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Journal of Physics C Solid State Physics

The stability and thermodynamic behaviour of spin-density waves II. Correlation theory

M J Morris, J. F. Cornwell

Published Oct 1, 1968• 2 citations
Publisher

Abstract

The Green function theory formulated in I is generalized to give a higher-order approximation to the correlation problem. The spin-density-wave stability in this approximation is compared in detail with the Hartree-Fock approximation results of I and are found to be in conflict in several respects.
DOI
10.1088/0022-3719/1/5/302

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A detailed investigation has been made of the application of the Hartree-Fock approximation to the stability and thermodynamic behaviour of spin-density waves in a model with a single electronic energy band and a delta-function-type interaction between electrons. It is shown that for a half-filled band the ground state at zero temperature is always a spin-density wave, provided only that the width of the band is sufficiently small. For other bands the conditions for the relative stability of the spin-density wave, ferromagnetic and paramagnetic states are more complicated, and are studied in detail for a special band form. For a half-filled band the energy per atom and specific heat have been calculated as functions of temperature for the spin-density wave, ferromagnetic and paramagnetic states. The temperature dependence of the amplitude for the spin-density wave and ferromagnetic states, and of the entropy for the spin-density wave and paramagnetic states have also been calculated. The formulation of the problem has been made using a Green function method in order to allow the development in a later paper of a higher-order approximation to the correlation problem.
A generalized Hartree-Fock theory in terms of the temperature Green's function is presented to take the electronic correlation effect into account. The correlation effect due to the exotonic pairs causes instabilities in the usual Hartree-Fock state and results in producing new states, e.g., SDW(spin density wave), CDW (charge density wave) and so on. Exitation processes are also examined by analyzing a vertex function, and it is pointed out that degeneracy in triplet states might be resolved due to electronic correlation.
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The noncollinear spin-spiral density wave of the uniform electron gas is studied in the framework of reduced-density-matrix-functional theory. For the Hartree-Fock approximation, which can be obtained as a limiting case of reduced-density-matrix-functional theory, Overhauser showed a long-time ago that the paramagnetic state of the electron gas is unstable with respect to the formation of charge- or spin-density waves. Here we not only present a detailed numerical investigation of the spin-spiral density wave in the Hartree-Fock approximation but also investigate the effects of correlations on the spin-spiral density wave instability by means of a recently proposed density-matrix functional.
An extension of density-functional theory, designed to treat spin-density waves and antiferromagnetic systems, is presented. The nonlocal nature of the antiferromagnetic correlations and possible noncollinearity in spin space are incorporated via an additional fundamental variable, the staggered density, which supplements the spin densities of conventional density-functional theory. Inclusion of this variable is justified by both physical and methodological considerations. We prove the corresponding Hohenberg-Kohn theorem, derive the pertinent Kohn-Sham equations, and present several approximate functionals depending explicitly on the staggered density. As a first test the formalism is applied to two simple model systems, a one-dimensional electron gas with a short-range interaction, and the three-dimensional electron gas with Coulomb interactions. These calculations serve to test the developed formalism, but also already allow us to draw a number of conclusions regarding the stability and nature of possible spin-density wave states in homogeneous electron systems.