  We propose a method of atom-interferometry using a spinor Bose-Einstein
condensate (BEC) with a time-varying magnetic field acting as a coherent
beam-splitter. Our protocol creates long-lived superpositional counterflow
states, which are of fundamental interest and can be made sensitive to both the
Sagnac effect and magnetic fields on the sub-micro-G scale. We split a
ring-trapped condensate, initially in the $m_f=0$ hyperfine state, into
superpositions of internal $m_f=\pm1$ states and condensate superflow, which
are spin-orbit coupled. After interrogation, relative phase accumulation can be
inferred from a population transfer to the $m_f=\pm1$ states. The counterflow
generation protocol is adiabatically deterministic and does not rely on
coupling to additional optical fields or mechanical stirring techniques. Our
protocol can maximise the classical Fisher information for any rotation,
magnetic field, or interrigation time, and so has the maximum sensitivity
available to uncorrelated particles. Precision can increase with the
interrogation time, and so is limited only by the lifetime of the condensate.
