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Nucleation of vortices in units of one quantum has been observed with c.w. NMR in a rotating cylinder filled with 3He-B. During acceleration a new vortex is created each time the counterflow velocity at the perimeter reaches a critical value vc(T, p). The measured vc resembles the calculated velocity vcb(T, p) of the bulk superflow instability, but is smaller by a factor with power law dependence on the superfluid coherence length. This indicates that a nucleation event takes place whenever the flow exceeds vcb locally at the nucleation site and the nucleation barrier vanishes.

Using NMR techniques we monitor the structure and number of vortices in a cylindrical container, rotating at constant angular velocity Ω, before and after the passage of the A-B interface. The initial A phase contains the equilibrium number of vortices. The final B phase is found to have a deficit of vortices which depends nonmonotonically on the measured time t AB of the A→B transition. We argue that a vortex layer is formed in front of the moving A-B interface. The measured vortex deficit can be understood by analyzing the stability of the layer

Insight in the dynamics of quantized vortex lines has been obtained by performing NMR measurements in uniformly rotating superfluid [sup 3]He-[ital B]. Compared to superfluid [sup 4]He, in [sup 3]He-[ital B] the viscosity of the normal component is three orders of magnitude larger and the pinning of vortices is weaker. The collective modes governing the hydrodynamic response of an array of vortex lines are highly overdamped. Two distinct modes are identified: (1) a relatively fast mutual-friction-resisted mode, which controls the redistribution of the vortex density on a time scale of a few seconds, and (2) an exponentially relaxing slow mode with a time constant of a few minutes, which governs asymptotically the approach to equilibrium at nearly constant vortex density. Measurement of the fast motion allows us to extract the dissipative mutual friction. The slow mode is dominated by the elastic tension along the vortex line and by weak pinning at the top and bottom surfaces of the rotating container. With increasing vortex density the surface pinning becomes a collective process, in which coherently moving groups of vortices are pinned in unison. Collective pinning is a result of the shear elasticity related to the crystalline order of the vortex lattice.more » Our measurements on the slow mode indicate that the crystalline correlation extends over many lattice spacings.« less

Exponentially damped relaxation with a time constant (1 ÷ 3) min after perturbation of steady rotation has been discovered in rotating 3He-B, using NMR techniques. The effect represents an overdamped collective mode of the vortex array, governed by vortex tension and pinning. Elastic-shear deformation of the array is found to influence pinning, but does not contribute in the bulk liquid. The presence of shear elasticity provides the first evidence for crystalline order of a vortex array in 3He.

We have observed spin-mass vortices (SMV) in rotating superfluid $^{3}\mathit{B}$. The SMV is a combined topological object formed of an ordinary vortex with mass current and of a disclination with spin current. A planar defect, so-called \ensuremath{\theta} soliton, is topologically bound to the SMV line. The SMV's were created primarily by cooling the $^{3}\mathrm{He}$ sample through a reversible A\ensuremath{\rightarrow}B transition at a constant rotation velocity, which was smaller than the critical velocity for the nucleation of vortices ${\mathrm{in}}^{3}$He-B. The observation of the SMV's is based on changes in the NMR absorption caused by the attached solitons: The absorption is shifted to higher frequencies in conventional NMR at low rf excitation and large additional absorption is observed in the homogeneously precessing domain (HPD) at high excitation. The presence of SMV's is deduced from the stability and from the rotation-speed dependence of the additional absorption.

In transverse NMR at high rf excitation, it is possible to separate a [sup 3]He-[ital B] sample into two magnetic domains. In one domain the spins are precessing coherently with a large tilting angle in relation to the polarizing magnetic field while in the other they are stationary and oriented parallel to the field. We have studied the two-domain system during vortex-free rotation and found that the boundary region between the precessing and static domains is sensitive to superfluid counterflow, flowing parallel to the boundary. The volume of the precessing domain decreases and the NMR absorption, associated with spin diffusion across the boundary, increases. The shift of the domain boundary is analyzed in terms of the competition between the kinetic energy of counterflow and the gradient in the Zeeman energy. From the shift we obtain the superfluid density anisotropy, induced by the magnetic field. A calculation in the weak-coupling approximation explains only half of the measured ansiotropy at low pressures. At high pressures the discrepancy is smaller.

We have observed spin-mass vortices (SMV) in superfluid $^{3}\mathit{B}$. The SMV is a combined topological object made up of a vortex line with mass current and a disclination line with spin current. It is also a termination line of a planar defect, the so-called \ensuremath{\theta} soliton. The SMVs are bound either as pairs or to the container wall by the soliton. They are nucleated when a rotating $^{3}\mathrm{He}$ sample cools slowly through the A\ensuremath{\rightarrow}B phase transition. The identification of the SMV is based on the NMR signatures of the soliton.

