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A photonic crystal (PhC) cavity formed by a closed interface between a dielectric PhC and a magnetooptical (MO) material PhC is proposed and analyzed theoretically. It is shown that such a cavity can support one-way rotating modes and thus the modal fields at different frequencies have a similar pattern. The loss effect of MO material is taken into consideration for the solution of quality-factors for the cavity. The coupling between a cavity with one-way state and a PhC waveguide is also studied through numerical simulations. Simulation results show that cavity mode only interacts with the waveguide mode propagating in a particular direction. This work paves the way to control waveguide-cavity interaction.