Fast growth of 3He-B into supercooled 3He-A

We report results of an investigation of the growth of ³He-B into supercooled, magnetized ³He-A. The B-phase growth was observed magnetically, with the difference between A- and B-phase susceptibilities generating signals in SQUID magnetometers. The form of the magnetization signal associated with the moving interface evolved radically with increased supercooling, indicating that the rapidly moving interface is no longer a simple boundary between equilibrium B phase and metastable equilibrated A phase. Magnetization changes were observed to travel through the superfluid as fast as 800 cm/s. Several features of the measurements can be explained by a model based on magnetization transport by a critical-velocity-limited spin super current. Other features of the data remain unexplained.     

Structure of isolated vortex lines in rotating3He-A and3He-B

First we calculate the texture of a Mermin-Ho vortex in a field of 284 Oe and compare its energy with the energies of singular vortices in³He-A as a function of rotation speed and temperature. Then we calculate the order parameter components ψ _r , ψ_φ and ψ _z (r, ф,z are cylindrical coordinates) for an isolated vortex line in³He-B. We find that in the core region the transverse components ψ _r and ψ_φ are strongly reduced in comparison to the component ψ _z along the rotation axis. A strong magnetic field has the reverse effect: ψ _z is reduced in comparison to ψ _r and ψ_φ. Finally we calculate the corrections of order (1?T/T _c ) to the Ginzburg-Landau solutions. These yield an interesting structure of the vortex core. For radial distances large compared to the coherence length, ψ_φ is reduced as the temperature decreases.     

Zero-sound attenuation in rotating and stationary3He-A and3He-B

We report on measurements of zero-sound attenuation in rotating and stationary³He-A and³He-B, in magnetic fields up to 350 mT. Strong and highly nonlinear rotation speed dependencies of sound amplitudes have been observed in both phases. The data gives information on vortex types and core sizes, although the analysis is not straightforward. The anomalous attenuation in³He-B at 200 mT near the AB transition, both in the stationary and in the rotating state, is interpreted to arise from the distortion of the energy gap of the B phase. Excess attenuation during the AB phase change was observed. Evidence for soft vortex cores in³He-B is presented. In addition, a critical velocity in the vortex free state, related to a textural transition, and the vortex creation times have been measured in³He-B. Furthermore, a metastable structure, possibly a new vortex state, has been observed in³He-B by rotating the sample through the A B transition.     

NMR experiments on rotating superfluid3He-A and3He-B and their theoretical interpretation

We have constructed a rotating nuclear demagnetization cryostat and used it for continuous-wave NMR experiments on superfluid³He-A and³He-B. The measurements were performed in a long cylindrical geometry of 5 mm diameter, with the cylinder axis parallel to the axis of rotation and with the external magnetic field H₀=284 or 142 Oe in the same direction. The angular velocity of rotation was varied between 0.2 and 1.5 rad/sec, and the experiments were done under 29.3 bar pressure at temperatures between T_c=2.72 and about 1.4 mK. As a guide to the new and esoteric field of superfluid³He in rotation, we first review the general theory at some length in relatively simple terms. Pictorial explanations are often given.In³He-A, a rotation-dependent NMR satellite was found; its intensity a rotation-dependent NMR satellite peak was discovered; its relative intensity increases linearly with . The position of the satellite is independent of and H, and does not depend on whether the sample was cooled from the Fermi-liquid region to the A phase while rotating or at rest. At temperatures 0.1<1–T/T_c<0.3, the frequency shift of the satellite can be described by the parameter R_t=0.86–1.1(1–T/T_c). Cooldown under rotation produced systematically larger satellite intensities than cooldown at rest. A second, metastable satellite, best seen at rest and disappearing in less than 30 min, was also discovered. Furthermore, the main NMR peak broadens during rotation, while the total NMR absorption remains the same. The behavior of the rotation-dependent satellite strongly supports the existence of vortices in³He-A, their number being proportional to ; the satellite is caused by localized spin wave modes trapped by vortex cores. Theoretical calculations agree quite well with our experimental data if continuous vortices, without a singularity in the order parameter, are assumed. Their presence is also responsible for the additional broadening of the main peak, due either to increased spin diffusion or to scattering of spin waves. The metastable satellite is caused by textural boundaries, probably by twist solitons in the superfluid, created by the rapid cooldown of the sample.In³He-B, a series of nearly equally spaced NMR satellites was found on the high-frequency side of the main peak with the cryostat at rest. Under rotation the separation between the satellites increases linearly with . The spacing displays a jump, proportional to , at 1–T/T_c=0.40. The discontinuity occurred only during start/stop experiments, not if the cryostat was continuously rotated while warming over the transition region. Immediately after rotation had been started the whole NMR spectrum shifted toward higher frequencies for about 30 sec; these transients were seen only at >0.25 rad/sec. In³He-B, the order parameter is strongly influenced by the wall of the container, producing the so-called flareout texture, with the angle between the vector andH equal to 63° at the walls. The satellites can be explained as spin wave modes arising from an almost harmonic potential well formed by the texture. The creation of vortices changes the texture and increases the steepness of the potential and therefore increases the satellite spacing during rotation. The vortices themselves perturb the texture due to the long-range orientating effect of their cores on the order parameter. The discontinuity in the satellite splitting at 1–T/T_c=0.40 is explained as being due to a first-order phase change in the vortex core at this temperature. The transient shift in the NMR spectrum, immediately after the start of rotation when vortices are not yet present, is caused by the large superfluid vs. normal liquid counterflow; this phenomenon thus gives an estimate for the time needed to create vortices in³He-B.     

