Viscosity of a Spin-PolarizedHe3-He

Abstract

We have made the first systematic observations of an increase in the viscosity of a dilute 3 He-4 He solution at very low temperatures on the application of a large magnetic field by measuring the damping of second sound. The zero-field viscosities are used to evaluate the quasiparticle-quasiparticle interaction potential which enables an unambiguous prediction of the viscosity increase. The experimental results are in good agreement with this prediction.

Giant Viscosity Enhancement in a Spin-Polarized Fermi Liquid

“…However, if the magnetic field exceeds a critical value, the Fermi energy is smaller than the spin splitting and the polarization tends exponentially to unity as the temperature is lowered [2]. Here we report an experiment that attains this regime for the first time in a 3 He- 4 He mixture, by employing extremely large field/temperature ratios B/T up to 5900 T/K. As a consequence the spin polarization attains values greater than 99%, and the viscosity we measure for the liquid increases by a factor of more than 500 over its low-field value.…”

“…The largest viscosity enhancement in 3 He- 4 He reported prior to the present work was a factor of 3.5, at 75% spin polarization [6]. That work used a viscometer made from fine (25 µm diameter) wire, to achieve sensitivity for the very low viscosity sample (η ∼ O(10 −6 Pa-s)).…”

“…The interaction between two 3 He quasiparticles in a 3 He-4 He mixture is thought to be well-understood; it is mediated by virtual 4 He phonons and velocity-dependent interactions should be small due to the small ratio of the 3 He Fermi velocity (v F = 4.3 m/s for x 3 = 150 ppm) to the 4 He sound velocity (240 m/s) [3]. Therefore, this system provides a stringent test of many-body and quantumstatistical effects upon transport.…”

“…To reach this regime the spin splitting µB must exceed 2 2/3 times the Fermi energy k B T F , where the factor of 2 2/3 arises because the favored-spin Fermi level increases when all of the spins are aligned (µ = magnetic moment of spins, B = applied magnetic field, k B = Boltzmann constant). In 3 He-4 He mixtures as employed here, the superfluid 4 He solvent serves as a "mechanical vacuum" that prevents the 3 He atoms from condensing at any temperature, thus providing one of Nature's best examples of a weakly-interacting Fermi gas [3]. The Fermi temperature is set by the concentration x 3 of 3 He atoms, T F = (2.66 K)x 2/3 3 , and the spin splitting energy in temperature units is µB/k B = (1.56 mK/T)B.…”

“…Spin polarization provides a powerful tool for investigating the quantum states of Fermi liquids, such as degenerate electrons, ultracold atoms, and 3 He- 4 He mixtures. Polarization affects the transport coefficients of the system due to Fermi statistics [1].…”