  The spin Hall effect (SHE) can generate a pure spin current by an electric
current, which is promisingly used to electrically control magnetization. To
reduce power consumption of this control, a giant spin Hall angle (SHA) in the
SHE is desired in low-resistivity systems for practical applications. Here,
critical spin fluctuation near the antiferromagnetic (AFM) phase-transition is
proved as an effective mechanism to create an additional part of SHE, named as
fluctuation spin Hall effect (FSHE). This FSHE enhances the SHA due to the AFM
spin fluctuation between conduction electrons and local spins. We detect the
FSHE with the inverse and direct spin Hall effect (ISHE and DSHE) set-up and
their temperature (T) dependences in the Cr/MgO/Fe magnetic tunnel junctions
(MTJs). The SHA is significantly enhanced when temperature is approached to the
N\'eel temperature (T_N) and has a peak value of -0.34 at 200 K near T_N. This
value is higher than the room-temperature value by 240% and comparable to that
of heavy metals Ta and W. Furthermore, the spin Hall resistivity of Cr well
fits the modeled T-dependence when T approaches T_N from low temperatures,
implying the AFM spin fluctuation nature of strong SHA enhancement. Thus, this
study demonstrates the critical spin fluctuation as a prospective way of
increasing SHA and enriches the AFM material candidates for spin-orbitronic
devices.
