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Momentum and spin transport properties of spin polarized Fermi systems

Wei Lijuan

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.

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Physical Review Letters•Aug 9, 1993•91 citations
We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.
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 (x3{\mathit{x}}_{3}x3​=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 TF{\mathit{T}}_{\mathit{F}}TF​, 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 x3{\mathit{x}}_{3}x3​ 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.
Abstract Very dilute solutions of 3He in superfluid 4He behave as an almost ideal Fermi gas at millikelvin temperatures, which can be strongly polarized in high magnetic fields. This has enabled studies of their equilibrium, transport, and dynamical spin properties to be made over a wide range of temperatures, concentrations, and polarizations covering systems that are highly degenerate to those that are non-degenerate. This chapter discusses polarized Fermi gas, model theories, equilibrium theories, transport properties, and spin dynamics.
We present vibrating - wire viscosity measurements on a very dilute 3 He -4 He mixture (χ3 = 150 ppm ) in fields up to 14.8 T and temperatures down to 3 mK. The 3 He spin polarization is greater than 99% for the highest field and lowest temperature used. In these conditions, the s-wave scattering rate decreases due to a lack of quasiparticles with the minority spin state. This enhances all transport coefficients including the viscosity. At the lowest temperature, the hydrodynamic damping of the viscometer in a 14.8 T field was more than 10 times larger than in low fields. This indicates a many-fold increase in the mixture viscosity due to spin polarization.
Experiments have been performed at high B/T to try to establish the existence and value of an anisotropy temperature (Ta) for pure 3He, and for 6.2% and 0.7% 3He-4He mixtures. The anisotropy of diffusion in dilute Fermi gases as the temperature T goes to zero has been predicted, though experimental evidence for such anisotropy has not been universally accepted.\n\nFinite size effects have required careful analysis of the theory of the cell for the 6.2% mixture. This alters the result as determined by the usual Leggett-Rice formula. Further investigation, beyond the scope of this thesis, is currently underway for the case of pure 3He.\n\nThe possibility of using a quartz tuning fork as a viscometer has also been investigated. It is shown that tuning forks can be used field-inpendently above 3 mK in saturated 3He-4He mixtures, and to detect the superfluid A and B-phase transitions in pure 3He. It is strongly suggested from the data that the tuning fork has great potential as a high-field viscometer; however further experiments are required to fully appreciate its useful range, in both normal and superfluids.
A vibrating-wire technique has been used to directly measure the viscosity increase in a dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He solution caused by brute-force spin polarization up to 40%. The viscosity of a solution with degeneracy temperature TF{\mathit{T}}_{\mathit{F}}TF​=19.5 mK was measured over the temperature range 6.1--100 mK in magnetic fields of 1.00 and 7.96 T. Spin polarization caused a marked decrease in the mechanical Q of the viscometer at low temperatures. The observed viscosity is compared with calculations of the transport coefficients of dilute quantum gases for all temperatures and spin polarizations.
We have studied NMR spin echoes in 3He^{3}\mathrm{He}3He liquid in a magnetic field B0{\mathit{B}}_{0}B0​=8 T for temperatures T\ensuremath{\ge}4.5 mK. The data are analyzed in terms of the Leggett-Rice effect to obtain the transverse spin-diffusion coefficient ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$(T). For T20 mK we find that ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$ is less than measured in earlier experiments at lower B0{\mathit{B}}_{0}B0​. This phenomenon has been predicted for degenerate Fermi systems, due to the phase space created for quasiparticle scattering by spin polarization. The effect we have measured is more pronounced than suggested by scaling a dilute-gas theory result by a Fermi-liquid factor.