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Physical review. B, Condensed matter

Spin waves in itinerant-electron spin-density-wave states

Rishabh Kishore

Published Jun 1, 1980• 1 citation
Publisher

Abstract

The transverse dynamical susceptibility and the spin-wave stiffness constant of spin-density-wave (SDW) states in itinerant-electron systems are studied. The Hamiltonian is transformed by using a transformation which rotates the spin coordinate system locally, so that the new $z$ direction lies in the direction of the local spin. For this transformed Hamiltonian, a self-consistent many-body theory developed by Fedro and Wilson and extended by Kishore is exploited to derive an exact expression for the transverse dynamical susceptibility. From the long-wavelength limit of the spin-wave spectrum, given by the poles of the transverse dynamical susceptibility, an exact formula for the spin-wave stiffness constant is obtained. Within the Hartree-Fock approximation, it reduces to the Fisher's formula for antiferromagnets.

DOI
10.1103/physrevb.21.5375

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The transverse dynamical susceptibility and the spin-wave stiffness constant of spin-density-wave (SDW) states in itinerant-electron systems are studied. The Hamiltonian is transformed by using a transformation which rotates the spin coordinate system locally, so that the new zzz direction lies in the direction of the local spin. For this transformed Hamiltonian, a self-consistent many-body theory developed by Fedro and Wilson and extended by Kishore is exploited to derive an exact expression for the transverse dynamical susceptibility. From the long-wavelength limit of the spin-wave spectrum, given by the poles of the transverse dynamical susceptibility, an exact formula for the spin-wave stiffness constant is obtained. Within the Hartree-Fock approximation, it reduces to the Fisher's formula for antiferromagnets.
A self-consistent many-body theory for the many-particle Green's function is developed and applied to derive an exact microscopic formula for the transverse dynamical susceptibility. As a concrete application of the above general results we consider the Hubbard Hamiltonian and obtain the spin-wave stiffness constant for an itinerant ferromagnet. It is found that earlier expressions for the stiffness constant obtained by Edwards and Hertz and Edwards are special cases of our general expression.
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
Spin density waves (SDW) provide a canonical example of quantum states with spontaneously broken symmetries. The dynamics of SDWs in Mott insulators is described by the well-known Holstein-Primakoff Hamiltonian, which is equivalent to the semiclassical Landau-Lifshitz equation. Based on a real-space formulation of the time-dependent Hartree-Fock method, the authors demonstrate how to extend the semiclassical dynamics description to the case of itinerant magnets or Mott systems with a moderate charge gap. They further show that, within the adiabatic approximation, the SDW dynamics is governed by a generalized quantum Landau-Lifshitz equation.
The spin-density wave (SDW) state of the uniform electron gas is investigated in the exact-exchange approximation of noncollinear spin-density functional theory (DFT). Unlike in Hartree-Fock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin-density wave for all densities, in exact-exchange spin DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a noninteracting SDW ground-state Slater determinant with energy lower than the corresponding paramagnetic state, this Slater determinant is not a self-consistent solution of the optimized effective potential (OEP) integral equations of noncollinear spin DFT. A self-consistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.
We investigate possible spin instabilities of integer quantum Hall systems as a function of the density within the framework of the self-consistent Hartree-Fock theory. We have found a spin density wave (SDW) state that is lower in energy than the paramagnetic and ferromagnetic states for the filling factor $\ensuremath{\nu}=2$ in the density region 2.01<rs<2.152.01<{r}_{s}<2.152.01<rs​<2.15. The new SDW phase is the very one that has been expected by the softening of excitation spectra of the spin density excitation. We have examined the SDW phase in detail using the density matrix.
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.