Three-dimensional oscillator in magnetic field: the de Haas-van Alphen effect in mesoscopic systems

The theoretical investigation of the cluster de Haas - van Alphen (dHvA) oscillations in three-dimensional systems performed for the first time. Applying a three-dimensional oscillator model to systems with electron numbers $10<N\le {10}^5$ we predict distinctive size effects: the dHvA oscillations can be observed only within a certain temperature range determined by $N$; the lower size limit for $N$ is $\approx 20$; the amount of the dHvA oscillations is reduced with decreasing $N$ which is accompanied by stretching the period of the oscillations.