  We present two novel matter-wave Sagnac interferometers based on ring- shaped
time-averaged adiabatic potentials (TAAP). For both the atoms are put into a
superposition of two different spin states and manipulated independently using
elliptically polarized rf-fields. In the first interferometer the atoms are
accelerated by spin-state-dependent forces and then travel around the ring in a
matter-wave guide. In the second one the atoms are fully trapped during the
entire interferometric sequence and are moved around the ring in two
spin-state-dependent "buckets". Corrections to the ideal Sagnac phase are
investigated for both cases. We experimentally demonstrate the key atom-optical
elements of the interferometer such as the independent manipulation of two
different spin states in the ring-shaped potentials under identical
experimental conditions.
