Macroscopic tunneling of the oscillatory part of the magnetization at quantizing magnetic fields

Tunneling of the oscillatory part of the magnetization is considered in small metallic samples at very low temperatures in quantized magnetic fields. By using the instanton approach, we calculate the action integral for the tunneling rate of the magnetization under conditions of the strong magnetic interaction between conduction electrons and the de Haas-van Alphen effect in specimens, which may undergo diamagnetic phase transitions. The obtained low tunneling temperature independent frequency may be detected by a resonance way. The temperature of the crossover between the classical and tunneling regimes of magnetization fluctuations is calculated.