  Multiferroic BaMnF$_4$ powder were prepared by hydrothermal method.
Hysteretic field dependent magnetization curve at 5 K confirms the weak
ferromagnetism aroused from the canted antiferromagnetic spins by
magnetoelectric coupling. The blocking temperature of 65 K for exchange bias
coincides well with the peak at 65 K in the zero-field cooled
temperature-dependent magnetization curve, which has been assigned to the onset
temperature of two-dimensional antiferromagnetism. An upturn kink of exchange
field and coercivity with decreasing temperature was observed from 40 K to 20
K, which is consistent with the two-dimensional to three-dimensional
antiferromagnetic transition at N\'eel temperature (~26 K). In contrast to the
conventional mechanism of magnetization pinned by interfacial exchange coupling
in multiphases, the exchange bias in BaMnF$_4$ is argued to be a bulk effect in
single phase, due to the magnetization pinned by the polarization through
magnetoelectric coupling.
