  We report the doping evolution of magnetic susceptibility $\chi (T)$ and Hall
coefficient $R_H$ 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 magnetic
susceptibility of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ compounds undergoes a crossover
from linear-$T$ dependence in the undoped and underdoped samples into
KFe$_2$As$_2$-type magnetic response in the overdoped samples with increasing K
content. Hall coefficient $R_H$ of underdoped sample $x$=0.22 shows a rapid
increase above spin-density-wave transition temperature $T_{SDW}$. Below
$T_{SDW}$, it increases slowly. $R_H$ of optimally doped and slightly overdoped
samples ($0.34 \leq x \leq 0.65$) shows relative weak temperature dependence
and saturation tendency below 150 K. However, $R_H$ of K heavily overdoped
samples ($0.80 \leq x \leq 1$) increases rapidly below 150 K. Meanwhile, Hall
angle $cot \theta _H$ displays a concave temperature dependence within the
doping range $0.22 \leq x \leq 0.55$, whereas it changes to a convex
temperature dependence within the doping range $0.65 \leq x \leq 1$. The
dramatic change coincides with Lifshitz transition occurred around the critical
doping $x$=0.80, where ARPES measurements had confirmed that electron pocket
disappears with excess hole doping in Ba$_{1-x}$K$_x$Fe$_2$As$_2$ system. It is
suggested that the characteristic temperature $T$* at around $120 \sim 150$ K
observed in susceptibility and Hall coefficient, as well as previously reported
resistivity data, may indicate an incoherence-coherence crossover in
Ba$_{1-x}$K$_x$Fe$_2$As$_2$ system.

Superconductivity