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The magnetic configurations of Ni-20at%Fe/Hf and Ta/Ni-20at%Fe/Mn-28at%Ir/ Ni-20at%Fe/Ta asymmetric ring dots have been studied. Recently, we proposed that asymmetric ring structures are suitable for magnetic memory cells and then demonstrated that asymmetric structures can control the chirality of the vortical magnetization with in-plane fields. The investigation of the Ni-20at%Fe(20 nm)/Hf(5 nm) asymmetric ring dots for free layers in magnetic memory cells demonstrated that switching fields cause a transition from the vortex state to the onion state that increases as the ring width decreases from 410 nm to 210 nm since a narrow ring has a higher demagnetizing field than that of a wide ring during the transition. The investigation of the Ta(3 nm)/Ni-20at%Fe(15 nm)/Mn-28at%Ir(10 nm)/Ni-20at%Fe(3 nm)/Ta(5 nm) asymmetric ring dots for the pinned layers in magnetic memory cells demonstrated that the chirality of the vortical magnetization is pinned regardless of the magnetic field direction.