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.     

Spin dynamics of superfluid3He-B in a slab geometry

The spin dynamics and the spin relaxation mechanisms of the superfluid³He-B were studied by using the NMR method in a slab geometry, where the superfluid3He-B was confined between narrow parallel plates with a gap smaller than the healing length of then-texture and the magnetic field was applied parallel to the plates. The relaxation parameter in the Leggett-Takagi (LT) equations was determined from a line width measurement of the transverse CW NMR. By using the pulsed NMR method, spin dynamics were studied in the nonlinear region. The observed spin dynamics were in good agreement with a numerical calculation of the LT equations together with the relaxation parameter determined by the CW NMR. When the tipping angle became larger than a certain critical value, the superfluid³He-B entered the Brinkman-Smith (BS) state. In this case, we observed the slow relaxation process in the BS state and then the rapid recovery process from the BS state to the initial non-Leggett configuration. The slow process in the BS state was attributed to the surface relaxation mechanism due to the torque from the surface-field energy.     

On the Local Stability of the Quadrupole Vortex in Superfluid 3He-B

Studies with a constrained Ginzburg–Landau approach have suggested that the Quadrupole core vortex in ³ He-B should be a saddle point of the free energy (G. E. Volovik and M. M. Salomaa, JETP Lett. 45 , 56 (1987)). We have carried out a careful numerical analysis in the framework of the quasiclassical theory with the conclusion that the core in fact is a local minimum. No constrains were imposed on the phase space. The Quadrupole vortex can be a contender for the second vortex in the Manchester group experiment (Bevan et al., JLTP (1987)).     

Simultaneous spin and space rotation experiments in3He-B

Observation of enhanced magnetic relaxation due to counterflow and quantized vortices is reported in rotating superfluid³He-B. These phenomena were studied using a novel method based on the homogeneously precessing domain (HPD) mode, characteristic of the B-phase spin dynamics. The additional HPD absorption can be related to the equilibrium vortex structures and, therefore, this method yields information complementary to textural CW-NMR measurements, which are sensitive to the static magnetic properties of vortex cores. Primarily, the HPD method provides a simple and effective means for studying transient processes, e.g., vortex creation in³He-B; a clear difference between axisymmetric and non-axisymmetric vortices was observed.     

Vortex textures in3He-A near the transition to the A1 phase

The decay of the nonsingular doubly quantized vortex in³He-A into a pair of Mermin-Ho vortex textures in the immediate vicinity of the transition to theA ₁phase is confirmed using the variational approach.     

Topology in superfluid3He: Recent results

We discuss: the topological phase transition in nonsingular vortices in³He-A; vortices in³He-B and solitons terminating on strings; topological defects of the A-B interface: the interaction of continuous A-phase vortices with singular B-phase vortices across the interface; extended degeneracy and topology of Larmor precession; and internal topology in thin³He-A film, responsible for chiral edge states of fermions and QHE.     

Investigation of quantized circulation in superfluid 3He-B

We have studied circulation in superfluid ³He-B with a vibrating wire. We find that the circulation quantum equals h/2m ₃ to within experimental error at several pressures. We have also measured circulation in rotating superfluid ³He-B, and have observed a precessional motion of a single vortex line. Finally, we have found the unexpected result that circulation around the wire does not affect the pair-breaking critical velocity.     

Measurement of Turbulence in Superfluid 3He-B

The experimental investigation of superfluid turbulence in ³He-B is generally not possible with the techniques which have been developed for ⁴He-II. We describe a new method by which a transient burst of turbulent vortex expansion can be generated in ³He-B. It is based on the injection of a few vortex loops into rotating vortex-free flow. The time-dependent evolution of the quantized vorticity is then monitored with NMR spectroscopy. Using these techniques the transition between regular (i.e. vortex number conserving) and turbulent vortex dynamics can be recorded at T ～ 0.6 T_c and a number of other characteristics of turbulence can be followed down to a temperature of T ? 0.4 T_c. PACS numbers: 47.37, 67.40, 67.57.     

