Field-induced non-Fermi-liquid resistivity of stoichiometric $\mathrm{YbAgGe}$ single crystals

We have investigated hexagonal $\mathrm{YbAgGe}$ down to $70\mathrm{mK}$ by measuring the magnetic-field and temperature dependence of the resistivity $\rho$ of single crystals in fields up to $14\mathrm{T}$. Our results extend the $H\text{−}T$ phase diagram to the lowest temperatures for $H$ applied in the basal plane and along the $c$ axis. In particular, critical fields for the suppression of several magnetic phases are determined. The temperature dependence of $\rho \left(T\right)$ is unusual: whereas at low $H$, $\rho \left(T\right)$ reveals a temperature exponent $n⩾2$, we find $1⩽n<1.5$ and strong enhancement of the temperature dependence of $\rho \left(T\right)$ close to and beyond the highest critical field for each field direction. For $H$ applied in the basal plane, at high fields a conventional $T^2$ dependence of $\rho \left(T\right)$ is reached above $10\mathrm{T}$ accompanied by an approach to saturation of a strong drop in the residual resistivity. $\mathrm{YbAgGe}$ appears to be one of few Yb-based stoichiometric systems, where quantum-critical behavior may be induced by a magnetic field.

Figure 1

Temperature dependence of the resistivity with no applied field. No qualitative change in the $\mathrm{mK}$ range is found upon altering the current direction. However, the resistivity is anisotropic with larger in-plane values. In the inset the first-order character of the transition between the AF1 and AF2 phases is shown. Arrows indicate the direction of the temperature sweeps.

Figure 2

Signatures in the temperature dependence of the resistivity $\rho \left(T\right)$ for $H\parallel a$. (a) $T_1$ (onset of drop in $\rho$) is gradually suppressed with field and fully disappears at $2.5\mathrm{T}$. (b), (c) Signatures of $T_3$: the shoulder (marked by arrows) also is suppressed with increasing field. In parallel, the initial slope of $\Delta \rho \left(T\right)$ increases from 3 to $4.6\mathrm{T}$.

Figure 3

Signatures in the field dependence of $\rho$ for $\rho (H\parallel a)$ at various temperatures. The field sweeps at different temperatures reveal the first-order transition ($H_1^a$, onset of jump in $\rho$), the second-order transition ($H_2^a$, bump), and a further feature ($H_3^a$, onset of strong drop of $\rho$ towards high fields), which indicates a further transition. A forth feature $\left(H_4^a\right)$ has yet to be confirmed by further measurements.

Figure 4

Temperature dependence of the resistivity for $H\parallel a$ and $I\parallel c$. The two graphs together with Fig. 2b illustrate the development of the low-temperature dependence of $\rho \left(T\right)$ with $H\parallel a$. The inset in (a) shows the field dependence of $\rho \left(75\mathrm{mK}\right)$ and ${\rho }_0$ determined from power-law fits (solid circles).

Figure 5

Temperature dependence of the resistivity for $H\parallel a$ and $I\parallel a$. The two graphs illustrate the development of the low-temperature dependence of $\rho \left(T\right)$ with $H\parallel a$.

Figure 6

Analysis of the low-temperature resistivity for $H\parallel a$. Measurements with current $I\parallel a$ (open symbols) or $I\parallel c$ (solid symbols) give similar results. The low-temperature exponent $n$ (diamonds) results from single-power-law fits of $\rho \left(T\right)$. The range, over which the single power law holds, is indicated in the upper part of the figure (down triangles). Close to $H_{c1}^a$ the jump in the resistivity prevents the determination of $n$. Below $H_{c3}^a$, $n$ is generally close to or above 2. Between $H_{c3}^a$ and $H\parallel a=7\mathrm{T}$, $n\approx 1$. At higher fields the exponent is increasing to $n\approx 2$. The evolution of the $A$ coefficient (squares) can only be determined at high fields where $n\approx 2$. $A$ is the result of the fit $\rho ={\rho }_0+A{T}^2$ up to $750\mathrm{mK}$. In general, the magnitude of the low-temperature dependence is measured by the size of $\mathrm{\Delta }\rho \left(250\mathrm{mK}\right)$ (circles). Note the maxima at $H\parallel a=4.75\mathrm{T}$ and $H\parallel a=6.5\pm 0.5\mathrm{T}$. The results of $A$ and $\mathrm{\Delta }\rho \left(250\mathrm{mK}\right)$ for $I\parallel a$ have been scaled down by a factor 0.56. These graphs are the result of analysing data shown in Figs. 2, 4, and 5.

