Mesoscopic Fluctuations in Small Metal Particles Studied by Nuclear Magnetic Resonance

In a small metal particle (SMP) of N atoms the en- ergy splittings D around the Fermi energy EF are of order D , EFyN. At thermal energies much larger than the interlevel spacings the system will behave like a bulk metal, but with decreasing temperature the gaps between levels can no longer be neglected and deviations from bulk behavior become predominant ( quantum-size ef- fect). Clear experimental observation of such a crossover from bulk to quantum size regime has been the goal of many experiments on assemblies of SMP's from the very beginning a few decades ago (1). Such assemblies (required for sufficient experimental sensitivity) were always characterized by substantial size distributions of the particles, blurring the results. But even in an assembly of particles of uniform size (monodisperse), the pre- cise energy level structure is expected to differ between particles due to such small perturbations as surface rough- ness and randomness in the packing, leading to a distribu- tion in D values (2). For the assembly the energy gap then becomes a pseudogap and to predict the thermodynamic behavior one has to use statistical theories for energy level distributions (3), such as the random matrix theory (4- 6). As realized a few years ago, not only the variation in the energy density of states ( DOS), but also multiple scatter- ing leading to local electron density fluctuations can be very important for the thermodynamic properties (7). To enable a clear separation of the thermodynamic behavior arising from these mesoscopic statistical effects from the effects due to size distribution, the availability of metal particles of uniform size is a conditio sine qua non. Re- cently evidence for quantum-size effects in the electronic specific heat and susceptibility was obtained in a series of molecular Pd clusters and colloids (8). Here we present the NMR properties of a related monodisperse Pt cluster compound. The conditions of uniform core size, surface roughness, and random packing together with electron ex- change (see below) allow us to obtain a detailed test of the mesoscopic predictions for nanoparticles for the first time. It is demonstrated that the statistical distribution of the energy levels goes hand in hand with strong local fluc- tuations in the electron density within each metal cluster. The nuclear relaxation rate T 21 1 is a convenient probe for