Quasiclassical equations for3He-A

The quasiclassical equations for superfluid³He are studied in detail, with emphasis on the equations for the A phase. A careful discussion of the collision operators is given; the1×T term in the energy current is calculated; and the gradient expansion is discussed from the quasiclassical point of view.This work was supported in part by a NATO fellowship through the Deutsche Akademische Austauschdienst, and by the National Science Foundation under Grant No. DMR-80-20429.     

Orbital motions in 3He-A

Orbital motions in ³He-A in very low magnetic field and driven by heat flow are studied using crossed detecting zero-sound fields. A precessional type of motion of the % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\] field is frequently observed, though a rich variety of phenomena are also observed. There is no evidence for phase slip due to motion of nonsingular vortices along the surface. Motion of the % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\] field following sudden parallel magnetic field turn-off is also observed above a threshold field change which is related to coherent dipolar energy. The time scale for these % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\]-field changes is, however, a factor of about 10² larger than expected for the formation of composite solitons.Work supported by the U.S. Department of Energy under contract EY-76-S-03-0034, P.A. 143.     

Vortex sheet in superfluid3He-A

A new state of rotating superfluid³He-A has been found recently. Usually superfluids respond to rotation by creating an array of vortex lines, which are parallel to the rotation axis, and the circulation around them is quantized. In the new state the vorticity is located on a 2 dimensional sheet instead of 1 D lines. The sheet is parallel to the rotation axis z but in the x — y plane it folds to equidistant layers. The distance between the layers is larger but on the same order of magnitude as the distance between vortex lines. In contrast to other superfluids, the sheet is stable in the A phase because of its internal structure. The sheet has as a backbone a topologically stable domain wall called soliton, to which non-singular vorticity is bound. Thus it can exist in spite of its presumably higher energy. The vortex sheet is distinguished by its NMR response, in particular because of its higher absorption at a characteristic frequency. Experiment and theory on the vortex sheet are in good agreement.     

Stable circulation in superfluid3He-A

We present evidence of stable nonzero circulation in superfluid³He-A around a 16 µm diameter wire. The measurements are made on a rotating cryostat at T0.15T_c. Circulation offects the splitting of the wire's normal modes, which changes the beat frequency in the emf across the wire as it vibrates in a magnetic field. The different beat frequencies at 14 and at 21 bar suggest that circulation is present at 21 bar. Furthermore, at 21 bar the beat frequency is a linear function of rotation velocity, as is expected if circulation is trapped around the wire. At 14 bar no effect of rotation is observed. We propose that at 21 bar the ground state texture has nonzero circulation of order h/2m₃.     

Vortex structures in rotating3He-A

In the hydrodynamic approximation, the free energy of high-field Seppälä-Volovik vortices in rotating³He-A is minimized with respect to an additional textural rotation angle. The transition from singular, singly quantized vortices to nonsingular, doubly quantized vortices is predicted to occur at a temperature-dependent angular velocity of order 1 rad / sec, in rough agreement with experimental observations.     

