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.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.

Physical review. B, Condensed matterFeb 1, 19943 citations

A criterion for the existence of spin waves in polarized gases in a wide temperature range

T. L. Andreeva, P. L. Rubin

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.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.

Journal of Experimental and Theoretical PhysicsMay 1, 20062 citations

Transverse spin diffusion and spin rotation in very dilute, spin-polarized −43 He mixtures

Donald Candela, D. R. McAllaster, L-J. Wei

We report measurements of the transverse-spin-diffusion coefficient ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$ and the spin-rotation parameter \ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ for two very dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures ( ${\mathit{x}}_{3}$ =1.82\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ and 6.26\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$) spin polarized by an 8-T magnetic field. Brute-force spin polarization up to 40% was achieved at the lowest temperature, 6 mK. We find that \ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ increases monotonically as the temperature is reduced through the Fermi temperature ${\mathit{T}}_{\mathit{F}}$ , in disagreement with the only previous experiment but in good agreement with recent theory. Unlike the earlier experiment, which measured spin echoes, the present experiments employed a spin-wave technique that avoids nonlinear excitation of the spin field. We compare our results with the recent calculations of Jeon and Mullin for spin transport in dilute gases with arbitrary polarization and degeneracy. The best fit to the data is obtained by scaling the quasiparticle interaction V(q) proposed by Ebner by a modest factor, 1.07. The corresponding s-wave scattering length is a=-1.21 \AA{}. Good agreement is found for \ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$(T) at both concentrations and all temperatures, and for ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$/\ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$(T) apart from the lower concentration at T20 mK. The discrepancy in ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$/\ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ at the lowest temperatures and ${\mathit{x}}_{3}$ could be explained by an unanticipated polarization dependence or by modification of the spin-wave boundary condition by processes occurring at the interface between the mixture and the silica cavity wall.We report measurements of the transverse-spin-diffusion coefficient ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$ and the spin-rotation parameter \ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ for two very dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures (${\mathit{x}}_{3}$=1.82\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ and 6.26\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$) spin polarized by an 8-T magnetic field. Brute-force spin polarization up to 40% was achieved at the lowest temperature, 6 mK. We find that \ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ increases monotonically as the temperature is reduced through the Fermi temperature ${\mathit{T}}_{\mathit{F}}$, in disagreement with the only previous experiment but in good agreement with recent theory. Unlike the earlier experiment, which measured spin echoes, the present experiments employed a spin-wave technique that avoids nonlinear excitation of the spin field. We compare our results with the recent calculations of Jeon and Mullin for spin transport in dilute gases with arbitrary polarization and degeneracy. The best fit to the data is obtained by scaling the quasiparticle interaction V(q) proposed by Ebner by a modest factor, 1.07. The corresponding s-wave scattering length is a=-1.21 \AA{}. Good agreement is found for \ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$(T) at both concentrations and all temperatures, and for ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$/\ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$(T) apart from the lower concentration at T20 mK. The discrepancy in ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$/\ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ at the lowest temperatures and ${\mathit{x}}_{3}$ could be explained by an unanticipated polarization dependence or by modification of the spin-wave boundary condition by processes occurring at the interface between the mixture and the silica cavity wall.

Physical review. B, Condensed matterOct 1, 199122 citations

{\mathit{x}}_{3}

=1.82\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ and 6.26\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$) spin polarized by an 8-T magnetic field. Brute-force spin polarization up to 40% was achieved at the lowest temperature, 6 mK. We find that \ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ increases monotonically as the temperature is reduced through the Fermi temperature

{\mathit{T}}_{\mathit{F}}

, in disagreement with the only previous experiment but in good agreement with recent theory. Unlike the earlier experiment, which measured spin echoes, the present experiments employed a spin-wave technique that avoids nonlinear excitation of the spin field. We compare our results with the recent calculations of Jeon and Mullin for spin transport in dilute gases with arbitrary polarization and degeneracy. The best fit to the data is obtained by scaling the quasiparticle interaction V(q) proposed by Ebner by a modest factor, 1.07. The corresponding s-wave scattering length is a=-1.21 \AA{}. Good agreement is found for \ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$(T) at both concentrations and all temperatures, and for ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$/\ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$(T) apart from the lower concentration at T20 mK. The discrepancy in ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$/\ensuremath{\Omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ at the lowest temperatures and

{\mathit{x}}_{3}

could be explained by an unanticipated polarization dependence or by modification of the spin-wave boundary condition by processes occurring at the interface between the mixture and the silica cavity wall.