Longitudinal spin diffusion and nonlinear spin dynamics in a dilute−43He solution

Abstract

We have used pulsed NMR to investigate longitudinal spin diffusion and nonlinear spin dynamics in a dilute (350 ppm) spin-polarized ( -60%) solution of 3 He in 4 He at temperatures between 4 and 400 mK. Our results for the spin diffusion are in good agreement with recent theoretical calculations. In addition, we have observed new, extremely long-lived modes in this system that appear to be driven by a nonlinear instability.PACS numbers: 67.65. +Z, 51.20.+d, 51.60.+a, 67.60.Fp Dilute spin-polarized solutions of 3 He in 4 He have been the subject of much recent experimental and theoretical interest. The possibility of nonlinear spin diffusion in degenerate Fermi systems (with small polarizations) was first pointed out by Leggett and Rice 1,2 and experimentally verified by Corruccini et ai 3 More recently, Bashkin has shown that similar "molecular field" effects are important in highly polarized systems which are at low temperatures, but which still obey Boltzmann, rather than degenerate quantum, statistics. 4 In their treatment of similar nondegenerate systems, Lhuillier and Laloe 5 used careful consideration of forwardscattering exchange effects (the "identical-spin-rotation" effect) to derive a nonlinear spin-diffusion equation identical to that of Leggett, 2 but which is valid at arbitrary polarizations. Levy and Ruckenstein 6 have also investigated these paramagnetic systems via a quasiparticle approach that emphasizes the relation between the dilute and degenerate regimes, and have successfully applied their results to experiments on spin-polarized atomic hydrogen. 7 The possibility that ordinary (i.e., linear) spin diffusion need not be isotropic in highly polarized systems was first pointed out by Meyerovich, who showed that in such a system, the spin-diffusion relaxation time for spin currents perpendicular (in spin space) to the direction of polarization could be significantly shorter than that for the parallel spin currents. 8 Jeon and Mullin have incorporated that idea into their recent derivation of a kinetic equation for systems of arbitrary polarization and arbitrary degeneracy, 9 and in their calculations of the longitudinal and transverse coefficients of spin diffusion. 1011 The spin dynamics derived from their kinetic equation contains nonlinear terms similar to those in Leggett's equation.Because their degeneracy temperatures can be arbitrarily set (by varying the 3 He concentration), and because they can be polarized with readily attainable magnetic fields, dilute solutions of 3 He in 4 He form a nearly ideal system for the experimental investigation of these nonliner phenomena. Gully and Mullin performed the first experiment on such a highly polarized system several years ago, and confirmed the presence of identical-spin-rotation effects in very dilute mixtures. 12 More recently, Candela et al. have directly observed spin waves in the Fourier-transformed NMR spectrum of a 3 He-4 He mixture, and have used their results to investigate the transverse spin dynamics of the system. 13 In this Let...

Viscosity increase upon spin polarization of a dilute Fermi gas

“…experiments [9,12,13,24] at very low T and x 3 is avoidance of these effects (the Fermi velocity in the present work is only 6.9 m/s). These experiments also minimize the modification of the effective interaction by finite-concentration effects, as calculated by Fu and Pethick [25].…”

“…We retain the term in q 2 for the practical reason that it gives significant corrections to the transport coefficients at all temperatures, even for the low 3 He concentrations of the present work (Fig. 2) and other recent experiments [9,12,13,24,27].…”

“…Many slightly different forms for V(q) have been proposed over the years; the Ebner potential is used here because recent work [27] has shown that it agrees moderately well with both longitudinal [24] and transverse [9] spin-transport measurements in very dilute solutions. This Vo corresponds to an s-wave scattering length of a = -1.13 A.…”

“…Rather than fitting each transport experiment by its own V(q), we feel it will be more physically significant to determine the single V(q) that best fits all of the recent experiments (viscosity [13], longitudinal [24] and transverse [9] spin diffusion, spin rotation [9], and secondsound damping [12]). The simple two-term form mentioned above should suffice to explain data taken below 50 mK with xi < 0.2%.…”

Quadrupole spin oscillations in polarized rarefied media

“…At the microscopic level the phenomenon is of a purely quantum-mechanical origin and may be understood in terms of the exchange effects in refraction of the wave function despite the fact that from the viewpoint of particle statistics the classical temperature range is considered. Nuclear spin waves were observed in experiments with spin-polarized atomic hydrogen Hj [18], gaseous 3 He| [19], and nondegenerate weak solutions of 3 He| in superfluid 4 He [8,10,11].On the other hand, it is rather obvious that spin dynamics of a system of particles (or excitations) with spin larger than y is more complicated and does not reduce to the equations of motion for total magnetization only. It is known that in the case of S = y any function of the spin operator S reduces to a linear in S function.…”