Field-dependent Hall effect in single-crystal heavy-fermion YbAgGe below $1\mathrm{K}$

We report the results of a low-temperature $(T⩾50\mathrm{mK})$ and high-field $(H⩽180\mathrm{kOe})$ study of the Hall resistivity in single crystals of YbAgGe, a heavy-fermion compound that demonstrates field-induced non-Fermi-liquid behavior near its field-induced quantum critical point. Distinct features in the anisotropic, field-dependent Hall resistivity sharpen on cooling down and at the base temperature are close to the respective critical fields for the field-induced quantum critical point. The field range of the non-Fermi-liquid region decreases on cooling but remains finite at the base temperature with no indication of its conversion to a point for $T\to 0$. At the base temperature, the functional form of the field-dependent Hall coefficient is field-direction-dependent and complex beyond existing simple models, thus reflecting the multicomponent Fermi surface of the material and its nontrivial modification at the quantum critical point.

Figure 1

Field-dependent Hall resistivity of YbAgGe [(a) $H\Vert ab$, (b) $H\Vert c$] measured at different temperatures. The curves, except for $T=50\mathrm{mK}$, are shifted by $1\mu \Omega \mathrm{cm}$ increments for clarity. For 400 and $500\mathrm{mK}$, data from our initial measurements (Ref. 7) are shown by × and ∗ for comparison. Note: for (b) the feature located near $H=20–30\mathrm{kOe}$ is an artifact of the measurements protocol and hysteresis in magnetoresistivity at the lower transition (see text).

Figure 2

Field-dependent Hall coefficient of YbAgGe [(a) $H\Vert ab$, (b) $H\Vert c$], defined as $R_H=d{\rho }_H∕dH$, measured at different temperatures. The curves, except for $T=50\mathrm{mK}$, are shifted by (a) $0.2n\Omega \mathrm{cm}∕\mathrm{Oe}$ and (b) $0.1n\Omega \mathrm{cm}∕\mathrm{Oe}$ increments for clarity. Low-field data in (b) (except for $750\mathrm{mK}$, above the lover magnetic transition) are truncated below $\sim 30\mathrm{kOe}$ (see text).

Figure 3

Field-dependent Hall resistivity $\left({\rho }_H\right)$, Hall resistivity divided by field $({\rho }_H∕H)$, and Hall coefficient $(d{\rho }_H∕dH)$ of YbAgGe [(a) $H\Vert ab$, (b) $H\Vert c$] at $T=50\mathrm{mK}$. Arrows and letters mark different features of the curves (see text for the discussion).

Figure 4

Composite anisotropic $H\text{−}T$ phase diagrams for YbAgGe: (a) $H\Vert ab$, (b) $H\Vert c$. Symbols: ▵, magnetic transitions from thermodynamic and magnetotransport measurements in Ref. 1; ●, magnetic transitions from magnetotransport measurements in Ref. 11; solid lines, tentative magnetic phase boundaries; +, coherence line defined as a high-temperature limit of the region of $\rho \left(T\right)={\rho }_0+A{T}^2$ resistivity behavior (Ref. 1); ★, Hall line defined from the maximum/minimum $\left(H\parallel ab∕H\parallel c\right)$ of the Hall resistivity [(a) in Fig. 3]; ∗, lines defined from the maximum and minimum in $d{\rho }_H∕dH$ [(b) and (c) in Fig. 3], area between these lines is accentuated by hatching; 엯, ⊕ in panel (a) and ⊕ in panel (b), point corresponding to high-field break of the slope in $d{\rho }_H∕dH$ [(d) and (e) in Fig. 3a and (d) in Fig. 3b]. Dashed lines are guide for the eye.