MAGNETISM AND STRUCTURE OF SMALL CLUSTERS - AN EXACT TREATMENT OF ELECTRON CORRELATIONS

The electronic, magnetic, and structural properties of small clusters are studied in the framework of the single-band Hubbard Hamiltonian. R esults for various ground-state and excited-state many-body properties are presented, which were calculated exactly by means of Lanczos's nu merical diagonalization method. A full geometry optimization is perfor med for N less than or equal to 8 atoms by considering all possible no nequivalent cluster structures with fixed nearest-neighbor bond length s, The most stable structure and the corresponding total spin S are ob tained rigorously as a function of the Coulomb interaction strength U/ t and number of electrons nu. The resulting interplay between electron correlations, magnetism, and cluster structure is analyzed and the ma in trends as a function of N, U/t, and nu are derived. The stability o f cluster ferromagnetism is studied from two complementary points of v iew. First, for N less than or equal to 8 and nu = N + 1, we determine exactly the stability of the ferromagnetic ground state with respect to electronic excitations and structural changes. It is shown that in small clusters the structural changes can be as important to the tempe rature dependence of the magnetization as the purely electronic excita tions. Second, we determine the stability of the saturated ferromagnet ic state with respect to single spin hips as a function of the band fi lling nu/N. In this case a few selected larger clusters (7 less than o r equal to N less than or equal to 43) in the strongly correlated limi t (U/t --> + infinity) are considered. It is shown that the nu/N depen dence of the spin-flip energy Delta(epsilon sf) shows interesting elec tronic-shell-like oscillations, which reflect the characteristics of t he single-particle energy-level structure and its dependence on the sy mmetry and size of the cluster. Finally, we conclude by discussing som e of the limitations of the model together with relevant extensions.