  We report the effect of remote surface optical (RSO) phonon scattering on
carrier mobility in monolayer graphene gated by ferroelectric oxide. We
fabricate monolayer graphene transistors back-gated by epitaxial (001)
Ba$_{0.6}$Sr$_{0.4}$TiO$_{3}$ films, with field effect mobility up to 23,000
cm$^{2}$V$^{-1}$s$^{-1}$ achieved. Switching the ferroelectric polarization
induces nonvolatile modulation of resistance and quantum Hall effect in
graphene at low temperatures. Ellipsometry spectroscopy studies reveal four
pairs of optical phonon modes in Ba$_{0.6}$Sr$_{0.4}$TiO$_{3}$, from which we
extract the RSO phonon frequencies. The temperature dependence of resistivity
in graphene can be well accounted for by considering the scattering from the
intrinsic longitudinal acoustic phonon and the RSO phonon, with the latter
dominated by the mode at 35.8 meV. Our study reveals the room temperature
mobility limit of ferroelectric-gated graphene transistors imposed by RSO
phonon scattering.