Dynamic Remanent Vortices in Superfluid 3He-B

We investigate the decay of vortices in a rotating cylindrical sample of ³He-B, after rotation has been stopped. With decreasing temperature vortex annihilation slows down as the damping in vortex motion, the mutual friction dissipation α(T), decreases almost exponentially. Remanent vortices then survive for increasingly long periods, while they move towards annihilation in zero applied flow. After a waiting period Δt at zero flow, rotation is reapplied and the remnants evolve to rectilinear vortices. By counting these lines, we measure at temperatures above the transition to turbulence ∼0.6 T _c the number of remnants as a function of α(T) and Δt. At temperatures below the transition to turbulence T≲0.55 T _c, remnants expanding in applied flow become unstable and generate in a turbulent burst the equilibrium number of vortices. Here we measure the onset temperature T _on of turbulence as a function of Δt, applied flow velocity v=v _n−v _s, and length of sample L.     

Intrinsic and extrinsic mechanisms of vortex formation in superfluid3He-B

We report on the first comprehensive measurements of critical superflow velocities in³He-B which allow different mechanisms of vortex formation to be identified. As a function of temperatureT and pressureP, we measure the critical angular velocity Ω_c(T, P) at which vortices start to form in slowly accelerating rotation in a cylindrical container filled with³He-B. Owing to the long coherence length ξ(T, P)∼10–100 nm, either trapped remanent vorticity or intrinsic nucleation may dominate vortex formation, depending on the roughness of the container wall and the presence of loaded traps. NMR measurement with a resolution of one single vortex line allows us to distinguish between different processes: (1) Three extrinsic mechanisms of vortex formation have been observed. One of them is the vortex mill, a continuous periodic source which is activated in a rough-walled container well below the limit for intrinsic nucleation. (2) In a closed smooth-walled container intrinsic nucleation is the only mechanism available, with a critical velocity v_c(T, P)=Ω_c(T, P), whereR is the radius of the container. We findv _c (T, P) to be related to the calculated intrinsic stability limitv _ch (T, P) of homogeneous superflow. The existence of this connection in the form of a scaling law implies that nucleation takes place at an instability, rather than by thermal activation or quantum tunneling which become impossible because of an inaccessibly high energy barrier.     

Evidence for a surface state with broken symmetry in3He-B from ROTA experiments at Helsinki

An unusual, newly observed, rotation-direction-dependent parity effect in nuclear magnetic resonance (NMR) experiments on rotating³He-B in a state void of vortices is here first explained in terms of the broken time-inversion symmetry (T) for the surface layer of the³He-B. Two possible types of such surface structures, both with brokenT symmetry, for superfluid³He-B near the wall of the container are consistent with properties of the parity effect: one has superfluid A phase on the³He-B surface, while the other one is characterized by a nonzero counterflow of the spin componentsS=0 andS=+-1 of the superfluid along the normal to the wall, but with the total mass supercurrent and the total spin supercurrent into the wall vanishing identically. The first surface structure is in better agreement with details of the experiment and our numerical results, which demonstrate, for the first time, absolute stability of an A-phase layer on the³He-B boundary in a certain region of the phenomenological parameters for the surface tension. We find it also possible for a first-order surface-wetting transition to occur by the A-phase layer between two different A-phase states: one with little A phase, the other with well developed A phase. We estimate the magnitude of the new surface-orientating effects by comparing the NMR data with computed spin-wave spectra. New types of point vortices on the surface, boojums, are possible for the³He-B with superfluid A phase on the boundary: unlike the usual boojums on the surface of³He-A, only these novel boojums on the³He-B surface display isolated half-integer quanta of superfluid circulation.     

Phase diagram of turbulence in superfluid 3He-B

No Heading In superfluid ³He-B mutual-friction damping of vortex-line motion decreases roughly exponentially with temperature. We record as a function of temperature and pressure the transition from regular vortex motion at high temperatures to turbulence at low temperatures. The measurements are performed with non-invasive NMR techniques, by injecting vortex loops into a long column in vortex-free rotation. The results display the phase diagram of turbulence at high flow velocities where the transition from regular to turbulent dynamics is velocity independent. At the three measured pressures 10.2, 29.0, and 34 bar, the transition is centered at 0.52–0.59 T_c and has a narrow width of 0.06 T_c while at zero pressure turbulence is not observed above 0.45 T_c.PACS numbers: 47.37, 67.40, 67.57     

Study of the orientational electric field effect in 3He-B

We have studied the orienting effect that an electric field has on the orbital motion of the pairs in superfluid ³He-B, using the orientation-dependent transverse NMR frequency shift as a probe. This method provides high resolution for studying the orienting effect for either sign of the orientational energy. Electric fields as high as 35,000 V/cm applied across the sample produced no measurable frequency shift at 0-, 10-, and 32-bar pressures. This gives upper limits to the orientational energy of 1.4 × 10^\s-3, 1.0 × 10^\s-3 and 4 × 10^\s-4 times the values expected from simple theory.     

