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Physical review. B, Condensed matter

Transverse dynamics and relaxation in spin-polarized or two-level Fermi systems

A. E. Meyerovich, Karen A. Musaelian

Published Feb 1, 1993• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.47.2897

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Zero-temperature attenuation and transverse spin dynamics in Fermi liquids. I. Generalized Landau theory

A. E. Meyerovich, Karen A. Musaelian

Journal of Low Temperature Physics•Dec 1, 1992•69 citations
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.
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.
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.
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 explain the anomalous temperature dependence of spin diffusion in liquid $^{3}\mathrm{\ensuremath{\uparrow}}$ and $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures. The anomaly is an experimental manifestation of a unique zero-temperature attenuation in the Fermi liquid theory. We extended our microscopic theory of spin dynamics in spin-polarized Fermi liquids to finite temperatures. The zero-temperature attenuation changes the behavior of the spectrum near the singular point. The data indicate that the superfluid transition temperature for 3He^{3}\mathrm{He}3He in $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures is much lower than the current estimates.