Fig. 3: Switching statistics and hysteresis with magnetic field suggest competing magnetic order.

a,b, Switching histograms at optimal hole-side doping and electric field at T = 20 mK, as a function of the in-plane magnetic field B∥ up to ±1 T in the up-sweep (a) and down-sweep (b) directions. The distributions show the magnetic-field-direction-dependent response. The arrows represent the direction of B∥ sweep. The histograms are shown in distinct colours for clarity. Yellow indicates the data collected first, whereas blue represents the data collected last. Each histogram is shifted along the y axis by 100 counts for clarity. c,d, Switching histograms at 1 T and –1 T for the field swept up (c) and swept down (d), pointing out the direction-dependent response of the device to B∥ in that the switching current Is is different for 1 T and –1 T. e, Plot of the longitudinal resistance Rxx in the n–D parameter space, zoomed in near the hole-side superconducting region. The switching data in a–d are taken at the hole-side superconducting region marked by a cyan hexagon. A normal (Rxx ≠ 0) region is marked by a magenta diamond, and identifies the doping and electric field at which the data in f are acquired. f, Longitudinal resistance Rxx plotted as a function of the in-plane magnetic field B∥, at a doping and electric field identified by a magenta diamond in e and marks the phase in the neighbourhood of the superconducting phase. We observe butterfly hysteresis features that evolve and subsequently vanish with increasing temperature. The arrows specify the direction of B∥ sweep. Plots at each temperature are shifted along the y axis by 0.3 kΩ for clarity.