  Antiferromagnets have attracted significant attention in the field of
magnonics, as promising candidates for ultralow-energy carriers for information
transfer for future computing. The role of crystalline orientation distribution
on magnon transport has received very little attention. In multiferroics such
as BiFeO$_3$ the coupling between antiferromagnetic and polar order imposes yet
another boundary condition on spin transport. Thus, understanding the
fundamentals of spin transport in such systems requires a single domain, a
single crystal. We show that through Lanthanum(La) substitution, a single
ferroelectric domain can be engineered with a stable, single-variant spin
cycloid, controllable by an electric field. The spin transport in such a single
domain displays a strong anisotropy, arising from the underlying spin cycloid
lattice. Our work shows a pathway to understand the fundamental origins of spin
transport in such a single domain multiferroic.
