Anomalous specific heat of liquid 3He above the superfluid transition temperature

The contribution to the specific heat due to order parameter fluctuations in liquid ³He just above the superfluid transition temperature T _c is calculated exactly within a Landau theory approach. The effect turns out to be unobservably small and thus cannot explain the large (9%) rise in specific heat above the normal state value at the saturated vapor pressure in a recently reported experiment. We do not find the divergence of the specific heat at T cobtained earlier by Thouless from a microscopic calculation and indicate how the difference can be reconciled.     

Relations between specific heat discontinuities and Ginzburg-Landau parameters for superfluid 3He

We show that the value of the ratio ₅/₂₄ deduced from specific heat experiments is extremely sensitive to the coefficient of the quadratic term in the Ginzburg-Landau functional. A strong coupling calculation of this coefficient implies that the experimental value of ₅/₂₄ is more than three times larger than previously believed.This work was supported in part by the National Science Foundation through Grant DMR7826530.     

Specific heat of normal and superfluid3He

Extensive measurements of the heat capacity of liquid ³ He in the normal and superfluid phases are reported. The experiments range from 0.8 to 10 mK and cover pressures from 0 to 32.5 bar in zero magnetic field. The phase diagram of ³ He, based on the platinum NMR temperature scale, is presented. In the normal liquid at low pressures and near the superfluid transitionT _c an excess specific heat is found. The effective massm* of³He is at all pressures about 30% smaller than the values reported earlier. The calculated Fermi liquid parameters F₀ and F₁ are reduced asm*/m, while the spin alignment factor (1 + Z₀/4)^–1 is enhanced from 3.1–3.8 to 4.3–5.3, depending on pressure. The specific heat discontinuity C/C atT _c is forP = 0 close to the BCS value 1.43, whereas at 32.5 bar C/C is 1.90±0.03 in the B phase and 2.04±0.03 in the A phase, revealing distinctly the pressure dependence of strong coupling effects. The temperature dependence of the specific heat in the B phase agrees with a model calculation of Serene and Rainer. The latent heatL at the AB transition is 1.14±0.02 µJ/mole forP = 32.5 bar and decreases quickly as the polycritical point is approached; at 23.0 bar,L = 0.03 ± 0.02 µJ/mole.Work supported by the Academy of Finland.     

Static magnetization of superfluid 3He

New measurements of the static magnetization of ³He-B in contact with a variety of wall configurations are presented and compared with previous measurements in both A and B phases. At high pressure the data tend toward agreement with resonant-magnetism experiments, while near the polycritical point a large discrepancy between the results of the two methods remains.Supported by the U. S. Energy Research and Development Administration under contract no. EY-76-S-03-0034, P.A. 143.     

Hydrodynamic heat flow in very dilute superfluid3He-4He mixtures

The superfluid hydrodynamics of heat flow is examined for very small mass concentrationsc of³He in⁴He in an effort to better understand recent results for the effective heat conductivity _eff, which appear to be in conflict with predictions. The full hydrodynamics contains a thermal boundary layer; within this layer the temperature and concentration gradients differ from those in the bulk fluid. An examination of finite heating effects based on the ansatz _eff c ^–p for smallc shows distinctly different behavior for experimental determinations of _eff whenp<1,p=1, andp>1. Thus, finite heating can be used as a probe to evaluate the exponentp.     

The vortices of superfluid 3He

In the superfluid phases of ³He quantized vortex lines have been investigated under uniform rotation, when they form a regular array of rectilinear objects. A large diversity exists in the structure and properties of vortices, owing to the complicated nature of symmetry breaking in the different superfluid phases. A review is presented here on the various experimentally verified types of vortices. Recent measurements open a puzzling problem about their interaction and interconnection at the first-order phase boundary separating the A and B phases of superfluid ³He.An invited contribution to the Symposium on Quantum Fluids and Solids 1992, June 15–19, Pennsylvania State University, University Park, Pennsylvania 16802.     

NMR in flowing superfluid 3He

The effects of flow on the NMR absorption in the A and B phases of ³He have been studied. While no flow-induced changes in the absorption were seen in the B phase, a variety of phenomena were observed in the A phase. The phenomena include the development of time-dependent satellite peaks, height reductions of the signal, and a splitting of the signal, with a fraction of the signal shifting to lower frequencies. These effects are described and discussed in light of the existing theoretical models. In addition, the NMR shift in the static B-phase liquid confined between 135-m-spaced parallel plates has been measured as a function of temperature and the angle between the magnetic field and the plates. These results are compared with previous measurements and are found to be in good agreement. Finally, two effects observed in the static liquid, the disappearance of the B-phase signal under certain conditions and the splitting of the A-phase signal, are described.Research supported by the National Science Foundation.     