Hydrostatic Theory of Superfluid 3He-B

The determination of the texture of the order parameter is important for understanding many experiments in superfluid ³He. In addition to reviewing the theory of textures in superfluid ³He-B we give several new results, in particular on the surface parameters in the Ginzburg–Landau region and bulk parameters at arbitrary temperature. Special attention is paid to separate the results that are valid at all temperatures from those which are limited to the Ginzburg–Landau region. We study the validity of a trivial strong-coupling model, where the energy gap of the weak-coupling theory is scaled by a temperature dependent factor. We compare the theory with several experiments. For some quantities the theory seems to work fine and we extract the dipole–dipole interaction parameter from the measurements.     

Anisotropy and flow in3He-A

Thermally driven counterflow in³He-A is investigated, using techniques that exploit the anisotropy of the fluid. The results are discussed in terms of both uniform-texture and helical-texture hypotheses. Anisotropy of heat flow is observed for the first time and a limitation of the superfluid velocity is strongly suggested.This work was supported by the U.S. Department of Energy under contract EY-76-S-03-0034, P.A. 143.     

Optical interferometry in superfluid3He-B

We report interferometric measurements on 0.1 ... 1 mm thick films of superfluid ³He-B. The menisci of three different rotational states of the superfluid were observed and analyzed theoretically using two-fluid hydrodynamics: These are (i) the equilibrium vortex state in which the superfluid and the normal components corotate (solid body rotation), (ii) the vortex-free state (the Landau state), in which only the normal component rotates, and (iii) the quasistationary vortex state in which only the superfluid fraction rotates (pure superfluid rotation). The Landau state manifested itself by a reduced parabolic meniscus at rotation speeds below the critical angular velocity 0.2 rad/s for vortex formation. Transition from the Landau state to the equilibrium vortex state yielded a sudden deepening of the meniscus when _c was exceeded. After a rapid halt of the cryostat, we observed a novel meniscus which was produced by the superfluid rotation while the normal component was at rest. The enhanced depth of this meniscus is governed by the reactive mutual friction parameter B'.By employing laser light, both for imaging and for thermomechanical excitation, we measured the response of a thin superfluid layer to a heat pulse and analyzed it within the theory of two-fluid hydrodynamics. The data were employed, using the dispersion relation for thin film oscillations, to deduce the second viscosity coefficient ₃ close to T_c.     

Planar textures in superfluid 3He-A

Making use of the Ginzburg-Landau free energy, singularities such as disgyrations and vortex lines and stable textures in the planar (or two-dimensional) texture are studied. Here both % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieqaceWFSbGbaK% aaaaa!3883!\[{\hat l}\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieqaceWFKbGbaK% aaaaa!387B!\[{\hat d}\] vectors, characterizing the texture in ³He-A, are assumed parallel to each other and lie always in a plane. The dynamics of disgyrations is also considered.Work supported by the National Science Foundation under grant number DMR76-21032.     

Energies of line singularities in 3He-A

We investigate a class of topologically equivalent line singularities in ³He-A to determine which of this class has the lowest free energy density. Most of our results concern the Landau-Ginzburg regime near T _c ; we offer a speculation on what might occur further below T _c .This research was supported in part by the National Science Foundation under Grant No. 77-18329 and through the Materials Science Center of Cornell University, Technical Report No. 4043.     

Transverse waves in superfluid3He-B

We examine the theory of collisionless transverse current waves in bulk superfluid³He-B, including the coupling to the order parameter collective modes. At low frequencies, Ω ≪ δ(T), the order parameter modes do not contribute to the restoring force for a transverse current, and the quasiparticle contribution drops rapidly as the gap in the spectrum develops. Thus, low-frequency transverse sound becomes overdamped at temperatures nearT _c . However, at low temperatures (T ≲0.3T _c ) the off-resonant coupling to the J = 2⁻,M = +-1 modes stabilizes a propagating transverse current mode, with a large phase velocity and low damping for frequencies above a critical frequency that is approximately that of theJ = 2 ⁻ mode. We also discuss the similarities and differences of longitudinal and transverse sound in the superfluid phases. For example, in zero field, right- and left-circularly polarized waves are degenerate. A magnetic field, with , lifts this degeneracy, giving rise to the analog of circular dichroism and birefringence of electromagnetic waves. Thus, transverse waves may be more easily detected in the B-phase than in normal³He.     

