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We report the doping evolution of magnetic susceptibility $\chi (T)$ and Hallcoefficient $R_H$ in high quality Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($0.13 \leq x\leq 1$) single crystals. It is found that the normal-state magneticsusceptibility of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ compounds undergoes a crossoverfrom linear-$T$ dependence in the undoped and underdoped samples intoKFe$_2$As$_2$-type magnetic response in the overdoped samples with increasing Kcontent. Hall coefficient $R_H$ of underdoped sample $x$=0.22 shows a rapidincrease above spin-density-wave transition temperature $T_{SDW}$. Below$T_{SDW}$, it increases slowly. $R_H$ of optimally doped and slightly overdopedsamples ($0.34 \leq x \leq 0.65$) shows relative weak temperature dependenceand saturation tendency below 150 K. However, $R_H$ of K heavily overdopedsamples ($0.80 \leq x \leq 1$) increases rapidly below 150 K. Meanwhile, Hallangle $cot \theta _H$ displays a concave temperature dependence within thedoping range $0.22 \leq x \leq 0.55$, whereas it changes to a convextemperature dependence within the doping range $0.65 \leq x \leq 1$. Thedramatic change coincides with Lifshitz transition occurred around the criticaldoping $x$=0.80, where ARPES measurements had confirmed that electron pocketdisappears with excess hole doping in Ba$_{1-x}$K$_x$Fe$_2$As$_2$ system. It issuggested that the characteristic temperature $T$* at around $120 \sim 150$ Kobserved in susceptibility and Hall coefficient, as well as previously reportedresistivity data, may indicate an incoherence-coherence crossover inBa$_{1-x}$K$_x$Fe$_2$As$_2$ system.

physical review. b, condensed matter and materials physics

Crossover in the magnetic response of single-crystalline  Ba$_{1-x}$K$_x$Fe$_2$As$_2$ and Lifshitz critical point evidenced by Hall  effect measurements