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.     

The stress tensor for the mixed phase of uniaxial anisotropic superconductors

The contribution of anisotropy to the stress tensor for a mixed phase is found; it turns out to have an antisymmetric part. Additional forces act on the vortex system due to the anisotropy. If an anisotropic material in a uniform external magnetic field is also inhomogeneous (e.g., deformed), macroscopic persistent currents accompany the inhomogeneity. These currents are calculated in a simple case.Work supported by the MINERVA fund (West Germany).     

Model formalism of liquid 3He-B at equilibrium

The approximate formal treatment of the nuclear spin system of normal liquid ³He given some time ago is extended to the ordered ³He phase. The formalism leads to the prediction of normal thermal behavior of ³He-B at lower pressures and at temperatures approaching its phase-boundary temperatures. In contrast to the disordered normal liquid phase, which is thermally anomalous, the entropy of the ³He-B decreases on isothermal compression, or its isobaric volume expansion coefficient is positive. The equilibrium thermal behavior of ordered ³He-B is thus qualitatively different from that of disordered liquid ³He. Experimental control of these aspects of the liquid ³He phase transformation is lacking at the present time. Both early and new ³He-B paramagnetic susceptibility data, extended recently over a wide reduced-temperature range, disclose a fundamental competition between the spontaneous ordering mechanism responsible for the existence of ³He-B and the specific ordering process imposed upon this phase on application of an external constant and uniform magnetic field. As a consequence, magnetized ³He-B will be shown to increase its entropy on isothermal magnetization and to cool on adiabatic magnetization. The magnetocaloric effect is, however, only moderate. The competition of the ordering process leads to the delay or possibly even to the suppression of the formation of the ordered phase, a state of affairs foreseen in our earlier work. At low or moderate magnetic field strengths, the zero-field phase-boundary temperatures are shown to shift toward lower temperatures while, simultaneously, the order of the phase change decreases, from second order, in the absence of the field, to first order. Although of model-theoretic character, involving limitations of various types, the rich physical content of ³He-B at equilibrium clearly emerges in the present work.Work performed under the auspices of the U.S. Department of Energy.     

Phase transitions in the growth of4He films

Using a microscopic, variational approach we examine the growth of⁴He absorbed to graphite and alkali substrates. We find that superfluid layers are formed and their behavior as a function of coverage is closely related to the one of a purely two-dimensional superfluid. The growth of a new layer undergoes a phase transition from a cluster formation into the connected superfluid when the coverage is increased. Based on the important connection to the two-dimensional fluid we propose a microscopic theory of quantum vortices in⁴He films at zero temperature, in which single vortices are treated as quasiparticles. We calculate the energy needed to create the single vortex, vortex inertial mass, microscopic interaction between vortices and binding energy of the vortex-antivortex pair as a function of density. We predict that at the⁴He superfluid density less than about 0.037 Å^–2 the binding energy of the pair becomes negative, indicating a phase transition into a new state where vortex-antivortex pairs are spontaneously created.     

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).     

Transition to Superfluid Turbulence

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid ³He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionless parameter 1/q which depends only on the temperature-dependent mutual friction—the dissipation which sets in when vortices move with respect to the normal excitations of the liquid. At large friction and small values of the dynamics is vortex number conserving, while at low friction and large vortices are easily destabilized and proliferate in number. A new measuring technique was employed to identify this hydrodynamic transition: the injection of a tight bundle of many small vortex loops in applied vortex-free flow at relatively high velocities. These vortices are ejected from a vortex sheet covering the AB interface when a two-phase sample of ³He-A and ³He-B is set in rotation and the interface becomes unstable at a critical rotation velocity, triggered by the superfluid Kelvin–Helmholtz instability.