  In magnetic topological insulators, quantized electronic transport is
interwined with spontaneous magnetic ordering, as magnetization controls band
gaps, hence band topology, through the exchange interaction. We show that
considering the exchange gaps at the mean-field level is inadequate to predict
phase transitions between electronic states of distinct topology. Thermal spin
fluctuations disturbing the magnetization can act as frozen disorders that
strongly scatter electrons, reducing the onset temperature of quantized
transport appreciably even in the absence of structural impurities. This
effect, which has hitherto been overlooked, provides an alternative explanation
of recent experiments on intrinsic magnetic topological insulators.
