Periodic and Disordered Anderson lattices/clusters.
Magnetic impurities in non-magnetic hosts is one of the central topics in the physics of strongly correlated systems. The key physical ingredients are localized states (atomic d-, f-levels) interacting with de-localized ones, so that competition among local moment formation, moment-moment interaction and magnetic screening occurs: such physics is essentially described by Anderson/Kondo-like impurity/lattice Hamiltonians. For macroscopic ordered/disordered d-, f-systems, a largely unresolved issue is to understand the variety of magnetic phases observed experimentally on varying pressure, temperature, species concentrations.
For the periodic case, significant insight can be gained already at the mean field level: by employing a Hartree-Fock -type local mean field approximation, the phase diagram reveals a ferromagnetic phase appearing at densities in the quarter-to half filling region. Such behavior is reflected by other type of calculations, for example by the Density Matrix Renormalization Group approach, where correlation effects are accounted for.
The relevance small systems with magnetic impurities to nanotechnology requires primarily to characterize how the infinite-size Kondo-like properties get modified at the nanoscale level due a finite energy spacing in the conduction band. Mean field approaches generally neglect spatial and/or temporal fluctuations, but the latter are especially important in small systems. To go beyond mean field treatmnets, one possibility is the use of exact diagonalization techniques. Such approaches are limited to small sizes, which makes them suitable when investigating systems which are actually small, such as nanoclusters, quantum dots, etc. For clusters with dense and/or disordered impurities may affect the competition between Kondo and RKKY interaction: a control of size effect/energy spacing can then provide a tunable Phase Diagram in small clusters.
The Phase Diagram of the periodic Anderson lattice model on a six-site cluster shows clearly the competition between RKKY and Kondo interactions and how this is affected by varying the energy spacing
Substitutional disorder in small clusters can cause additional qualitative changes in the nature of the (cluster) ground states: depending on alloy concentration, cluster geometry and conduction level energy spacing , disorder may induce competing magnetic phases, enhance the Kondo screening and magnetic crossover in the ground state and low-temperatures properties.
Exact diagonalization results for the disorder-averaged magnetic susceptibility ? of a 6-atom, binary alloy cluster (selected configurations). The alloy constituents A, B are respectively in the Kondo and mixed-valence regimes as schematically depicted in the inset. For each ? curve, the relative alloy configuration (and its ground state spin ) is also shown. For TĘ0, ? vanishes (diverges) when the total ground state spin S=0 (S > 0).