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Physical Review A

Spin waves in a persistent spin-current Fermi liquid

J. D. Feldmann, Kevin S. Bedell

Published Jun 14, 2010• 0 citations
Publisher

Abstract

We report two theoretical results for transverse spin waves, which arise in a system with a persistent spin current. Using Fermi liquid theory, we introduce a spin current in the ground state of a polarized or unpolarized Fermi liquid, and we derive the resultant spin waves using the Landau kinetic equation. The resulting spin waves have a ${q}^{1}$ and ${q}^{1/2}$ dispersion to leading order for the polarized and unpolarized systems, respectively.

DOI
10.1103/physreva.81.063622

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We report two theoretical results for transverse spin waves, which arise in a system with a persistent spin current. Using Fermi liquid theory, we introduce a spin current in the ground state of a polarized or unpolarized Fermi liquid, and we derive the resultant spin waves using the Landau kinetic equation. The resulting spin waves have a q1{q}^{1}q1 and q1/2{q}^{1/2}q1/2 dispersion to leading order for the polarized and unpolarized systems, respectively.
Linear equations for the transverse spin dynamics in a weakly polarized degenerate Fermi liquid are derived from the Landau-Silin phenomenological kinetic equation with a general two-particle collision integral. Unlike a previous treatment where the Fermi velocity and density of states were taken to be constant independent of polarization we make no such assumption. The equations found describe the spin dynamics in a paramagnetic Fermi liquid with finite polarization as well in an itinerant ferromagnet. The results are confirmed by field theoretical calculations based on the integral equation for the vertex function. The transverse spin wave frequency in a polarized paramagnetic Fermi liquid is found to be proportional to k2{k}^{2}k2 with a complex diffusion coefficient such that the damping has a finite value proportional to the quasiparticles scattering rate at T=0T=0T=0. This behavior of a polarized Fermi liquid contrasts with the behavior of a Heisenberg ferromagnet in the hydrodynamic regime where the transverse spin-wave attenuation appears in terms proportional to k4{k}^{4}k4. The reactive part of the diffusion coefficient in a paramagnetic state at T=0T=0T=0 proves to be inversely proportional to the magnetization whereas in a ferromagnetic it is directly proportional to the magnetization. The dissipative part of the diffusion coefficient at T=0T=0T=0 in the paramagnetic state is polarization independent, whereas in the ferromagnetic state it is proportional to the square of the magnetization. Moreover, the spin wave spectrum in a ferromagnetic Fermi liquid proves to be unstable demonstrating the difficulty of applying a Fermi liquid description to itinerant ferromagnetism.
The linear equations for transverse spin dynamics in a weakly polarized degenerate Fermi liquid with arbitrary relationship between temperature T and polarization $\ensuremath{\gamma}H$ are derived from Landau-Silin phenomenological kinetic equation with general form of two-particle collision integral. The temperature and polarization dependence of the spin current relaxation time is established. It is found in particular that at finite polarization transverse spin wave damping has a finite value at T=0.T=0.T=0. The analogy between temperature dependences of spin wave attenuation and ultrasound absorption in degenerate Fermi liquid at arbitrary temperature is presented. We also discuss spin-polarized Fermi-liquid in the general context of the Fermi-liquid theory and compare it with ``Fermi liquid'' with spontaneous magnetization.
A microscopic derivation of the equations of transverse spin dynamics of a spin-polarized Fermi liquid at zero temperature is given in the leading-order approximation in the frequencies and wave vectors characterizing the spin motion. The equations are applicable for arbitrary degree of polarization and arbitrary deviations of the spin direction from the equilibrium orientation. The solutions describing a coherently precessing two-domain structure and spin waves are examined. In contrast to the assertion discussed in the literature that spin waves are damped at zero temperature, spin waves are found to be undamped in the long-wavelength limit.
We study the spin dynamics of a normal Fermi liquid taking into account the demagnetizing field produced by the spin system itself. Linear solutions of the spin dynamics equations in the form of standing spin waves in a finite volume of liquid are found. At almost all known experimental conditions the influence of demagnetizing field can be satisfactorily described by the first order of perturbation theory. We carried out perturbational calculations for two geometries of experimental cell---spherical and finite cylindrical. We performed also exact numerical simulations of the spin-wave spectra in a spherical cell at an arbitrary strength of the demagnetizing field. The obtained results are applied in particular to conditions of recent experiment [G. Vermeulen and A. Roni, Phys. Rev. Lett. 86, 248 (2001)] related to the problem of zero-temperature transverse relaxation in a polarized Fermi liquid. We found that not taking into account the demagnetizing field leads to negligible errors in the measured relaxation time, thus supporting the conclusion of the absence of zero-temperature spin-wave damping.
A microscopic theory is proposed for transverse dynamics and zero-temperature attenuation in polarized Fermi liquids. The transport equations are a set of two coupled equations in two ``partial transverse densities,'' which do not reduce to a single equation in a mixed component of a single-particle distribution. The effective interaction is linked to an irreducible vertex by an integral equation, and cannot be given as a limit of a full vertex. A framework for a generalized nonlocal Landau theory is established. The spectrum of attenuating spin waves is calculated at arbitrary polarizations and densities.