Figure 7

Deviation of the temperature dependence of the resistivity from quadratic behavior for $H\parallel a$. (a) At $7\mathrm{T}$ there is a clear deviation from a $T^2$ form of $\mathrm{\Delta }\rho \left(T\right)$. The deviation is reduced towards higher fields. The curves at high fields are shown on reduced scales to allow better comparison of the qualitative temperature dependence. (b) Above $10\mathrm{T}$ the resistivity becomes quadratic (horizontal line of $\mathrm{\Delta }\rho ∕T^2$ vs $T$). In this case, $\mathrm{\Delta }\rho ∕T^2$ corresponds to the $A$ coefficient.

Figure 8

Signatures of magnetic phase transitions in $\rho \left(T\right)$ for $H\parallel c$. The first transition ($T_1$, onset of a drop of $\rho$) is suppressed with field and fully disappears at $5\mathrm{T}$. The suppression does not happen continuously. At $2\mathrm{T}$ and above, the jumplike drop gets washed out and a shoulder ($T^{*}$, indicated by arrows) occurs.

Figure 9

Signatures of the two magnetic phase transitions in $\rho (H\parallel c)$ at low temperatures. The large arrows indicate the directions of the field sweeps. The sweeps show the clear first-order character of the first transition. Due to the small temperature dependence of $\rho$ below $100\mathrm{mK}$, the field sweeps at $75\mathrm{mK}$ are very similar to ${\rho }_0(H\parallel c)$ determined from power-law fits (solid circles). The difference between $\rho \left(H\right)$ at $75\mathrm{mK}$ and $240\mathrm{mK}$ illustrates the $H\parallel c$ dependence of the strength of the low-temperature resistivity.

Figure 10

Temperature dependence of the resistivity for $H\parallel c$. The two graphs illustrate the development with field of the low-temperature dependence of $\rho \left(T\right)$, which is strongest at $9.25\mathrm{T}$.

Figure 11

Analysis of the low-temperature resistivity for $H\parallel c$. The low-temperature exponent $n$ results from single-power-law fits of $\rho \left(T\right)$ (diamonds). The range over which the single-power law holds is indicated in the upper part of the figure (down triangles). Close to $H_{c1}^c$ the shoulder in $\rho \left(T\right)$ does not allow a determination of $n$. In the AF1 phase $x⩾2$. At higher fields $n<2$ in a considerable range with a minimum $n\approx 1$ close to $H_{c3}^c$. The magnitude of the low-temperature dependence of $\rho \left(T\right)$ is measured by the size of $\Delta \rho \left(250\mathrm{mK}\right)$ and reaches a maximum close to $H_{c3}^c$. These graphs are the result of analyzing measurements shown in Fig. 10.

Figure 12

Field-temperature phase diagrams of $\mathrm{YbAgGe}$. The magnetic phase boundaries are mapped by combining results of this study (representative data sets shown in Figs. 2, 3, 8, 9 solid symbols) and a recent study (open symbols) (Ref. 16). Indications for phase transitions have been seen in the resistivity (from up-sweeps in $T$, circles), the magnetoresistance (from up-sweeps in $H$, squares), and in the specific heat (triangles). Features in the Hall resistivity (crosses, $R_H$) define a further line in the phase diagrams (Ref. 21). (a) For $H\parallel a$ at lower fields two antiferromagnetic phases (AF1 and AF2) are found, as well as region III with yet unknown magnetic properties, and a high-field regime. The crossover in the high-field regime between non-Fermi-liquid (NFL) and Fermi-liquid (FL) resistivity sets in where $\mathrm{\Delta }\rho \left(T^2\right)$ ceases to follow a straight line. This phase diagram is the combined result of the in-plane and $c$-axis resistivity. (b) For $H\parallel c$, the various order parameters are unknown but regions I and III correspond to AF1 and AF2 order at zero field, respectively. At high fields an NFL regime is found.