Domain Walls in Superfluid 3He-B

No Heading We consider domain walls between regions of superfluid ³He-B in which one component of the order parameter has the opposite sign in the two regions far from one another. We report calculations of the order parameter profile and the free energy for two types of domain wall, and discuss how these structures are relevant to superfluid ³He confined between two surfaces.PACS numbers: 67.57.Np     

The collective excitations in3He-A1

The collective mode spectrum of the superfluid A₁-phase of³He is calculated by a path integration technique. It is shown that there is one pairbreaking mode E(k=0)₀ (1, 96-i0, 31) and two clapping modes E(k=0)₀(1, 17-i0, 13), eight modes E=2µH and one goldstone mode E=0. Six other modes have an imaginary spectrum. This fact is connected with the instability of the A₁-phase under small perturbations.     

Textural singularities in superfluid3He-B

The absorption signal occasionally found missing in the middle of resonance absorption lines in NMR is explained on the basis of a textural singularity of the anisotropy axis in the B phase of ³ He. The singularity combines with the field gradient present to give rise to an asymmetric hole in the signal with a singularity on the high-frequency side. The line shapes and temperature dependence are predicted and agree well with experiment. Spin waves are found to be trapped by the potential well formed by the texture and the field gradient. The frequency intervals predicted for the spin waves also agree well with experiment.Work supported in part by National Science Foundation Grant No. NSF DMR 74-18030.     

Theory of sound propagation in superfluid 3He-A

The theory of sound propagation in pair-correlated Fermi liquids developed previously by Wölfle is applied to the Anderson-Brinkman-Morel state, believed to describe ³He -A. The effect of quasiparticle collisions is included. Expressions for the anisotropic sound absorption and velocity valid at arbitrary frequency, temperature, and pressure are derived in terms of averages in momentum space of certain simple functions. Numerical results are in good agreement with lower pressure data but deviate by 10–20% at the melting pressure. The discrepancies are attributed to strong coupling effects not included in the theory.     

Diffusive thermal conductivity of superfluid 3He-B

The diffusive thermal conductivity (t) of superfluid ³He-B is calculated in the s-p-d-wave approximation by solving the Boltzmann equation for the Bogoliubov-Valatin quasiparticles variationally. A new set of Landau para- meters calculated from recent heat capacity data as well as old ones given in Wheatley's review are used to estimate the scattering amplitudes of the collision integral. Landau parameters F ₂ ^s, F ₁ ^a, and F ₂ ^a are treated as free parameters under the constraint that _exact(T _c) = _exp(T _c), where _exact and _exp are the exact theoretical value and the experimental value, respectively. We have varied F ₂ ^s, F ₁ ^a, and F ₂ ^a over a wide range % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaai4Eaiabgk% HiTiaaigdacaaIWaGaeyizImQaaeyqamaaDaaaleaacaqGXaaabaGa% ae4CaiaabYcacaqGHbaaaOGaeyyyIORaaeOramaaDaaaleaacaqGXa% aabaGaae4CaiaabYcacaqGHbaaaOGaai4laiaacUfacaaIXaGaey4k% aSIaaeOramaaDaaaleaacaqGXaaabaGaae4CaiaabYcacaqGHbaaaO% Gaai4laiaacIcacaaIYaGaamiBaiabgUcaRiaaigdacaGGPaGaaiyx% aiabgsMiJkaaigdacaaIWaGaaiyFaaaa!570F!\[\{ - 10 \leqslant {\text{A}}_{\text{1}}^{{\text{s,a}}} \equiv {\text{F}}_{\text{1}}^{{\text{s,a}}} /[1 + {\text{F}}_{\text{1}}^{{\text{s,a}}} /(2l + 1)] \leqslant 10\} \] and found the possible range of the reduced diffusive thermal conductivity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqOUdSMbaG% aacaGGOaGaaeivaiaabMcacaqG9aGaeqOUdSMaaeikaiaabsfacaqG% PaGaaeivaiaab+cacqaH6oWAcaGGOaGaaeivamaaBaaaleaacaqGJb% aabeaakiaacMcacaqGubWaaSbaaSqaaiaabogaaeqaaaaa!46ED!\[\tilde \kappa ({\text{T) = }}\kappa {\text{(T)T/}}\kappa ({\text{T}}_{\text{c}} ){\text{T}}_{\text{c}} \]. The behavior of \~(T) in the s-p-d-wave approximation does not much depend on the values of the Landau parameters, and \~(t) decreases monotonically with decreasing tem- perature.