Abstract
An s-d exchange model of a magnetically ordered metal is formulated in terms of a generating functional that describes the interaction of the system with fluctuating fields. The electron and spin Green's functions are represented by variational derivatives of this functional with respect to fields. Such an approach, which was recently successfully applied by the authors to the isotropic Heisenberg model, now is extended to the case where localized spins interact with conduction electrons. Exact equations were obtained for the electron and magnon Green's functions and the structure of the self-energy part of electrons and magnons was investigated. The iteration of these equations generates a perturbation theory in s-d interaction in the form of a diagrammatic technique for spin and Fermi operators. Exact graphical representations for the electron and magnon Green's functions through vertex parts of the electron-magnon interaction are given. Several approaches are suggested for approximately solving the equations for vertex parts. As limiting cases, all earlier known results concerning the spectrum and damping of spin waves in a ferromagnet are obtained, as well as those concerning the magnetic polaron and dynamic magnetic susceptibility. In the limit of a strong s-d exchange interaction, the spectrum of magnon for the ferromagnetic state of the system has been calculated.
Highlights
A tJ-model is the basic working model in the theory of strongly correlated electron systems
Hopping matrix elements tij and exchange integrals Jij are usually taken in the nearest neighbours approximations, so the model contains only two energy parameters: t and J
The self-consistent Born approximation (SCBA) is an approximation leading to a magnetic polaron picture inside the antiferromagnetic phase
Summary
A tJ-model is the basic working model in the theory of strongly correlated electron systems. It is well known that in high-Tc-compounds the superconducting state appears outside the antiferromagnetic phase when δ > δc , the question about applicability of the magnetic polaron picture for this concentration region is left open. For this reason a lot of new attempts are made to study the properties of the model (1.1) at δ > δc [1]. As the result of such an approach, equations for generating functional Z and variational derivatives of Z over these fields are derived These equations are convenient for iterations with respect to parameters t and J, in contrast to Kadanoff-Baym equations convenient for iterations with respect to Coulomb interaction U. The first attempt of such an approach was given by us in [3]
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