Anomalous peak effect in iron-based superconductors Ba1−xKxFe2As2 ( x ≈ 0.69 and 0.76) for magnetic-field directions close to the ab plane and its possible relation to the spin paramagnetic effect

We report magnetic torque measurements on iron-pnictide superconductors ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ ($x\ensuremath{\approx}$ 0.69 and 0.76) 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 sides 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. Since the upper critical field for the $ab$-plane direction is comparable to the Pauli limit, we also consider possible influence of the spin paramagnetic effect on the anomalous peak effect.