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When a magnetic ion vibrates in a metal, it inevitably introduces a newchannel of hybridization with conduction electrons and in general, thevibrating ion induces electric dipole moment. In such a situation, we find thatmagnetic and non-magnetic Kondo effects alternatively occur due to thescreening of spin moment and electric dipole moment of vibrating ion. Inparticular, electric dipolar two-channel Kondo effect is found to occur forweak Coulomb interaction. We also show that magnetically robust heavy-electronstate appears near the fixed point of electric dipolar two-channel Kondoeffect. We believe that the {\it vibrating} magnetic ion opens a new door inthe Kondo physics.

Electric Dipolar Kondo Effect Emerging from Vibrating Magnetic Ion