Anomalous peak effect in iron-based superconductors Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($x \approx$ 0.69 and 0.76) for magnetic-field directions close to the $ab$ plane
We report magnetic torque measurements on iron-pnictide superconductors Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($x \approx$ 0.69 and 0.76) up to an applied field of $B_a$ = 45 T. The peak effect is observed in torque-vs-field curves below the irreversibility field. It is enhanced and becomes asymmetric as the field is tilted from the $c$ axis. For field directions close to the $ab$ plane, increasing- and decreasing-field curves peak at markedly different fields, and exhibit a sharp jump, suggestive of a first-order phase transition, on the high- and the low-field side of the peak, respectively. Complicated history dependence of the torque is observed in the peak-effect region. We construct and discuss the temperature ($T$)--applied-magnetic-field ($B_a$) phase diagram.