Magnetic excitations in superfluid 3He

Localized magnetic excitations (solitons) in superfluid ³He are studied theoretically. In the A phase, we determine the dispersion of solitons in both the longitudinal and the transversal configurations, while in the B phase we limit ourselves to the longitudinal soliton in the Leggett configuration. In the wall pinned configuration of the B phase we show that the magnetic perturbation propagates as spin wave. The effects of the spin-diffusion term on solitons as well as spin waves are considered. The soliton velocity decreases exponentially in time owing to the spin-diffusion term with a characteristic time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% qedmvETj2BSbacfaGae83KdCKae8hiaaIae83waSLaeyyyIORaaiik% aiaaiodacaGGPaGaaiikaiaadogadaahaaWcbeqaamaaCaaameqaba% GaaGOmaaaaaaGcciGGVaGaamiraiabfM6axnaaCaaaleqabaWaaWba% aWqabeaacaaIYaaaaaaakiaacMcacaGGDbaaaa!4DB4!\[\Gamma [ \equiv (3)(c^{^2 } /D\Omega ^{^2 } )]\] where D is the spin-diffusion constant, is the Leggett frequency, and c is the spin-wave velocity.Supported by the National Science Foundation.     

Heat flow in superfluid 3He

The thermal resistance in both superfluid phases of ³He has been measured at 20.0 and 29.6 bar in zero magnetic field. Heat conduction in ³He-B is shown to be primarily hydrodynamic, and a regime of reproducible heat flow behavior in the A phase is reported. The viscosity of each phase as a function of temperature is calculated using an equation of the two-fluid model, and critical velocity effects are discussed.Work supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34 P.A. 143.     

Persistent currents in superfluid3He

Measurements are reported of persistent currents in superfluid³He-B and³He-A. An ac gyroscope filled with 20 µm powder and mounted into a rotating nuclear refrigerator was employed. In³He-B, undiminished circulation was observed for 48 h; this implies an effective viscosity at least 12 orders of magnitude lower than in the normal fluid at the same temperature. AtP<15 bar, the observed critical velocity is independent of temperature but it is a weak function of pressure;v _c varies between 4 and 6 mm/sec. The response to rotation is hysteretic, with elastic potential flow at slow rotation and irreversible vortex flow at higher angular velocities. The persistent angular momentumL is reversible when thermally cycled in the B phase, and proportional to the superfluid fraction _s /. Above 15 bar the B phase splits into separate regions with different critical velocities. The measuredv _c in the phase existing only at high pressures is dependent on magnetic field; for example, at 23.0 bar,v _c (H=0) =5 mm/sec, butv _c (H=40 G) =15 mm/sec. In the low pressure phase,v _c is insensitive to a change in the magnetic field. The phase transition is of first order; the latent heatQ _G (1 µJ/mole) depends on the maximum angular velocity at which the cryostat was rotated. The transition is proposed to occur in the core structure of pinned quantized vortices sustaining persistent currents. In³He-A, currents could not be found to persist on an observable level. Direct measurements ofL atH=0 and atH=40 G, and repeated thermal cycling, showed that either the current decays rapidly orv _c <0.5 mm/sec.     

Orbital modes in superfluid3He

The equation describing the rotation of the orbital coordinate in superfluid³He is obtained. It is shown that the orbital modes obey a diffusion-like equation with a finite energy gap. The transient behavior of the vector in the A phase after thed vector is suddenly rotated is considered.Supported by the National Science Foundation.On leave from Department of Applied Science, Tohoku University, Sendai, Japan.     

Zero-sound studies in superfluid 3He

The propagation of 5-, 15-, and 25-MHz sound in superfluid ³He has been studied in zero magnetic field over a wide pressure range. Measurements of the structure and location of the attenuation peaks, velocity changes, and the low-temperature attenuation are described. The degree of strong coupling in the B phase is discussed. Observations of superheating and supercooling near the polycritical point have been extended and comparison is made with theory.Work supported by the U.S. Energy Research and Development Administration under Contract No. E(04-3)-34, P.A. 143.     

