P. C. Main

Calculations of static properties of spin-polarized3He-4He mixtures

The theory of dilute mixtures of3He in4He that have been polarized by a strong magnetic field is developed. The interaction between the quasiparticles is taken to be constant, an approximation valid at low temperatures. The polarization of the mixture depends on the strength of the interaction. The internal energy, the specific heat, the osmotic pressure, and the velocity of second sound are also calculated. The specific heat is relatively insensitive to the interaction, but it does change significantly with magnetic field. The osmotic pressure is more sensitive to the effects of the interaction for some3He concentrations and temperatures. The velocity of second sound behaves qualitatively like the osmotic pressure. The measurement of these quantities as a function of temperature and magnetic field is discussed with a view to obtaining the strength of the interaction between quasiparticles.

Heat capacity of3He/4He mixtures

We measured the specific heat capacity of three dilute mixtures (2.6, 1.07, and 0.44%) of3He in4He and of pure4He. The4He contribution to the specific heat of the mixture is subtracted, leaving only the3He part. This is fitted to a theoretical expression over the whole temperature range from 10 to 700 mK. Assuming a dispersion relation of the form ε=ħ2k2(1+γk2)/2m*, the fits yield the value of γ and the effective mass m* of each mixture. The average value of γ is −0.076±0.01 A2 and the effective mass in the limit of zero concentration is (2.23±0.02)m3. These are compared to values deduced from other measurements.

Second Sound Measurements in 3He–4He Mixtures

We report measurements of the damping of second sound in a 0.1% 3He–4He mixture in the temperature range 100 mK to 1K and for frequencies from the fundamental cavity resonance of -700 Hz to 12 KHz. The measurements enable us to examine the phonon contribution to the damping over a much wider frequency range than hitherto. The data are compared to a theory based on ideas which are developed in detail elsewhere.

The effect of a strong magnetic field on the damping of second sound in dilute3He-4He mixtures below 100 mK

We have measured the increase in damping of second sound in 0.1% and 0.05%3He-4He solutions upon application of a magnetic field of 10 T. The increase is caused by changes in the thermal conductivity and viscosity of the mixture as the system becomes spin polarized. We show how to fit the data for the viscosity in zero-field to obtain an estimate of the interaction between the3He quasiparticles. It is then possible to predict the viscosity in a field of 10 T using the calculation of Hampson et al. The data agree with the theory to within 2%.

The Viscosity of Spin Polarized 3He–4He Mixtures

We report measurements of the viscosity of a 0.1% 3He–4He mixture obtained from the damping of second sound at low temperatures and in a magnetic field of 10T. The damping of second sound arises from the bulk viscosity, the surface viscosity and from losses on reflection from the ends of the cavity. From the frequency dependence of the widths of the resonance we obtain the viscosity accurate to 3%. The viscosity is observed to increase when a field is applied and this increase is in agreement with the recent prediction of Hampson et al. who calculated changes in the transport properties of 3He–4He mixtures for temperatures of order the fermi temperature.