  Quantum coherence of electrons can produce striking behaviors in mesoscopic
conductors, including weak localization and the Aharonov-Bohm effect. Although
magnetic order can also strongly affect transport, the combination of coherence
and magnetic order has been largely unexplored. Here, we examine quantum
coherence-driven universal conductance fluctuations in the antiferromagnetic,
canted antiferromagnetic, and ferromagnetic phases of a thin film of the
topological material MnBi$_2$Te$_4$. In each magnetic phase we extract a charge
carrier phase coherence length of about 100 nm. The conductance
magnetofingerprint is repeatable when sweeping applied magnetic field within
one magnetic phase, but changes when the applied magnetic field crosses the
antiferromagnetic/canted antiferromagnetic magnetic phase boundary.
Surprisingly, in the antiferromagnetic and canted antiferromagnetic phase, but
not in the ferromagnetic phase, the magnetofingerprint depends on the direction
of the field sweep. To explain these observations, we suggest that conductance
fluctuation measurements are sensitive to the motion and nucleation of magnetic
domain walls in MnBi$_2$Te$_4$.
