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Physical review. B, Condensed matter

Boundary effects and spin waves in spin-polarized quantum gases

A. E. Meyerovich, Sergey B. Stepaniants

Published Feb 1, 1994• 3 citations
Publisher

Abstract

Boundary conditions are derived for spin dynamics of spin-polarized quantum gases near nonmagnetic walls. We are interested mostly in boundary-induced line shifts and attenuation of spin waves, and in the possibility of having a macroscopic boundary condition for systems close to a Knudsen ballistic regime. We consider the effects caused by roughness of the wall and by surface adsorption. By a proper coordinate transformation, we reduce the problem of particle collisions with an inhomogeneous nonmagnetic wall to an equivalent problem with a specular homogeneous wall but with stochastic bulk imperfections. As a result, the boundary effects are described by some additional bulklike transverse spin-diffusion coefficient inversely proportional to the angular harmonics of the correlation function of surface inhomogeneities. This leads to an effective macroscopiclike boundary condition for transverse spin dynamics responsible for the boundary effects in spin-wave resonances. The situation changes drastically at low temperatures because of an appearance of an adsorbed boundary layer which renormalizes the molecular field near the wall, and leads to additional effective spin-exchange processes. The experimental implications for helium and hydrogen systems are discussed.

DOI
10.1103/physrevb.49.3400

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Boundary conditions are derived for spin dynamics of spin-polarized quantum gases near nonmagnetic walls. We are interested mostly in boundary-induced line shifts and attenuation of spin waves, and in the possibility of having a macroscopic boundary condition for systems close to a Knudsen ballistic regime. We consider the effects caused by roughness of the wall and by surface adsorption. By a proper coordinate transformation, we reduce the problem of particle collisions with an inhomogeneous nonmagnetic wall to an equivalent problem with a specular homogeneous wall but with stochastic bulk imperfections. As a result, the boundary effects are described by some additional bulklike transverse spin-diffusion coefficient inversely proportional to the angular harmonics of the correlation function of surface inhomogeneities. This leads to an effective macroscopiclike boundary condition for transverse spin dynamics responsible for the boundary effects in spin-wave resonances. The situation changes drastically at low temperatures because of an appearance of an adsorbed boundary layer which renormalizes the molecular field near the wall, and leads to additional effective spin-exchange processes. The experimental implications for helium and hydrogen systems are discussed.
Accurate measurements on the nuclear-spin waves observed in the NMR spectrum of spin-polarized atomic hydrogen provide a quantitative test of theory. Results for temperatures between 160 and 537 mK and densities between 7\ifmmode\times\else\texttimes\fi{}1015{10}^{15}1015 and 5\ifmmode\times\else\texttimes\fi{}1016{10}^{16}1016 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ display the expected magnitude and ${T}^{\mathrm{\ensuremath{-}}1/2}$ divergence predicted for the spin-wave quality factor \ensuremath{\mu}. It is shown that spin waves persist at low enough densities (Knudsen regime) that elastic wall collisions are more probable than atom-atom exchange collisions. An anomalous increase in spin-wave widths at low temperatures is explained in terms of the enhanced effects of sticking collisions of the atoms with the walls.
The nature of spin-type zero sound, "paramagnetic spin waves" (PSW's), in free-electron gases is studied by means of the time-dependent Hartree-Fock approximation. The importance of attractive interactions is emphasized. A short-wavelength cutoff in the spectrum at microwave or low infrared frequencies is found. The effect of the application of magnetic fields is studied. The frequencies are shifted by the Larmor precession. Some branches of the spectrum are effectively eliminated; others are strengthened and split. Spin wave fronts travel in helices about magnetic field lines. PSW's are damped by electron collisions with crystal imperfections. The relaxation time is identical with the relaxation time as determined by the dc conductivity. Electron-electron collision damping is also studied and found to be negligible by comparison. The observation of Landau-damped modes is considered and conditions where this is possible are indicated. A boundary condition is found: A surface must be at an antinode of the spin density. A microwave, "thin"-film resonance experiment is suggested. The strength of the resonance lines is considered. An expression for power dissipation at PSW resonance is derived.
Field-inhomogeneity-induced relaxation of atomic spins confined in vapor cells with depolarizing walls is studied. In contrast to nuclear spins, such as noble-gas spins, which experience minimal polarization loss at cell walls, atomic spins in uncoated cells undergo randomization at the boundaries. This distinct boundary condition results in a varied dependence of the relaxation rate on the field gradient. By solving the Bloch-Torrey equation under fully depolarizing boundary conditions, we illustrate that the relaxation rate induced by field inhomogeneity is more pronounced for spins with a smaller original relaxation rate (in the absence of the inhomogeneous field). We establish an upper limit for the relaxation rate through calculations in the perturbation regime. Moreover, we connect it to the spin-exchange-relaxation-free magnetometers, demonstrating that its linewidth is most sensitive to inhomogeneous fields along the magnetometer's sensitive axis. Our theoretical result agrees with the experimental data for cells subjected to small pump power. A deviation in high input-power scenarios arises from pump field attenuation, resulting in a nonuniformly distributed light shift that behaves like an inhomogeneous magnetic field.
We study the transverse spin dynamics of trapped polarized Fermi gases in the high temperature limit. In the non-interacting collisionless regime, a magnetic field gradient induces collective spin wave oscillations. In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two limits have been extensively studied both experimentally and theoretically, but the crossover between them has received less attention. In this paper, we use a quantum Boltzmann equation to study transverse spin dynamics and show how the excitations evolve from dispersive to diffusive in the high temperature limit. We provide analytical solutions in the two limiting regimes, which agree well with our numerical results.
The identical spin rotation effect is the quantum mechanical collisional effect underlying the transverse nuclear spin waves recently seen in dilute non degenerate gases in Paris [3He] and at Cornell University [H↓]. This mechanism could in principle give rise, at low enough temperatures, to hydrodynamic oscillatory modes associated with any non diagonal elements of the atomic internal density matrix (generalized spin waves or coherences waves). Starting from a quantum Boltzmann equation recently derived for the study of 4-component atomic hydrogen, we show that the current of any transverse quantity (hyperfine or Zeeman coherence) does indeed precess around molecular exchange fields. Unhappily, in most cases, the oscillatory modes associated with these transverse quantities are heavily damped. The first intrinsic cause of damping of these waves is spin exchange. We study the conditions under which this damping is minimized in both zero field and in high magnetic field. Numerical values of all relevant parameters for the description of spin transport properties in atomic hydrogen are given in the appendices.
A complete quantum phase shift calculation of several transport coefficients in spin polarized quantum gases (3He, H↑ and D↑) has been carried out for temperatures ranging from 0.04 K to 10 K and nuclear polarizations M varying from 0 to 1. After a detailed analysis of the dynamical features of the collision, the various direct and exchange « cross sections » necessary to describe the collision between two spin-polarized atoms are studied Emphasis is then placed on some particle-indistinguishability consequences that could be seen in 3He or H↑ systems, such as the strong M dependence of the heat capacity, a mode coupling between heat capacity and longitudinal spin diffusion and the oscillatory character of the evolution of the transverse components of M.