Evolution of $c\mathrm{\text{−}}f$ Hybridization and Two-Component Hall Effect in $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$

$\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ is the unique heavy fermion superconductor that exhibits unconventional quantum criticality without tuning in a strongly intermediate valence state. Despite the large coherence temperature, set by the peak of the longitudinal resistivity, our Hall effect measurements reveal that resonant skew scattering from incoherent local moments persists down to at least $\sim 40\mathrm{K}$, where the Hall coefficient exhibits a distinct minimum signaling another formation of coherence. The observation strongly suggests that the hybridization between $f$ moments and conduction electrons has a two-component character with distinct Kondo or coherence scales $T_K$ of $\sim 40\mathrm{K}$ and 200 K; this is confirmed by the magnetic field dependence of ${\rho }_{xy}$.

Figure 1

(a) $R_H$ of $\beta -{\mathrm{YbAlB}}_4$ vs $T$ for different RRR samples at ${\mu }_{0}H=0.1\mathrm{T}$ $\parallel c$ axis; solid lines and points indicate $T$ and $H$ sweeps, respectively. Also shown are $R_H$ for ${\mathrm{YbAl}}_3$ [13] and the Hall mobility $\mu$ [defined in Eqs. (3, 4)] for sample $\mathrm{RRR}=180$. (b) $\chi \equiv M/H$ (left-hand axis), at ${\mu }_{0}H=0.1\mathrm{T}$ of $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ vs $T$ with CW fits for $T>150\mathrm{K}$ and $6<T<15\mathrm{K}$ [16] and ${\rho }_m$ vs $T$ (right-hand axis) (see 8 for details). (c) $R_H$ vs $\chi$ at ${\mu }_{0}H=0.1\mathrm{T}$.

Figure 2

(a) ${\rho }_{xy}$ of $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ vs $H\parallel c$ axis at various $T$s for sample with $\mathrm{RRR}=180$. (b) Percentage deviation of ${\rho }_{xy}$ from the $H=0$ linear slope $d{\rho }_{xy}/dH{|}_{(H=0)}$ vs $H\parallel c$ axis (intervening 10 K intervals shown in gray). (c) $M$ vs ${\mu }_{0}H$ at fixed temperatures. (d) Percentage deviation of $M$ from the $H=0$ linear slope vs $H\parallel c$ axis.

Figure 3

(a) ${\rho }_{xy}$ (sample $\mathrm{RRR}=180$) vs $H$ (successively higher $T$s offset by $+0.5$ for clarity). (b) as in panel (a) for sample $\mathrm{RRR}=130$. (c) as in panel (a) for sample $\mathrm{RRR}=250$ crossing $T=T^{*}=8\mathrm{K}$. In all panels ${\rho }_{xy}$ is fit to the two-component model [Eq. (3)] for every $T$ (black broken lines).

Figure 4

(a) $\mu$ [Eq. (4)] vs $T$ extracted from the two-component model (Fig. 3). Also shown is the ESR $g$ value of $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ [22] after subtracting the one for $\beta \mathrm{\text{−}}{\mathrm{LuAlB}}_4$ and rescaled by a constant. (b) Measured ${\rho }_{xx}$ vs $T$ together with fit resistivities ${\rho }_1$, ${\rho }_2$ [Eq. (4)]. (c) $R_H(0)$, $R_1$, $R_2$ [Eqs. (3, 4)]. ${\rho }_2$ and $R_2$ are divided by 100.