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...
We describe the design of a modified split-ring resonator, especially suited to low-temperature experiments, which enables cavities with dimensions of order 1 cm to resonate at frequencies as low as a few hundred megahertz.
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