Magnetism and structure of small clusters: An exact treatment of electron correlations.

Abstract

The electronic, magnetic, and structural properties of small clusters are studied in the framework of the single-band Hubbard Hamiltonian. Results for various ground-state and excited-state many-body properties are presented, which were calculated exactly by means of Lanczos's numerical diagonalization method. A full geometry optimization is performed for N\ensuremath{\le}8 atoms by considering all possible nonequivalent cluster structures with fixed nearest-neighbor bond lengths. The most stable structure and the corresponding total spin S are obtained rigorously as a function of the Coulomb interaction strength U/t and number of electrons \ensuremath{\nu}. The resulting interplay between electron correlations, magnetism, and cluster structure is analyzed and the main trends as a function of N, U/t, and \ensuremath{\nu} are derived. The stability of cluster ferromagnetism is studied from two complementary points of view. First, for N\ensuremath{\le}8 and \ensuremath{\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 temperature dependence of the magnetization as the purely electronic excitations. Second, we determine the stability of the saturated ferromagnetic state with respect to single spin flips as a function of the band filling \ensuremath{\nu}/N. In this case a few selected larger clusters (7\ensuremath{\le}N\ensuremath{\le}43) in the strongly correlated limit (U/t\ensuremath{\rightarrow}+\ensuremath{\infty}) are considered. It is shown that the \ensuremath{\nu}/N dependence of the spin-flip energy \ensuremath{\Delta}${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{sf}}$ shows interesting electronic-shell-like oscillations, which reflect the characteristics of the single-particle energy-level structure and its dependence on the symmetry and size of the cluster. Finally, we conclude by discussing some of the limitations of the model together with relevant extensions. \textcopyright{} 1996 The American Physical Society.