Quantum size effect observed in ultrafine magnesium particles

The static magnetic susceptibilities of ultrafine Mg particles were measured as a function of particle diameter in the temperature range from 2 to 240 K. The temperature-independent paramagnetism enhancement was observed and found to be inversely proportional to the cube of particle size, revealing for the first time direct evidence for the zero-dimensional magnetism in a small metal particle. The importance of the electronic state of corner atoms of a particle is suggested for this zero dimensionality. It was also suggested that this enhanced paramagnetism exhibits a phase transition at 150 K. The marked decrease in magnetic susceptibility at low temperature with the onset of moderate increase in intermediate temperature has been analyzed in terms of the quantum size effect. We first clarify experimentally the energy-level statistics of small metals by the combination of Poisson and orthogonal distributions. The effect of surface irregularity is discussed with the aid of Tanaka's formulas, which indicate that the surfaces of small particles are not rough. This is inconsistent with commonly accepted assumptions.