Theory of localized magnetic moments in metals I finite cluster approach

The origin of localized magnetic moments formation in metals is investigated theoretically using a self-consistent local spin density molecular cluster approach. Clusters with up to 55 atoms are employed to describe isolated impurity local moment behavior in the cases of Fe$\text{Ag}$ and Fe$\text{Pd}$. Densities of states and spin magnetic moments were determined and compared with results of spectroscopic (notably photoemission) and magnetization measurements, respectively. In the case of a noble metal host, the spin magnetization density is found to be highly localized around the Fe site; the iron moment is ≈ 3.9μ_B and the polarization of the host Ag atoms is small. In the case of a transition metal host, the iron moment is ≈ 3.2 μ_B but here the strong hybridization of the Fe-3d and Pd-4d states results in a large induced magnetic moment in the host PD metal — in essential agreement with experiment for this giant moment system.     

Indirect interaction of the localized magnetic moments

The methods of the indirect interaction operator derivation for the quantum particles locally coupled with the quasi-particles of another physical subsystem are reviewed. A variant of the consecutive canonical transformations method which allows one to obtain a nonperturbative solution of the problem is proposed for the systems which do not contain Fermi particles.     

Variational approach to spin fluctuations in the Hubbard model

We study a one parameter variational wave function to improve the spin density wave ground state of the Hubbard model by inclusion of quantum spin fluctuations. Using a perturbative approach and novel lattice summation techniques we present analytical as well as numerical results for the correlation energies and the staggered magnetizations in one and two dimensions. We find ground state energies which are satisfyingly close to known exact results and are significantly lower than those of existing Gutzwiller and numerical treatments.     

A field-theoretical approach to the extended Hubbard model

We transform the quartic Hubbard terms in the extended Hubbard model to a quadratic form by making the Hubbard–Stratonovich transformation for the electron operators. This transformation allows us to derive exact results for mass operator and charge–charge and spin–spin correlation functions for s-wave superconductivity. We discuss the application of the method to the d-wave superconductivity.     

A generating functional approach to the Hubbard model

The method of generating functional, suggested for conventional systems by Kadanoff and Baym, is generalized to the case of strongly correlated systems, described by the Hubbard X operators. The method has been applied to the Hubbard model with arbitrary value U of the Coulomb on-site interaction. For the electronic Green’s function constructed for Fermi-like X operators, an equation using variational derivatives with respect to the fluctuating fields has been derived and its multiplicative form has been determined. The Green’s function is characterized by two quantities: the self energy Σ and the terminal part Λ. For them we have derived the equation using variational derivatives, whose iterations generate the perturbation theory near the atomic limit. Corrections for the electronic self-energy Σ are calculated up to the second order with respect to the parameter W/U (W width of the band), and a mean field type approximation was formulated, including both charge and spin static fluctuations. This approximation is actually equivalent to the one used in the method of Composite Operators, and it describes an insulator-metal phase transition at half filling reasonably well. The equations for the Bose-like Green’s functions have been derived, describing the collective modes: the magnons and doublons. The main term in this equation represents variational derivatives of the electronic Green’s function with respect to the corresponding fluctuating fields. The properties of the poles of the doublon Green’s functions depend on electronic filling. The investigation of the special case n=1 demonstrates that the doublon Green’s function has a soft mode at the wave vector Q=(π,π,...), indicating possible instability of the uniform paramagnetic phase relatively to the two sublattices charge ordering. However this instability should compete with an instability to antiferromagnetic ordering. The generating functional method with the X operators could be extended to the other models of strongly correlated systems.     

Constant-cutoff approach to magnetic moments of hyperons

We calculate the magnetic moments of hyperons in the simplified CHK model, with the stabilizing term proportional toe ^–2 omitted, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishna, Sanyuk, Schechter, and Subbaraman, which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. Thus we show that there is qualitative agreement with the experimental values and the accuracy is similar to that obtained with the complete CHK model.     

Indirect interactions between localized magnetic moments in intrinsic semiconductors

The indirect interaction between localized magnetic moments in insulators and semiconductors is investigated at T = 0°K. This interaction arises from virtual excitations of the valence electrons to the conduction band and is oscillatory as a function of distance. The passage from the case of small gap semiconductors to insulators is studied in detail, as a function of the energy gap and the effective masses. The Bloembergen-Rowland interaction is derived as a limiting case for insulators. Possible applications are also discussed.     

Indirect interactions between localized magnetic moments in doped semiconductors

The coupling between localized magnetic moments via conduction electrons is calculated taking into account the temperature and the mean free path of the electrons. For a fully degenerate electron gas and an infinite electronic mean free path the oscillatory RKKY interaction is obtained. On the limit of Boltzmann population and for infinite electronic mean free path the interaction can only be ferromagnetic. Taking into account the electronic mean free path the possibility of antiferromagnetism is restored. Furthermore the range of the interaction decreases. Several intermediate cases and possible applications are discussed.     

