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Physical review. B, Condensed matter

Spin diffusion in paramagnetic quantum fluids

Andrei E. Ruckenstein, Laurent P. Lévy

Published Jan 1, 1989• 23 citations
Publisher

Abstract

We derive the linearized spin dynamics for paramagnetic quantum liquids. In these systems, the existence of quantum-mechanical exchange in the presence of (an externally induced) broken symmetry in spin space gives rise to a coherent precession of the spins damped by diffusion. Such collective oscillations occur as a result of the precession of the spin current about a macroscopic local exchange field generated either by an external polarizing magnetic field (as in dilute nondegenerate spin-polarized gases) or by the long-lived nonequilibrium polarization (as in degenerate Fermi liquids). We use a unified approach based on the Kadanoff-Baym formulation of the kinetic equations to describe these phenomena. The connection between strongly and weakly interacting paramagnetic systems is made obvious by considering two special cases: (1) a weakly interacting spin-polarized quantum gas and (2) a parametrization of strongly correlated degenerate Fermi liquids in terms a weakly interacting gas of ``quasiparticles.'' Transport coefficients are calculated with a novel method which may be generalizable to systems with no translational invariance.

DOI
10.1103/physrevb.39.183

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Physical review. B, Condensed matter•Dec 1, 1991•6 citations
We derive the linearized spin dynamics for paramagnetic quantum liquids. In these systems, the existence of quantum-mechanical exchange in the presence of (an externally induced) broken symmetry in spin space gives rise to a coherent precession of the spins damped by diffusion. Such collective oscillations occur as a result of the precession of the spin current about a macroscopic local exchange field generated either by an external polarizing magnetic field (as in dilute nondegenerate spin-polarized gases) or by the long-lived nonequilibrium polarization (as in degenerate Fermi liquids). We use a unified approach based on the Kadanoff-Baym formulation of the kinetic equations to describe these phenomena. The connection between strongly and weakly interacting paramagnetic systems is made obvious by considering two special cases: (1) a weakly interacting spin-polarized quantum gas and (2) a parametrization of strongly correlated degenerate Fermi liquids in terms a weakly interacting gas of ``quasiparticles.'' Transport coefficients are calculated with a novel method which may be generalizable to systems with no translational invariance.
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.
We calculate the effective spin diffusion coefficient of weak ferromagnet and quasiequilibrium paramagnetic systems using Landau Fermi liquid theory. We find that the behavior of the diffusion coefficient of the quasiequilibrium system is determined primarily by the internal magnetic field, which, in turn, depends upon the nonequilibrium magnetization and the antisymmetric Landau parameters. We also show that this is qualitatively similar to the diffusion coefficient of the weak ferromagnetic system. We discuss its implication for the spin-polarized state created in cold atom systems.
We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization, and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity ${D}_{\ensuremath{\parallel}}$ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity ${D}_{\ensuremath{\perp}}$ has a strong polarization dependence and approaches a finite value for $T\ensuremath{\rightarrow}0$ in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length, the diffusivities reach a minimum near the quantum limit of diffusion $\ensuremath{\hbar}/m$ in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, ${D}_{\ensuremath{\perp}}$ attains a minimum at strong coupling $\ensuremath{-}1\ensuremath{\lesssim}\mathrm{ln}({k}_{F}{a}_{2D})\ensuremath{\lesssim}1$ and reaches ${D}_{\ensuremath{\perp}}\ensuremath{\sim}0.2...\phantom{\rule{0.16em}{0ex}}0.3\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/m$ at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.
We present a finite temperature calculation of the transverse spin-diffusion coefficient ${D}_{\ensuremath{\perp}}$ in a dilute degenerate Fermi gas, in the presence of a small external magnetic field HHH. While the longitudinal diffusion coefficient displays the conventional Fermi-liquid dependence, ${D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$, the behavior of ${D}_{\ensuremath{\perp}}$ shows three separate regimes: (a) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{H}^{\ensuremath{-}2}$ for $T\ensuremath{\ll}H$, (b) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{T}^{\ensuremath{-}2}$, $\frac{{D}_{\ensuremath{\perp}}}{{D}_{\ensuremath{\parallel}}}\ensuremath{\ne}1$ for $T\ensuremath{\gg}H$ and large spin-rotation parameter $\ensuremath{\xi}\ensuremath{\gg}1$, and (c) ${D}_{\ensuremath{\perp}}={D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ for $T\ensuremath{\gg}H$ and $\ensuremath{\xi}\ensuremath{\ll}1$. Our results are qualitatively consistent with the experimental data in weakly spin-polarized 3He^{3}\mathrm{He}3He and 3He^{3}\mathrm{He}3He- 4He^{4}\mathrm{He}4He mixtures.
A theory of magnetotransport phenomena in low-density paramagnetic systems at low temperature is proposed. The main contentions are based on considering a dissipation mechanism due to the inelastic scattering of paramagnetic particles with transverse collective spin fluctuations. In the presence of an external magnetic field and in the low-momentum limit the corresponding cross section may be very large. Theoretical estimates are in good agreement with recent indirect measurements of intrabeam scattering for cooled H atoms. The extra scattering channel results in a drastic reduction in the mean free path and, consequently, a decrease in the thermal conductivity and viscosity, in contrast to previous theories. In the case of degenerate Fermi systems, the calculations yield quite different temperature dependencies compared with those given by the Fermi-liquid approach. Application of the theory to gaseous H\ensuremath{\downarrow}, $^{3}\mathrm{\ensuremath{\uparrow}}$, and dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures are briefly discussed, and it is shown that the thermal conductivity and viscosity of gaseous H\ensuremath{\downarrow} under common conditions are expected to be roughly 102{10}^{2}102 times less than the normal gas-kinetic values.