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Journal of Experimental and Theoretical Physics

Dynamics of the magnetic moment in a polarized Boltzmann gas allowing for dissipation

T. L. Andreeva, P. L. Rubin

Published Oct 1, 2000• 1 citation
Publisher

Abstract

An equation is derived for the dynamics of the spin magnetic moment in a polarized Boltzmann gas allowing for spin loss processes. The general form of the T matrix for collisions between two spin 1/2 particles allowing for inelastic processes is used. It is shown that the rate of spin loss depends on the degree of polarization of the gas. As a result, the damping of deviations of the magnetic moment from the average becomes anisotropic where the degree of anisotropy depends on the amplitude of the zero-angle scattering of atoms.

DOI
10.1134/1.1326968

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An equation is derived for the dynamics of the spin magnetic moment in a polarized Boltzmann gas allowing for spin loss processes. The general form of the T matrix for collisions between two spin 1/2 particles allowing for inelastic processes is used. It is shown that the rate of spin loss depends on the degree of polarization of the gas. As a result, the damping of deviations of the magnetic moment from the average becomes anisotropic where the degree of anisotropy depends on the amplitude of the zero-angle scattering of atoms.
We derive a kinetic equation for a polarized paramagnetic gas that is exact in the Boltzmann (binary) approximation. The equation is written in a compact form and applies to both Fermi and Bose gases in a wide temperature range as long as the Boltzmann approximation remains applicable. The derived equation is used to analyze the conditions for the propagation of spin waves in polarized Fermi and Bose gases. We deduce a universal criterion for the propagation of weakly damped spin waves in a wide temperature range. The criterion is reduced to the condition that the real parts of the particle zero-angle scattering amplitudes (or T matrices) be much larger than their imaginary parts. We derive dispersion equations for spin waves at high and low gas temperatures and show that spin waves can propagate in both these limiting cases.
Experimental data on the decay of spin polarization in rubidium vapor are compared with inferences of the theory developed by the authors for spin-polarized Boltzmann gases. It is demonstrated that the nonexponential pattern of polarization decay points to the anisotropy of the indicatrix of inelastic scattering of rubidium atoms at high temperatures. Estimates are obtained of the degree of anisotropy of such inelastic scattering, i.e., scattering with variation of total spin. Under the experimental conditions, the indicatrix of inelastic scattering turns out to be highly extended forward, with the degree of anisotropy of the order of 1000.
In this work, we study the dynamics of an atomic harmonically trapped large-spin Fermi gas in one dimension (1D). We investigate the interplay of different collision processes. Coherent spin oscillations, driven by spin-changing forward scattering are captured by a mean-field description and scale linearly with density regardless of the dimension of the system. Conversely, "incoherent" collision processes which e.g. lead to the damping of spin oscillations, behave differently. In the usual three-dimensional (3D) case, the rate of incoherent processes increases faster with density than mean-field effects, but in 1D it increases slower. This means, that in the 1D case, incoherent collisions become more important at lower densities. We study these effects by deriving and integrating a quantum Boltzmann equation. We demonstrate that the well known fact that in one dimension, interaction-induced correlations become more dominant at low densities can be observed in far-from-equilibrium spin dynamics.
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.