Quantum Bicriticality in the Heavy-Fermion Metamagnet YbAgGe

Bicritical points, at which two distinct symmetry-broken phases become simultaneously unstable, are typical for spin-flop metamagnetism. Interestingly, the heavy-fermion compound YbAgGe also possesses such a bicritical point (BCP) with a low temperature $T_{\mathrm{BCP}}\approx 0.3\mathrm{K}$ at a magnetic field of ${\mu }_0{H}_{\mathrm{BCP}}\approx 4.5\mathrm{T}$. In its vicinity, YbAgGe exhibits anomalous behavior that we attribute to the influence of a quantum bicritical point that is close in parameter space yet can be reached by tuning $T_{\mathrm{BCP}}$ further to zero. Using high-resolution measurements of the magnetocaloric effect, we demonstrate that the magnetic Grüneisen parameter ${\Gamma }_H$ indeed both changes sign and diverges as required for quantum criticality. Moreover, ${\Gamma }_H$ displays a characteristic scaling behavior but only on the low-field side $H\lesssim H_{\mathrm{BCP}}$, indicating a pronounced asymmetry with respect to the critical field. We speculate that the small value of $T_{\mathrm{BCP}}$ is related to the geometric frustration of the Kondo lattice of YbAgGe.

Figure 1

$H\mathrm{\text{−}}T$ phase diagram of YbAgGe for fields within the $ab$ plane focusing on the region with the BCP. Black and red symbols are obtained in this and previous studies [14, 15, 17], respectively. The solid red lines are guides for the eye. The dotted black line $H_{\mathrm{cr}}(T)$ shows maxima in entropy identified by the location of zeros of ${\Gamma }_H$ (diamond). Solid black symbols denote anomalies in $T$ sweeps (filled circle) and $H$ sweeps (filled square) of ${\Gamma }_H$. Red symbols are transitions observed in magnetization ($M$, open triangle), specific heat ($C$, open square), thermal expansion coefficient and magnetostriction ($\alpha$ and $\lambda$, respectively, open circle) and thermoelectric power (TEP, filled triangle). Within the shaded area, ${\Gamma }_H$ exhibits scaling behavior (see Fig. 4) with a crossover indicated by the dotted green line. The inset shows the magnetic Grüneisen ratio ${\Gamma }_H$ as a function of temperature for fields applied parallel to the $ab$ plane; arrows indicate phase transitions.

Figure 2

Schematic phase diagrams with spin-flop bicriticality at different frustration strengths $Q$. (a) Bicritical point at a finite temperature $T_{\mathrm{BCP}}>0$. (b) Frustration suppresses the transition temperatures and thus $T_{\mathrm{BCP}}$, leading to a QBCP; the dotted line represents a crossover line separating two paramagnetic states with different short-range orders of frustrated moments. (c) Suppressing the transition temperature further results in a field-induced quantum spin liquid (QSL) present in a finite window of magnetic field. (d) Schematic $T\mathrm{\text{−}}H\mathrm{\text{−}}Q$ phase diagram. Field-induced phase transition at $H_{\mathrm{BCP}}$ is of first order. QSL phase for strong frustration $Q$ is indicated by orange color.

Figure 3

${\Gamma }_H$ as a function of magnetic field applied parallel to the $ab$ plane for low temperatures $T<0.7\mathrm{K}$. The solid gray line is the power law $0.31/({\mu }_{0}H\mathrm{\text{−}}4.8\mathrm{T})$. The inset shows a change of entropy calculated from ${\Gamma }_H$ with the help of the reported specific heat [15] (shifted vertically such that $\Delta S=0$ for ${\mu }_{0}H=13\mathrm{T}$). Arrows indicate the positions of phase transitions at $T=0$.

Figure 4

Scaling plot of $h{\Gamma }_H$ vs $T/|h{|}^{1.1}$ for data only within the shaded regime of Fig. 1 with $h=H-H_{\mathrm{cr}}(T)$, where $H_{\mathrm{cr}}(T)$ is defined by the zeros of ${\Gamma }_H$ (dotted line in Fig. 1). An arrow indicates the crossover at $0.5\mathrm{K}/{\mathrm{T}}^{1.1}$ of the scaling function also shown by the dotted green line in Fig. 1. The solid gray line represents the asymptotics ${\Gamma }_H\sim h/T^{1.8}$. The inset shows the scaling plot on a linear scale but as a function of $h/T^{0.9}$.