Collisionless spin waves in normal and superfluid3He

Standing spin-wave modes in liquid³He have been studied by cw NMR at Larmor frequencies of 1, 2, and 4 MHz and pressures of 0, 6.3, and 12.3 bar. The spin waves, which produce peaks in the NMR line, are visible at temperatures below 5 mK at zero pressure. With the assumption of a slightly simplified sample shape and no transverse spin relaxation at the walls, the theory of Leggett fits the spin-wave frequencies in the normal liquid very well, giving a value of the Fermi liquid parameterF ₁ ^a =–0.6±0.2 at zero pressure. The width of some of the peaks is larger than expected from other determinations of the quasiparticle diffusion time _D . This could be due to wall relaxation or to deviations from the assumed sample geometry. In the superfluid A₁ and A phases, where the data cannot be fitted to existing theories, the spin-wave modes are shifted in frequency and suffer additional damping as the temperature is decreased. At still lower temperatures in the B phase an inversion of the spin-wave spectrum from one side of the NMR line to the other is observed, agreeing quantitatively with the predictions of the 1975 theory of Combescot.     

Electric dipole moment and spin supercurrent in superfluid3He

The SU(2) gauge invariant theory of the relativistic interaction of the electrically neutral superfluid³He with electric and magnetic fields is formulated. The spin supercurrent response on the electric field is calculated for this interaction. The comparison with the nonrelativistic flexoelectric effect, arising due to the distortion of the atomic shell by the gradients of the superfluid order parameter, is made.     

Flow of superfluid3He through micrometer-size channels

Measurements of the critical mass currentJ _c through 0.8-µm-diameter channels in the superfluid phases of³He are reported. Experiments were made at pressures from 0 to 27.4 bar in zero external magnetic field. The pressure difference ΔP along the flow channels is immeasurable within our resolution of ±0.1 µbar for sufficiently low currents in both the A and B phases, implying small or zero dissipation. In the B phase ΔP grows rapidly with increasing current aboveJ _c. At low pressuresJ _c behaves like (1?T/T _cyl)^3/2, whereT _cyl is interpreted as the reduced superfluid transition temperature inside the flow channels;T _cyl/T _c=0.935 atP=0. If the liquid in the channels is in the A phase, the behavior of ΔP vs. the mass currentJ _s depends on the phase A or B outside the channels. During warming a drop of about30% inJ _c is found both atT _BA(cyl) and at;T _BA(cyl) is the reduced B→A transition temperature in the channels. AboveT _BA a second dissipation mechanism, with a smallerd(ΔP)/dJ _s, is observed at lower currents. These features indicate that in the A phase the ends of the channels have an important effect on the flow.     

Surface spin waves in the superfluid A phase of 3He

A generalization of the Leggett-Takagi theory of NMR is presented in the case when the order parameter in the equilibrium is space dependent. The equations of spin dynamics are solved and the frequencies and damping in the cases of specular and diffuse scattering of quasiparticles from the plane wall are found. It is shown that in the case of diffuse scattering, surface spin waves exist. The contribution of this mode to the absorption of a uniform rf field is found.     

Localized spin wave states of superfluid3He in a magnetic field gradient

It is shown that in the presence of a magnetic field gradient, spin wave states in superfluid³He split into discrete levels, just as for a charged particle in an electric field near the surface. The energy levels and the intensity of the magnetic absorption due to localized states are determined for the simplest cases in superfluid³He A and B. The localized states will provide a unique way to determine the spin wave velocity and spin diffusion constant in superfluid³He.Work supported by National Science Foundation under Grant No. DMR76-17702.     

The influence of spin on second sound in superfluid3He-4He mixtures

The second-sound velocity of a superfluid mixture increases when a static and homogeneous magnetic field is applied. In particular, for dilute mixtures (molar ³ He concentration <0.1) and low temperatures, (0.1<T<0.6 K) the relative velocity increase is independent of concentration and is given by u ₂/u ₂5×10^–16 B _e ² T ^–2. It should be easily observed wheneverB _e T ^–1is larger than 10 ⁵ G K^–1 and can lead to a novel measurement of the magnetic susceptibility.     

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.     

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.     

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.     

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.     

Solution of spin dynamics equations for 3He superfluid phases in a strong magnetic field

A general method of investigating the solutions of spin dynamics equations of superfluid phases of ³He in strong magnetic fields is proposed. The effect of longitudinal spin oscillations upon the frequency of precession is taken into account. The motion of a spin near singular points at which the longitudinal oscillation frequency becomes zero is considered. The formulas derived are applied to A and B phases in the open geometry and to the B phase in the plane-parallel geometry.     

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.     

Temperature dependence of the condensate fraction of superfluid4 He

The roton contribution to the temperature dependence of the condensate density is discussed. The analysis is carried out through the inclusion of a gauge symmetry breaking field. Under the hypothesis that the thermal excitation of rotons is the main responsible for the depletion of the condensate, we obtain an explicit result for the temperature dependence of the condensate density which rather well agrees with the available experimental data.     

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.     

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.