Spin macroscopic quantum coherent (MQC) states of fine antiferromagnetic particles in a magnetic field acting perpendicular to its easy axis are analysed. Field oscillations of frequency of spin macroscopic quantum tunnelling (MQT) between degenerative energy states originated from instanton interference in magnetic field are predicted. The periodicity of these oscillations is determined by the exchange field divided by a number of bound macroscopic spins in the particle. This phenomenon is similar to some extent to the electron quantum interference induced by magnetic potential in the Aharonov-Bohm effect.
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