Gutzwiller wave-function approach to spiral magnetic order in the two-dimensional Hubbard model: A variational Monte Carlo study

The magnetic groundstate properties of the two-dimensional Hubbard model are investigated using generalized Gutzwiller wave-functions with spiral magnetic order. Employing variational Monte Carlo simulations these wave-functions are treated without approximations on finite lattices. The resulting phase diagram shows para-, ferro-, antiferro- and spiral magnetic phases of different types.     

Asymptotically exact variational approach to the strong coupling Hubbard model

In this contribution we use a generalization of Bogoljubov's variational principle, in order to develop a molecular field theory of the Hubbard model, which becomes asymptotically exact in the strong coupling limit. For this purpose the Hamiltonian is rotated by a unitary two-particle transformation in a way which was previously introduced by Kapustin, before the variational principle is applied.Project of the Sonderforschungsbereich 65 Festkörperspektroskopie Darmstadt-Frankfurt financed by special funds of the Deutsche Forschungsgemeinschaft.     

Baryon magnetic moments in quark-diquark model

The baryon magnetic moments in quark-diquark model are studied and it is found that the diquark (spin 1 and 0) mixing which may arise as a result of quarkgluon interaction inside a hadron, leads to a good agreement of theory with experiment.     

Variational master equation approach to dynamics of magnetic moments

Non-equilibrium properties of a model system comprised of a subsystem of magnetic moments strongly coupled to a selected Bose field mode and weakly coupled to a heat bath made of a plurality of Bose field modes was studied on the basis of non-equilibrium master equation approach combined with the approximating Hamiltonian method. A variational master equation derived within this approach is tractable numerically and can be readily used to derive a set of ordinary differential equations for various relevant physical variables belonging to the subsystem of magnetic moments. Upon further analysis of the thus obtained variational master equation, an influence of the macroscopic filling of the selected Bose field mode at low enough temperatures on the relaxation dynamics of magnetic moments was revealed.     

Perturbational approach to the one particle properties of the Hubbard model

It is shown that the Hubbard model can be viewed as limiting case of a periodic Anderson model. This relation is used to set up a perturbation theory for the Hubbard model with the transfermatrixelementt as expansion parameter. One particle properties of the three dimensional Hubbard model in the half filled band case for several values of the local Coulomb interactionU calculated with this method are presented. The results give clear hints towards the formation of a gap in the excitation spectrum. The variation of the free energy on the model parameters is found to be in good agreement with expectations.This work was performed within the research program of SFB 252 Elektronisch hochkorrelierte metallische Materialien     

Nuclear magnetic moments in the hybrid quark-hadron model

A model (HQHM) of quark deconfinement at short distances, and baryon and pion degrees of freedom at large distances, has been shown to give a good representation of few-nucleon systems up to momentum transfers of about 1 GeV/c. This model is extended to complex nuclei. In a detailed HQH shell model calculation the magnetic dipole moments of mediummass closed shell ±1 nuclei are shown to be in good agreement with experiment, even with a sizable probability of six-quark matter. Preliminary calculations of M1 transitions give damping in the direction indicated by experiment.     

Dynamical spin magnetic susceptibility in the 2D Hubbard model

Magnetic properties of the two-dimensional Hubbard model are investigated by studying the imaginary part of the dynamical spin magnetic susceptibility as a function of momentum and doping. The calculations are performed by means of the composite operator method in the static approximation. It is shown that the results are in good qualitative agreement with the experimental data for LaSrCuO compounds.     

Extended Hubbard model in the presence of a magnetic field

Within the Green’s function and equations of motion formalism it is possible to exactly solve a large class of models useful for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard model with on-site U and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h, in the narrow band limit. At zero temperature our results establish the existence of four phases in the three-dimensional space (U, n, h) – n is the filling – with relative phase transitions, as well as different types of charge ordering. The magnetic field may dramatically affect the behavior of thermodynamic quantities, inducing, for instance, magnetization plateaus in the magnetization curves, and a change from a single to a double-peak tructure in the specific heat. According to the value of the particle density, we find one or two critical fields, marking the beginning of full or partial polarization. A detailed study of several thermodynamic quantities is also presented at finite temperature.     

Metal-insulator transition in the Hubbard model with incommensurate magnetic structures

The metal-insulator transition for the square, simple cubic, and body centered cubic lattices has been studied within the Hubbard model at half-filling taking into account nearest- and next-nearest-neighbor electron hopping. Both staggered antiferromagnetic and incommensurate magnetic states (spin-spiral wave) have been considered. The inclusion of the latter states for the three-dimensional lattices does not change the general pattern of the metal-insulator transition, but opens the fundamentally new possibility of the metal-insulator transition of the first order between the magnetically ordered states for the square lattice.