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Physical review. B, Solid state

Spin Susceptibility of an Interacting Electron Gas

Harjinder Singh, K. N. Pathak

Published Oct 15, 1972• 6 citations
Publisher

Abstract

A simple calculation of the wave-vector- and frequency-dependent paramagnetic spin susceptibility of an interacting electron gas is presented. The equation of motion of the double-time Green's function is solved using a moment-conserving decoupling approximation. For the short-range interaction, our expression for the dynamic spin susceptibility reduces to a previous result of Wolff. In the static and long-wavelength limit, our result for the Stonerenhanced spin susceptibility coincides with that obtained from consideration of the groundstate energy in the Hartree-Fock approximation.

DOI
10.1103/physrevb.6.2978

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Journal of Applied Physics•Mar 1, 1981•1 citation
A simple calculation of the wave-vector- and frequency-dependent paramagnetic spin susceptibility of an interacting electron gas is presented. The equation of motion of the double-time Green's function is solved using a moment-conserving decoupling approximation. For the short-range interaction, our expression for the dynamic spin susceptibility reduces to a previous result of Wolff. In the static and long-wavelength limit, our result for the Stonerenhanced spin susceptibility coincides with that obtained from consideration of the groundstate energy in the Hartree-Fock approximation.
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The spin susceptibility of the electron gas is studied using a functional integral formulation. A Hubbard-Stratonovich transformation is used to decouple the electron-electron interaction. A uniform Fock mean field is chosen, and effects of small fluctuations about this mean field are retained up to second order. The term that gives the usual spin random-phase approximation susceptibility is identified, with the ladder sum contained in the propagator for the field fluctuations. Computations of the static spin susceptibility outline the region of stability as a function of electron-gas coupling parameter and wave vector. These computations parallel those of Hamann and Overhauser [Phys. Rev. 143, 183 (1966)] for the Yukawa interaction. We use the analytic continuation method of Staunton et al. [Phys. Rev. Lett. 82, 3340 (1999)] to extend the calculations to nonzero frequency. The resulting spectral density shows the increase in low-energy spin fluctuations as the spin-density-wave transition is approached, and the development of a pseudogap in the spin fluctuation spectrum near the wave vector of the transition.
The problem of the many-body enhancement of the static spin susceptibility at long wavelengths and its relation to the quasiparticle effective mass is investigated for a normal electron gas in two-dimensional space as a function of the electronic density. We start from a discussion of the results of the simple Hartree-Fock approximation for various interaction potentials and proceed to develop a complete theory. We find that the effects of the electron-electron interaction are significantly larger than in the familiar three-dimensional case. Our approach is based on a new self-consistent scheme which goes beyond the simple random-phase approximation by explicitly allowing for charge- and spin-fluctuation-induced vertex corrections of the Hubbard type. We show that when the latter are neglected, the many-body enhancement of the spin susceptibility can be cast in a remarkably simple and elegant analytic form.
The Green's function method is applied to investigate the magnetic spin resonance spectra of three-dimensional and two-dimensional spin-polarized quantum gases. The Hartree-Fock approximation is employed to calculate the one-particle Green's function of the atoms, then this one-particle Green's function is used for the calculation of the vertex part of the Green's function. Such a combination yields a self-consistent result. The absorption spectra are obtained from the calculation of the susceptibility in terms of the two-particle Green's function (bubble diagram). Some general expressions for the dispersion relation, for the effective mass of a spin wave, and for the dipolar frequency shift are given in the calculation. In order to estimate the shift of the electron-spin-resonance (ESR) frequency, the effective dipole-dipole interactions among the hydrogen atoms are included in the calculation. These effective interactions are deduced from the ladder approximation, and hence are characterized by the scattering amplitude. The scattering amplitude is calculated numerically. The result shows that the theoretical value of the shift is smaller than the experimentally observed value by about 35%.
Investigation have been carried out on the spin wave energy of a ferromagnet using the random-phase approximation (RPA) in the Stoner model. Based on the Hubbard-Hirsch Hamiltonian, in this paper we study the spin excitation in an itinerant-electron system with the Hartree-Fock Approximation (HFA) to derive the analytic expressions of the dynamical susceptibility of the spin system, by setting up the equation of motion and solving it in a generalized HFA of the susceptibility tensor, Χ-+, and quoting the result for the first derivative of the Green's function. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 579-582
We have made a study of the effect of exchange and correlation on spin density waves in the uniform electron gas. In order to take these effects into account, we have used two new magnetic susceptibility formulas which we have recently derived. The first of these is the time-dependent Hartree-Fock (TDHF) formula which contains exchange but no correlation, while the second one is the generalized random phase approximation (GRPA) formula which contains both exchange and correlation. Both of these formulas were evaluated for the uniform electron gas. The TDHF susceptibility was found to have an absolute maximum at a nonzero value of q, while the GRPA susceptibility was found to have an absolute maximum at q = 0. This indicates that when exchange effects are included in the susceptibility, the ground state of the uniform electron gas contains a spin density wave, but when correlation effects are also included, then the spin density wave is no longer present in the ground state of the uniform electron gas.