 45$ and $\sim 70\text{kOe}$. On the low-field side of this region, $H>H_c\sim 45\text{kOe}$, the sign of the TEP changes from negative to positive; on the high-field side of this region, $H\approx 70\text{kOe}$, a non-Fermi-liquid state is evidenced as the logarithmic temperature dependence of $S\left(T\right)/T$, in agreement with previous specific heat results $C\left(T\right)/T\propto -\text{log}\left(T\right)$. For higher fields, $H>70\text{kOe}$, the observed large value of $\alpha$, $S\left(T\right)=\alpha T$, is indicative of the heavy fermion state and shows a correlation with $C\left(T\right)/T$.

Figure 1

(Color online) $H\text{−}T$ phase diagram of YbAgGe for $\mathbf{H}\parallel \mathbf{a}\mathbf{b}$, constructed from the specific heat $C_p\left(T\right)$ (Refs. 6, 9), magnetizaion $M\left(T,H\right)$ (Ref. 9), Hall resistivity ${\rho }_H\left(T,H\right)$ (Ref. 11), and resistivity $\rho \left(T,H\right)$ (Refs. 6, 8) measurements. Thick solid and dotted lines represent the magnetic phase boundaries. Dashed lines $T_{Hall}$ and $T^{\ast }$ are the crossover lines determined from the thermodynamic and transport measurements. The Fermi-liquid region denoted by the dashed, $T_{\text{FL}}$ crossover line was determined from the region satisfying $\Delta \rho =A{T}^2$. See text for details.

Figure 2

(Color online) $S\left(T\right)$ of YbAgGe for $\Delta T\parallel \mathbf{a}\mathbf{b}$ and $\Delta T\parallel \mathbf{c}$ at $H=0$ (symbols) and 140 kOe (lines), applied along hexagonal $\mathbf{a}\mathbf{b}$ plane $\left(\mathbf{H}\parallel \mathbf{a}\mathbf{b}\right)$ in a transverse configuration, $\mathbf{H}\perp \Delta T$, for both heat flow directions. Arrows indicate the local minimum $\left(T_{\text{min}}\right)$ and maximum $\left(T_{\text{max}}\right)$ temperature. Inset: $S\left(T\right)$ of LuAgGe and TmAgGe at $H=0$.

Figure 3

(Color online) Low-temperature $S\left(T\right)$ of YbAgGe for $\Delta T\parallel \mathbf{a}\mathbf{b}$ (a) and $\Delta T\parallel \mathbf{c}$ (b) in selected fields, $H=0$, 40, 50, 60, 70, 80, 90, 110 (only for $\Delta T\parallel \mathbf{a}\mathbf{b}$), 140 kOe (bottom to top), applied along the $\mathbf{a}\mathbf{b}$ plane in a transverse configuration $\left(\mathbf{H}\perp \Delta T\right)$ for both heat flow directions. Symbols and lines are taken from ${}^4\text{H}\text{e}$ and ${}^3\text{H}\text{e}$ measurement setup, respectively. The local maximum temperature $T_{\text{max}}$, inflection point $T_0$, magnetic order $T_N$ and $T_{N1}$, and field-induced local maximum $T^{\ast }$ are marked by arrows. Inset: (a) low-temperature $S\left(T\right)$ for $\Delta T\parallel \mathbf{a}\mathbf{b}$ at $H=0$, taken data both warming up and cooling down the temperature. Arrow indicates the phase transition temperature $T_{N1}$. Inset: (b) low-temperature $S\left(T\right)$ for $\Delta T\parallel \mathbf{c}$ at $H=0$, taken data both warming up and cooling down the temperature. Arrows indicate the phase transition temperature $T_{N1}$ and the local minimum temperature corresponding to $T_N$.

Figure 4

(Color online) Low-temperature $S\left(T\right)$ of YbAgGe for $\mathbf{H}\parallel \mathbf{a}\mathbf{b}$ and $\Delta T\parallel \mathbf{a}\mathbf{b}$ $\left(\mathbf{H}\perp \Delta T\right)$. $S\left(T\right)$ curves in (a), (b), (c), and (d) correspond to the region I, II, III, and IV in Fig. 1, respectively. $S\left(T\right)$ curves in (a) and (c) are shifted for clarity. (a) Squares and triangle symbols indicate phase transition temperatures determined from $dS\left(T\right)/dT$ and the arrows represent the local minimum. The data, taken for both warming and cooling the temperature, are plotted. Arrows in (b), (c), and (d) indicate the local minimum and slope change. The data are presented only taken upon warming the temperature. Solid lines are guide to the eyes. See text for details.

