Observation of field-induced spin-current relaxation in a Fermi liquid

Abstract

We have studied NMR spin echoes in 3 He liquid in a magnetic field #o = 8 T for temperatures T>4.5 mK. The data are analyzed in terms of the Leggett-Rice effect to obtain the transverse spindiffusion coefficient D± (T). For T<20 mK we find that D± is less than measured in earlier experiments at lower Bo. 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.PACS numbers: 67.65. +Z, 67.55.-s In degenerate Fermi liquids in which interparticle collisions dominate scattering ( 3 He and certain metallic systems), the transport coefficients diverge as the temperature T-* 0. This fundamental property is due to the restriction of scattering phase space to a shell of width kg about the Fermi surface. Recently, it was independently predicted by Meyerovich [1] and by Jeon and Mullin [2] that the divergence in the transverse spin-diffusion coefficient D± oc T~2 is removed by arbitrarily small spin polarization P of the system. Below a temperature T a which depends upon P, spin diffusion becomes anisotropic, with D±<D\\, and D± is predicted to have a finite value at zero temperature [3]. We report the first clear experimental evidence for this effect.The effect is predicted because spin polarization opens a gap between spin-up and spin-down Fermi surfaces, which provides phase space for scattering that can relax transverse spin currents. By equating the energy gap in a magnetic field Z?o with the thermal energy at T = T a one estimates T a -hyBo/kB, where y is the gyromagnetic ratio. For 3 He in a strong laboratory field, Bo-8 T, the estimate is 7^ = 12.4 mK, but an earlier experiment [4] in which D± was measured at Z?o = 8 T and T>6 mK found no significant deviation from either the expected low-field behavior or the measured behavior [5] of D\\ at BQ=9.2 T. These earlier experiments used very dilute 3 He-4 He mixtures in which the 3 He quasiparticles form a weakly interacting gas. Thus, if polarization does cause D± < D\u this must occur at lower temperatures or higher fields.Reason to expect a lower value for T a has come from the kinetic-equation calculations of Jeon and Mullin [2]. For a dilute, weakly polarized Fermi gas with s-wave interactions, they obtained Ta^hyBjlTtkB.Unfortunately this suggests spin-diffusion anisotropy should be difficult to observe in available laboratory fields unless nuclear demagnetization were used to achieve much lower temperatures.In an attempt to observe the effect using conventional dilution refrigeration, we have studied spin diffusion in pure 3 He liquid at BQ^S T. Pure 3 He is a strongly in-teracting system, but for T<£T F it is successfully described by Fermi-liquid theory as a weakly interacting quasiparticle gas with strong mean-field effects. At zero pressure 7> = 1.8 K and mean-field effects enhance the effective magnetic field by a factor of (1 -FFg) _1 = 3.3, wh...

Low-Temperature Spin Diffusion in a Spin-Polarized Fermi Gas

“…Some comments are in order concerning the possible relevance of our findings to experiment. First we note that the available experimental data in weakly polarized 3 He [6] deviate systematically from the naive theoretical fit which uses a single adjustable parameter (T a in [6]) to cover the entire temperature range including both, ξ > 1 and ξ < 1. Much better agreement is obtained by restricting the fit to the ξ ≤ 1 region with an overall prefactor smaller than the one implied by fitting to the value of D in the low field, high temperature regime (we use for the inverse overall prefactor the value A ≈ 7.7 × 10 5 sec/cm 2 K 2 instead of 5.8 × 10 5 sec/cm 2 K 2 as in Reference [6] and for the "anisotropy temperature" T a ≈ 12.5 mK instead of 16.4 mK).…”

“…As can be shown by analysing the eigenvalue spectrum of the relaxational part of the collision integral I rel1 [f ] the spin current decays to its steady state value in a microscopic time scale, τ ⊥ , beyond which the time derivative terms in equations (5)(6) can be omitted. In addition, since ∂ M ⊥ (x)/∂x = const or equivalently ∂g/∂x is independent of x, equation (6) implies ∂f /∂x = 0.…”

Leggett-Rice effect in a finite geometry

“…Using the data of Candela et al, 7 the corresponding apparent anisotropy temperature would be 3 mK in pure 3 He at 8 T, which is much smaller than the value of 16 mK reported in Ref. 16.…”

“…In terms of anisotropy temperature, such a saturation value of the spin rotation parameter would correspond to an apparent T a of 9 mK for 6.4% 3 He-4 He mixture at 11.3 T, based on the spin rotation parameter data of Ishimoto et al 17 Consequently, we infer that the value of T a ϭ13 mK reported in our earlier publication 5 is largely due to finite-size effects. By contrast, for the experiment of Wei et al, 16 the value of parameter b L was 7.4 ϫ10 4 , so we expect the effect of restricted diffusion to be relatively small. Using the data of Candela et al, 7 the corresponding apparent anisotropy temperature would be 3 mK in pure 3 He at 8 T, which is much smaller than the value of 16 mK reported in Ref.…”

“…Unfortunately, the experiments so far have given contradictory results. 4,5,15,16 As we shall show, restricted diffusion effects may explain some of the discrepancies between the experimental results.…”