Magnetic oscillation at remanence is a key technological route for the realization of bias-field-free passive microwave devices and magnonic waveguides that support magnon transport. Here, exchange biased NiFe/FeMn bilayers have been shown to offer excellent opportunities for a new class of bias-field-free magnonic/microwave medium. Magnetic hysteresis measurements reveal a dependence on the exchange bias effect as a function of FeMn layer thickness. Ferromagnetic resonance measurements reveal magnetic oscillations at remanence for various thicknesses of FeMn, which also determines the frequency of the mode oscillations. Angular field dependent results indicate uniaxial anisotropy present in the bilayers. The in-plane magnetic anisotropy field is found to be decreased with an increase in the FeMn thickness. Further investigation on the invariance of resonance field and linear increase of linewidth with frequency shows the negligible extrinsic contribution to the overall effective damping. Relatively large effective Gilbert damping values are obtained for the higher FeMn thickness and can be attributed to the exchange bias anisotropy. Observation of low inhomogeneous linewidth broadening indicates a good quality of magnetic layer and the interfaces in our systems. Our results offer a novel route for the bias-field-free magnetic medium that supports high-frequency oscillations along with its suitability for on-chip device integration. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.