Textural Transitions in a Rotating Slab of 3He-A

The operation of a torsional oscillator for detection, of flow-driven textural transitions in, ³He-A is described. The detection technique, tracking the shift of the resonant frequency of the torsional oscillator, allows us to observe textural changes and the presence of vortices in zero magnetic field. It relies on. the anisotropic superfluid density of ³He-A and its change due to reorientation of the Î-texture caused by counterflow.     

NMR Spectroscopy of the Double-Quantum Vortex in Superfluid 3He-A

The double-quantum vortex line with continuous (singularity-free) structure is the most common linear defect in rotating ³He-A. Its well-known experimental signature is a frequency-shifted satellite peak in the NMR spectrum. It arises from the absorption of spin wave excitations, which are localized bound states in the dipole-unlocked soft vortex core. In first approximation, the intensity of the satellite peak is proportional to the number of vortex lines. With increased measuring resolution we have found that the absorption contribution of individual vortex lines is not identical, but displays small variations, which depend on the non-uniform global orbital ^ l texture. We attribute the effect to small texture-dependent changes in the ^ l distribution in the soft core, which modify the attractive potential of the localized spin waves. This property can be used for studying the global order parameter texture in the rotating container.     

Quasi-classical Theory of the A-phase of Superfluid 3He-A in a Cylinder

We develop a quasi-classical theory to study the A-phase texture with a coreless vortex like the Mermin-Ho texture in a cylinder. We consider both the cases of cylinder with specular surface and diffusive surface. In case of the diffusive surface, we find a Mermin-Ho type texture at higher temperatures but with the order parameter suppressed near the surface. In the case of specular surface, however, we find a surface correction to the order parameter. The mass current distribution and the total angular momentum are also discussed.     

Orientation of the Angular Momentum in Superfluid 3He-A in a Stretched Aerogel

Superfluid ³He-A in a fully characterized stretched aerogel, used in previous work by Pollanen et al., has been studied for parallel and perpendicular orientations of the magnetic field relative to the anisotropy axis of the aerogel. Consistently, we find that an equal spin pairing state (ESP) is stabilized down to the lowest temperature. From our pulsed NMR frequency shifts as a function of temperature and tip angle, the orientation of the orbital angular momentum $\hat{l}$ has been determined. The aerogel anisotropy introduced by uniaxial stretching tends to align $\hat{l}$ in the axial state parallel to the strain axis, consistent with the theory proposed by Sauls and contrary to Volovik’s prediction based on an impurity calculation of Rainer and Vuorio.     

Field Dependence of the Superfluid 3He A 1 and A 2 Transitions

We present new results on the magnetic field dependence of the superfluid transition temperatures of the A ₁ and A ₂ phases of ³He. The transition temperature has been measured up to 15 T, the up to 12 T, at the melting pressure. The temperature was measured by an in situ field independent glass thermometer. The results are in agreement with extrapolations from earlier experiments, and with calculations of the splitting versus magnetic field. We were also able to obtain an estimate of the quadratic terms of the splitting, and of each of the transition temperatures. The measured quadratic terms are smaller than calculated, the negative coefficient for the quadratic term being quite unexpected.     

Textural Effects and Spin-Wave Radiation in Superfluid 3He Weak Links

The Josephson coupling between two volumes of superfluid ³He-B also couples the phase difference to the spin-orbit texture of the order parameter. As a result, the equilibrium configuration of the macroscopic texture depends on the phase difference. If the junction is biased by a pressure head, the Josephson oscillations of the supercurrent are accompanied by an oscillation of the texture close to the junction. This leads to a radiation of spin waves from the weak link, and thus contributes to the dissipative dc currents flowing through it. PACS numbers: 67.57.De, 67.57.Fg, 67.57.Np.     

