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Physical review. B, Condensed matter

Photoemission, inverse photoemission, and fluctuations in an exactly soluble many-body cluster model of bcc iron

Erik C. Sowa, L. M. Falicov

Published Mar 15, 1987• 24 citations
Publisher

Abstract

An exact solution for a two-site crystal model, the smallest body-centered-cubic crystal, is presented for iron. The model consists of five d-like orbitals per site per spin, with interatomic hopping terms and an on-site Coulomb interaction of the fullest generality allowed by atomic symmetry. The ground state, depending on the choice of one-electron parameters, is found in one case to be a fully saturated ferromagnet, and in another to be an unsaturated ferromagnet with strong antiferromagnetic fluctuations. The many-body energy-level spectrum, intracluster charge and spin fluctuations, and photoemission and inverse photoemission densities of states for both cases are calculated and compared with experiment.

DOI
10.1103/physrevb.35.3765

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An exact solution for a two-site crystal model, the smallest body-centered-cubic crystal, is presented for iron. The model consists of five d-like orbitals per site per spin, with interatomic hopping terms and an on-site Coulomb interaction of the fullest generality allowed by atomic symmetry. The ground state, depending on the choice of one-electron parameters, is found in one case to be a fully saturated ferromagnet, and in another to be an unsaturated ferromagnet with strong antiferromagnetic fluctuations. The many-body energy-level spectrum, intracluster charge and spin fluctuations, and photoemission and inverse photoemission densities of states for both cases are calculated and compared with experiment.
An exact solution of an eight-site crystal model with periodic boundary conditions, a {001} thin film with face-centered-cubic crystal structure, is presented for the case of a heavy-fermion system. The object is to study modifications of the many-body electronic structure in the presence of surfaces. The model consists of (a) a single, fully symmetric orbital per site, with nearest-neighbor and second-nearest-neighbor hopping; (b) an infinite Coulomb repulsion between electrons on the same site; (c) antiferromagnetic superexchange interactions; and (d) a nearly half-filled band ((7/8 electron per site). Two structures are investigated: a two-layer and a four-layer fcc slab. The nature of the change from bulk to surface is studied by introducing a variable coupling between periodically extended slabs. The many-body spectrum, the one-electron occupancy, and the change in properties from bulk to surface are obtained and discussed.
The t-t'-J model (strongly interacting limit of a particular Hubbard model) is solved exactly on small clusters of eight sites with periodic boundary conditions for the simple-, body-centered-, and face-centered-cubic lattices and for the two-dimensional square lattice. The symmetry, k vector, and spin of the ground state are studied as functions of crystalline environment, interaction strength, and electron concentration. Phase diagrams are presented for stable solutions, and regions of parameter space that exhibit ferromagnetism and heavy-fermionic behavior are identified.
We present a theoretical description of the one-particle excitation spectra in strongly correlated systems with nonlocal interactions. Using exact diagonalization techniques, photoemission and inverse photoemission spectra of an extended Hubbard model with an intersite Coulomb interaction are calculated. The single-particle and many-body aspects are treated on an equal footing. The hopping and interaction parameters are adjusted to simulate various Hubbard and charge-transfer systems. In contrast to normal expectations, the intersite interaction is found to suppress the spectral features driven by the on-site interaction, leading to a narrowing in the overall spectral distribution. It also produces qualitatively new behavior in the spin polarization of the spectra and in the doping dependence of the low-energy spectral weight. The degree of sensitivity of the spectra to the single-particle and interaction parameters is systematically investigated. General implications of the calculated results for strongly correlated systems are discussed.
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.
The exact eigenvalues (for ground and excited states) of the constant-coupled one-band model for Nf{N}_{f}Nf​ fermions on NNN sites were obtained. Both electrons (T<0T<0T<0, where TTT is the coefficient of the term representing the "hopping energy") and holes (T>0T>0T>0) were considered, and results were obtained for $2\ensuremath{\le}{N}_{f}\ensuremath{\le}N$ and N=2,3,and4N=2, 3, \mathrm{and} 4N=2,3,and4. Only the Nf=2{N}_{f}=2Nf​=2, N=3N=3N=3 and Nf=3{N}_{f}=3Nf​=3, N=4N=4N=4 with T>0T>0T>0 cases gave a purely ferromagnetic ground state. These cases also showed a ferromagnetic state at higher energy. The eigenvalues were calculated as a function of UT\frac{U}{T}TU​, where UUU represents the Coulomb energy of repulsion for electrons on the same site. The total spins of the states were obtained from their splitting in a magnetic field. The hopping term was found to be dominant for ∣UT∣|\frac{U}{T}|∣TU​∣ as large as one. The calculations support the suggestion that the ground state is usually antiferromagnetic.
We perform exact numeric calculations for the two-orbital Hubbard model on the four-site cluster.In the limit of large on-site coupling the model becomes equivalent to the spin S " 1 Heisenberg model.By comparing energy spectra of these two models, we quantified the range of interaction parameters for which the Heisenberg model satisfactorily reproduces the two-orbital Hubbard model.Then we examined how the spectrum evolves when we are outside of this region, focusing especially on checking of how it is modified when various ways of interatomic hoppings of electrons between different orbitals are taken into account.We finally show how these modifications affect the dependence of specific heat on temperature.