In rotating 3He-B the critical flow velocity for the nucleation of singular vortex lines is high and allows the existence of different rotating states: vortex-free counterflow, the equilibrium vortex state, and metastable states with a well-defined vortex cluster containing less than the equilibrium number of vortices. These states can be distinguished and characterized using CW NMR techniques. We derive an estimate for the magnetic field induced anistropy of the superfluid energy gap from an analysis of the spatial distribution of the order parameter texture in the vortex-free state. When vortices are introduced, their number in the vortex cluster can be counted using a simple experimental procedure. This allows us to measure the critical rotation velocity for the nucleation of vortices, which proves to correspond to the maximum flow velocity in the cylindrical NMR cell.

We present experimental proof that in rotating {sup 3}He-{ital B} the vortex-core transition temperature {ital T}{sub {ital V}} separates axisymmetric vortices above {ital T}{sub {ital V}} from vortices with spontaneously broken axial symmetry below {ital T}{sub {ital V}}. The nonaxisymmetry is observed in the presence of coherent spin precession as a new soft Goldstone mode, manifested as oscillations and spiral twisting of the core anisotropy axis. These are driven by the precessing spin via spin-orbit coupling and lead to magnetic relaxation from viscous losses, which depend on vortex pinning.

The order-parameter texture has been studied in rotating {sup 3}He-{ital B} in the vortex-free state with NMR techniques. A sequence of textural phase transitions is observed with increasing rotation speed. It is generated by competing interactions with magnetic field, surfaces, and rotation. Two surface interactions are extracted: the susceptibility anisotropy at the wall and the gyromagnetism due to a magnetic-field-induced surface supercurrent. The results are consistent with an order-parameter structure approaching the planar state with diffuse quasiparticle scattering at the wall.

Negative ion mobility in rotating 3He-B at magnetic fields H 0.1 T has been measured along the common direction of H and the rotation axis Ω. When Ω > 0, we observed an increase of mobility, which originates from a reorientation of the anisotropic energy gap. The increase can be understood quantitatively only if soft vortex cores, predicted by Sonin, are assumed. Their size was found to be on the order of the magnetic Healing length ξH.

We have studied the B⇌A phase transitions in a rotating container. The initial state contains the equilibrium number of vortices, and after the A-B interface has traversed the container, the vortex state was studied using NMR. We find that the A-phase state resulting from a B→A transition contains the equilibrium number of continuous vortices. Possible explanations are discussed.

The phase-shifted NMR absorption response of an array of vortices to a harmonic modulation of the rotation velocity is discussed. The measured phase lag between the rotation drive and its response can be explained by a torque, which acts on the nonaxisymmetric vortex core cross-section and derives contributions from both the vortex displacement and velocity. The result supports the earlier conclusion that the NMR absorption signal can be employed for studying vortex motion in rotating3He-B.

The homogeneously precessing domain (HPD) is a coherent dynamic order parameter state of 3He-B, which originates from the stiffness of the spin part of the order parameter. We have investigated the HPD state in the presence of vortex-free counterflow as a function of the rotation velocity ω. The energy difference between the orbital textures across the domain boundary leads to a shift of the boundary, such that the precessing domain shrinks ∝ω2. In the equilibrium vortex state no such shift is observed. By monitoring the shift vs ω we have studied the B phase superfluid density anisotropy in a magnetic field, the nucleation of quantized vortex lines at the side wall of the rotating container, and the spatial distribution of counterflow and vortices, when the number of vortices is less than in equilibrium.

A unique property of 3 He-B is vortex-free rotation, due to a high nucleation threshold of the singular vortices. In contrast to other superfluids, rotational states consisting of a vortex cluster surrounded by vortex-free counterflow form spontaneously and can also be prepared with a fixed number of vortices. The clusters can be analyzed by means of NMR measurements with high precision. These techniques have been exploited to study rotational states in the presence of different phase boundaries.

We have constructed an experimental chamber permitting simultaneous observation of both the transverse cw-NMR spectrum and the time-of-flight of negative ions from a rotating sample of vortices in 3He. Our measurements in the A-phase confirm that the vortex state, causing the large delay and strong deformation of the ion pulses drifting parallel to the rotation axis, is also responsible for the satellite peak corresponding to continuos vortices in the NMR spectrum. Unfortunately, singular vortices, whose distinct ion response was detected earlier, could not be observed in the present setup.

Superfluid counterflow in rotating vortex-free 3 3He-B induces distinct changes in the homogeneously precessing resonance domain: its volume is reduced and the NMR absorption increased. Both effects disappear if the domain fills the whole experimental cell.

NMR absorption by vortices in the homogeneously precessing spin domain is discussed in terms of a torque, which arises from spin-orbit coupling between the coherently precessing spins and the nonuniformity in the orbital order parameter in the vortex core. A new soft mode of the nonaxisymmetric vortex core has been observed to contribute to spin relaxation.

The measurement of cw NMR absorption in a homogeneously precessing spin domain of 3 He-B is discussed. The absorption is divided into several contributions, based upon their different dependences on the domain length. Within our experimental accuracy, we found no contribution linear with domain size which would be caused by surface relaxation on the cell wall.