Pulsed NMR studies of superfluid3He

We present a review of our pulsed NMR experiments in the A and B phases of superfluid³He, at pressures of 23 and 27 bar. We have measured the dipole frequency in³He-A, spin susceptibility in³He-B, and tip-angle-dependent frequency shifts in both phases. In general, we find excellent agreement with results by other workers. In³He-B, complex spin motions were observed involving long-lived free induction decays with a time-dependent precession frequency. Spin relaxation measurements for both³He-A and³He-B are discussed and compared with those of other workers. After driving the magnetization far from equilibrium, anomalous frequency shifts were found to persist in the A phase. We discuss a soliton-texture model by Bruinsma and Maki which accounts for these resonances.Work supported by the National Science Foundation Grant DMR-78-10901 and through the Cornell Materials Science Center through NSF Grant DMR-79-24008 A02. (MSC Report #4459).     

On the strong-coupling effects in superfluid3He

Following a general formalism recently developed by Rainer and Serene and using a plausible approximation for the normal-state vertex function, we calculate the strong-coupling corrections F _SC to the free energy of superfluid³He. We express F _SC in terms of the Fermi liquid scatteirng amplitudesA ₀ ,A ₁ ,B ₀ , andB ₁ and the invariant combinations of the order parameter. We also calculate the jump in specific heat atT _c for theA ₁ , Balian-Werthamer (BW), and Anderson-Brinkman-Morel (ABM) states, the initials slope of the superfluid mass density and nuclear spin susceptibility in the BW and AMB states vs.T/T _c atT _c , the initial slope of theT _AB line vs. pressure at the polycritical point, and the effect of a small magnetic field on theT _AB line. The calculated values of all the above properties are in reasonable agreement with the experimental ones.Work supported in part by grant No. 4630 of the National Research Council of Canada.For a preliminary version of this work see Ref. 1.     

Spin waves in anisotropic superfluid3He

Spin waves in the A phase of superfluid³He are studied theoretically. It is assumed that the condensate in the A phase consists of theP-wave triplet pairs of the type suggested by Anderson and Brinkman. We show that the spin wave mode with a finite energy gap exists throughout the A phase. In particular atT=0 K the dispersion of the spin wave is given by, forvq<Δ, $$\omega ^2 = \omega _0^2 + 2(1 - \bar I)A\Delta ^2 + \tfrac{1}{3}(1 - \bar I)v^2 q^2 $$ where θ is the spin wave energy, ω _T =[ω ₀ ² +2(1?ī)AΔ²]^1/2 is the nuclear magnetic resonance energy,v is the Fermi velocity,q is the wave vector of the spin wave, andī=IN(0)=?1/4Z ₀ is the Landau-Fermi liquid parameter.     

Unresolved problems in the superfluid phases of3He

The early studies of the superfluid phases of³He were marked by often spectacular agreements between theoretical predictions and experimental results. Nevertheless, several experiments have failed to achieve either agreement with the prevailing theory or consistency with each other — and improved experiments do not remove these discrepancies. We will discuss two recent experiments at U.S.C. which indicate that there remain fundamental questions beyond experimental uncertainties. One of these is the stability of superflow in a complex texture in the A-phase. Experimental evidence indicates that superflow may actually be stabilized by the existence of a texture. The other is the long-standing discrepancy between static (SQUID) and dynamic (NMR) measurements of the magnetization discontinuity at the A-B transition. Our recent experiments using a first principles measurement of M support the continued existence of the discrepancy.     

Longitudinal magnetic relaxation in superfluid 3He

Longitudinal magnetic relaxation in both ³He-A and ³He-B is studied in a variety of magnetic fields and three different geometries. Relaxation as described by Leggett and Takagi is observed for particular geometries in both ³He-A and ³He-B within a very limited range of magnetic field and temperature near T _c. Under certain other conditions the longitudinal magnetization in ³He-A does not relax monotonically in time. Relaxation in ³He-B very near the critical temperature is shown to be remarkably different following nominal 90 and 180 pulses. Other observations using RF pulses with a time-dependent frequency provide evidence for a negative frequency shift in ³He-B at large tipping angles in certain geometries.Supported by the U.S. Department of Energy under contract number EY-76-S-03-0034, P.A. 143.     

Effects of4He coverage on the propagation of fourth sound in superfluid3He

We report measurements on the effects of⁴He coverage and pressure on the fourth sound propagation in superfluid³He in confined geometries of four different pore sizes.