Figure 5

(Color online) Low-temperature $S\left(T\right)$ of YbAgGe for $\mathbf{H}\parallel \mathbf{a}\mathbf{b}$ and $\Delta T\parallel \mathbf{c}$. In zero field up-arrows indicate the abrupt jump $\left(T_{N1}\right)$ and local minimum $\left(T_N\right)$, respectively, determined from $dS\left(T\right)/dT$ (inset). Down-arrows indicate the local minimum temperatures corresponding to the $T_N$. Inset: $dS\left(T\right)/dT$ at $H=0$.

Figure 6

(Color online) $S\left(H\right)$ of YbAgGe for $\Delta T\parallel \mathbf{a}\mathbf{b}$ (a) and $\Delta T\parallel \mathbf{c}$ (b) at selected temperatures of 0.4, 2.4, and 5.2 K, and for magnetic field applied along $\mathbf{H}\parallel \mathbf{a}\mathbf{b}$ in a transverse configuration $\left(\mathbf{H}\perp \Delta T\right)$. Arrows indicate phase transitions ($H_c$ and $H_{N1}$) and local maximum field $\left(H^{\ast }\right)$, determined from $dS\left(H\right)/dH$. Inset: (a) $S\left(H\right)$ for $\Delta T\parallel \mathbf{a}\mathbf{b}$ at 0.4 K, taken data with both increasing and decreasing magnetic field. (b) $dS\left(H\right)/dH$ for $\Delta T\parallel \mathbf{c}$ at 0.4 K.

Figure 7

(Color online) $S\left(H\right)$ of YbAgGe for $\Delta T\parallel \mathbf{a}\mathbf{b}$ and for magnetic field applied along $\mathbf{H}\parallel \mathbf{a}\mathbf{b}$ in a transverse configuration $\left(\mathbf{H}\perp \Delta T\right)$. (a) $S\left(H\right)$ at 0.4, 0.5, 0.6, and 0.8 K, taken data with increasing magnetic field. Curves for $T=0.5$, 0.6, and 0.8 K are shifted for clarity. Arrows indicate phase transitions $H_{N1}(\leftarrow )$ and $H_c$ $(\downarrow )$, a sign reversal $(\Uparrow )$, and a local maximums $H^{\ast }$ $(\uparrow )$. Inset: hysteresis curves of $S\left(H\right)$ measurements at $T=0.4$, 0.5, and 0.6 K. (b) Normalized TEP $\left[S\left(H\right)-S\left(H=0\right)\right]$ as a function of $H$ at $T=0.8$, 1, 1.5, 2, 2.4, 5.2, 10, and 15 K. Arrows indicate a local maximum $H^{\ast }$.

Figure 8

(Color online) $H\text{−}T$ phase diagram of YbAgGe for $\mathbf{H}\parallel \mathbf{a}\mathbf{b}$. Solid symbols are inferred from $\Delta T\parallel \mathbf{a}\mathbf{b}$ data and open symbols are inferred from $\Delta T\parallel \mathbf{c}$ data, plotted on the top of phase and crossover lines in Fig. 1; ▲ (△,○) from up-sweeps in $T$, ▼ from down-sweeps in $T$, $▶$ $(▷)$ from up-sweeps in $H$, $◀$ from down-sweeps in $H$, and other symbols (●, ◼, ◆, $★$, ×, $+$) from up-sweeps in $T$ and $H$. The × symbols indicate the sign reversal on TEP from negative to positive. The $+$ symbols correspond to the local maximum developed in $S\left(T,H\right)$. The FL region was taken from earlier $\rho \left(T\right)$ $\left(\Delta \rho =A{T}^2\right)$ measurements (Refs. 6, 8).

Figure 9

(Color online) $S\left(T\right)/T$ of YbAgGe on a $\text{log}\left(T\right)$ scale for both (a) $\Delta T\parallel \mathbf{a}\mathbf{b}$ and (b) $\Delta T\parallel \mathbf{c}$ in selected magnetic fields, applied along $\mathbf{H}\parallel \mathbf{a}\mathbf{b}$ in a transverse configuration $\left(\mathbf{H}\perp \Delta T\right)$. Solid line in (b) on the top of 70 kOe data is a guide to the eyes.

Figure 10

(Color online) (a) $S\left(H\right)/T$ of YbAgGe at $T=0.4\text{K}$ for both $\Delta T\parallel \mathbf{a}\mathbf{b}$ and $\Delta T\parallel \mathbf{c}$, plotted as a function of magnetic field, applied along $\mathbf{H}\parallel \mathbf{a}\mathbf{b}$ in a transverse configuration $\left(\mathbf{H}\perp \Delta T\right)$. Solid symbols (triangles and circles) are taken from temperature sweeps $S\left(T\right)/T$. Sommerfeld coefficient ($C\left(T\right)/T$, right axis) at 0.39 K was taken from the previous specific heat measurements (Ref. 9). (b) The estimated $q$ values at $T=0.4\text{K}$ for both $\Delta T\parallel \mathbf{a}\mathbf{b}$ and $\Delta T\parallel \mathbf{c}$, plotted as a function of $H$.