  Memory effects of gravitational waves from astronomical events or primordial
universe might have the information of new physics. It is intriguing to observe
that the memory effect exists in electrodynamics as a net momentum kick, while
the memory effect in gravity appears as a net relatively displacement. In
particular, Winicour has shown that the B-mode memory, which characterizes
parity odd global distribution of memory, does not exist. We study the memory
effect in axion electrodynamics and find that the B-mode memory effect can
exist provided the existence of coherently oscillating axion background field.
Moreover, we examine the detectability of the axion dark matter using this
effect. We also argue the existence of the B-mode gravitational memory effect
in the presence of the axion dark matter.
