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Physical review. B, Condensed matter

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

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

Published Oct 1, 1991• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.44.7510

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Transverse spin dynamics have been measured for a very dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He mixture (${\mathit{x}}_{3}$=1.82\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$) polarized by an 8-T magnetic field. The sample was confined to a small spherical resonator, resulting in well-defined spin-wave modes for temperatures below 50 mK. Results are presented for the spin-rotation parameter ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{int}}$${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ and spin-wave dispersion ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$/${\mathrm{\ensuremath{\Omega}}}_{\mathrm{int}}$${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$. It is found that ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{int}}$${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ increases monotonically as the temperature is decreased below the degeneracy temperature ${\mathit{T}}_{\mathit{F}}$, in apparent disagreement with an earlier experiment.

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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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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.

International Journal of Modern Physics B•Aug 30, 2002•3 citations
We report measurements of the transverse-spin-diffusion coefficient D\ensuremath⊥{\mathit{D}}_{\mathrm{\ensuremath{\perp}}}D\ensuremath⊥​ and the spin-rotation parameter \ensuremath{\Omega}\ensuremathτ\ensuremath⊥{\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}\ensuremathτ\ensuremath⊥​ for two very dilute 3\ensuremath−4^{3}\mathrm{\ensuremath{-}}^{4}3\ensuremath−4He mixtures (x3{\mathit{x}}_{3}x3​=1.82\ifmmode\times\else\texttimes\fi{}10\ensuremath−3{10}^{\mathrm{\ensuremath{-}}3}10\ensuremath−3 and 6.26\ifmmode\times\else\texttimes\fi{}10\ensuremath−4{10}^{\mathrm{\ensuremath{-}}4}10\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}\ensuremathτ\ensuremath⊥{\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}\ensuremathτ\ensuremath⊥​ 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}\ensuremathτ\ensuremath⊥{\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}\ensuremathτ\ensuremath⊥​(T) at both concentrations and all temperatures, and for D\ensuremath⊥{\mathit{D}}_{\mathrm{\ensuremath{\perp}}}D\ensuremath⊥​/\ensuremath{\Omega}\ensuremathτ\ensuremath⊥{\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}\ensuremathτ\ensuremath⊥​(T) apart from the lower concentration at T20 mK. The discrepancy in D\ensuremath⊥{\mathit{D}}_{\mathrm{\ensuremath{\perp}}}D\ensuremath⊥​/\ensuremath{\Omega}\ensuremathτ\ensuremath⊥{\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}\ensuremathτ\ensuremath⊥​ 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.
Transverse spin dynamics have been measured for a very dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He mixture (x3{\mathit{x}}_{3}x3​=1.82\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$) polarized by an 8-T magnetic field. The sample was confined to a small spherical resonator, resulting in well-defined spin-wave modes for temperatures below 50 mK. Results are presented for the spin-rotation parameter ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{int}}$${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ and spin-wave dispersion ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$/${\mathrm{\ensuremath{\Omega}}}_{\mathrm{int}}$${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$. It is found that ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{int}}$${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ increases monotonically as the temperature is decreased below the degeneracy temperature TF{\mathit{T}}_{\mathit{F}}TF​, in apparent disagreement with an earlier experiment.
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 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.
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.
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 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.