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 $10< N leq 10^5$ 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.
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