The interaction between negative ions and 3 He superfluids was studied by using a time-of-flight spectrometer having a 10−3 relative resolution. The ions guided through a sample of rotating3He-A were found to be focused into the cores of the vortices present in this rotating superfluid. Two different types, with different core structures and presumably different numbers of circulation quanta associated with them, were found. The ion mobility along the vortex cores, μ c , observed in the absence of external magnetic field, can be explained by the mobility anisotropy of the A phase, which indicates that the vortices are continuous, i.e., consist of the A phase even in the core. In finite magnetic fields, a qualitatively similar continuous vortex structure was found, a result compatible with the earlier nuclear magnetic resonance (NMR) experiments, but also a new vortex type with an anomalously high μ c was seen when the vortex sample was prepared “adiabatically.” The observed strong ion focusing indicates broken w-symmetry in the core textures. This is in contradiction with the earlier numerical calculations on the optimal continuous vortex texture. Experiments to observe trapping of ions into the vortex cores were performed both in A and B phases. No trapping could be detected. Mobility measurements in stationary liquid were extended down toT=0.3T c . Comparison with the calculated transport coefficients yieldsΔ A (T)=1.32Δ BCS (T) for the maximal A phase gap atP=29.3 bar, andΔ B (T)=1.12Δ BCS (T) for the B phase gap at 4.8 bar. In the normal Fermi liquid a shallow minimum of ion mobility was detected aroundT≃2T c =5 mK.

Ion-mobility experiments on rotating superfluid 3He–A show that the l-vector texture in the liquid strongly focuses ions to vortex cores and that two different kinds of vortices, with clearly different ion mobilities along their cores, exist in the A phase, depending on the preparation of the rotating state and on the external magnetic field.

Experiments with negative ions in rotating superfluid 3He-A show strong retardation and deformation of ion pulses drifting parallel to the angular velocity Ω. This is caused by the interaction between the ions and the l texture in the soft cores of A-phase vortices. The interaction is mediated by the anisotropic ion mobility: v=μ⊥E-Δμ(E·l)l. The (Ω,T) dependence of the retardation is explained by a model that assumes focusing of ions into the vortex cores, along which the mobility μc is lower than that in the bulk liquid, μ⊥. We find μc=μ⊥-0.6Δμ.

A thermometer based on the temperature dependence of the negative ion mobility in superfluid 3 He is described. The device can be used for monitoring the temperature of an open geometry sample of 3 He in the range 0.4 ≲ T / T c ≤ 1. The ion thermometer is most sensitive immediately below T c , in the Ginzburg-Landau region; above T ≈ 0.95 T c a resolution of 0.1 μK can be achieved. The measuring technique provides an on-line display of the relative mobility, μ ( T )/ μ ( T c ), and the ions probe the temperature of the 3 He sample directly, which leads to a short time constant τ versus T / T c is insensitive to the external magnetic field and the pressure of the sample. Only a low electric field, E ≲ 10 V cm −1 , with essentially no homogeneity requirements is needed. Parasitic heating due to the flow of ions is of the order of 1 pW.

First experiments suggesting the presence of singular vortices in rotating /sup 3/He-A are reported. Our studies on the interaction between negative ions and vortex textures verify the existence of the continuous vortices seen earlier by NMR, but evidence for a new vortex state with high ion mobility along the core is also found. The nucleation of the new vortex depends on the external magnetic field and the rotation history of the sample.

First experiments suggesting the presence of singular vortices in rotating 3He–A are reported. We have studied the interaction between negative ions and vortices by utilizing the focusing of ions by vortices. Our results verify the existence of continuous vortices seen earlier by NMR, but evidence for a new vortex state with high ion mobility along the core was also found. The nucleation of the new vortex state depends on the external magnetic field and the rotation history of the sample.

A thermometer based on the temperature dependence of the negative ion mobility in superfluid 3He is described. The device can be used in the range 0.4c< 1, and it is most sensitive immediately below Tc, where a resolution of 0.1 µK can be achieved, the measuring system includes an on-line display, and the ions probe the temperature of the sample directly. The thermometer is insensitive to the external magnetic field and to the pressure of the liquid. A low electric field, E< 10 V/cm with no homogeneity requirements is needed. The parasitic heating due to the flow of ions is of the order of 1 pW.

We have studied continuous vortices in rotating 3He–A in the high external magnetic field H = 28.4 mT. The time-of-flight of negative ion pulses, drifting parallel to \vecΩ, increases considerably and the pulses lengthen drastically in rotating liquid, compared with Ω=0. This is caused by an interaction between the ions and the \hatℓ texture in the soft cores of the vortices. The interaction is mediated by the anisotropic ion mobility: \vecv=µ⊥\vecE-Δµ(\vecE·\hatℓ)\hatℓ. The (Ω, T)-dependence of the retardation can be described by a model that assumes focusing of ions into the vortex cores, where Ions focused into vortex cores drift approximately the mobility is lower than in the bulk liquid, parallel to \hatℓ.