Vortex Core Transitions in Superfluid 3He in Uniaxially Anisotropic Aerogel

Vortex core transitions (VCTs) in the superfluid phases of liquid ³He in uniaxially stretched and compressed aerogels are theoretically investigated. Uniaxial deformation imposed on the aerogel alters superfluid pairing symmetries in aerogels and the axial and polar pairing states are favored. In this study, we examine whether the effects of the uniaxial anisotropy on the pairing symmetries are reflected in core states of a single vortex extending along the deformation axis. By numerically solving the Ginzburg-Landau equations, we find that in the compressed aerogel, the first order VCT appears at any pressure in the B-like phase, while in the stretched aerogel, the VCT in the B-like phase is lost. Further, the vortices in the A-like phase in the stretched aerogel, have a polar core state in place of the A-phase core of the nonsingular Mermin-Ho vortex.     

High-Energy Low-Temperature Physics: Production of Phase Transitions and Topological Defects by Energetic Particles in Superfluid 3He

I review three sets of experiments conducted in the last decade, in which superfluid ³ He was irradiated with high-energy particles and the nucleation either of vorticity or of the A–B phase transition reported. I consider how far the known atomic physics constrains possible scenarios for such nucleation, and comment on two such scenarios which have appeared in the literature, namely the baked-Alaska and cosmological (Kibble–Zurek–Volovik) models. I point out that there is a fundamental difference between the problems of nucleation of vorticity on the one hand and the B phase on the other: and that as a result, it is by no means necessary that the same scenario should describe both phenomena. In an appendix I discuss possible sinks of energy in the calorimetric (Grenoble–Lancaster) experiment, with the conclusion that it is entirely consistent with the data to assume that no vorticity at all was produced in this experiment.     

Phase diagram for the helical texture in 3He-A

The stability region of the helical textures in³He-A in thev _s-H phase diagram is theoretically determined. Herev _sis the superflow velocity andH (v _s) is the external magnetic field. The pitch of the helixk ^–1 that minimizes the Gibbs free energy and the corresponding inclination angles ofl andd are determined numerically as functions ofv _sandH. The NMR frequencies (two longitudinal and four transverse frequencies) associated with the helical texture are obtained.Work supported by the National Science Foundation under Grant No. DMR 76-21032.     

Phase Transition of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He in 97.5% porosity aerogel by NMR method. Above 1.0 MPa, superfluid phase transition has been observed. The transition temperature T _c ^a is strongly suppressed from its bulk value. The Pressure-Temperature diagram suggests that superfluid phase will not appear below near 0.8 MPa. The A-B phase transition has been observed above 1.3 MPa, below which a state of superfluid phases remains to be identified. The temperature dependence of NMR frequency shifts Δf in the A-like and the B-like phases are almost linear at pressures below 2.4 MPa. We obtained the differential coefficient of NMR frequency shifts ∂(Δf)/∂(T/T _c ^a ) at 0.9T _c ^a as a function of pressure, and it suggests that superfluid phase will not appear below near 0.8 MPa which is the same pressure estimated by P-T diagram.     

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.     

Evidence for Magnon BEC in Superfluid <Superscript>3</Superscript>He-A

The phenomenon of phase-coherent precession of magnetization in superfluid ³He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different states of coherent precession have been observed in ³He-B: homogeneously precessing domain (HPD); persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. Here we present evidence of magnons Bose-Einstein condensation in ³He-A in a compressed aerogel.     

Magnetic Phase Transitions in bcc 3He

We study magnetic phase transitions in the bcc solid ³He by means of Monte Carlo simulations. We employ a classical spin model on the bcc lattice with multiple ring-exchange interactions. In the present study, we take into account up to 4-spin ring exchanges. In order to clarify the character of phase transitions we examine energy histograms generated by Monte Carlo simulations. It is shown that the phase transition between the cnaf and the paramagnetic phases is discontinuous at low magnetic fields while it is continuous at high magnetic fields. This result agrees qualitatively with experimental observations.     

Macroscopic Dynamics of the Polar Phase in Superfluid 3He

Recent NMR experiments on superfluid³He in an aerogel suggest that the superfluid phase found might be different from theA andB phases present in the bulk. Theoretical calculations indicate that the polar phase is the leading alternative candidate. In the present paper we derive the hydrodynamics of the polar phase. We study the influence of the magnetic dipole interaction and of a weak external magnetic field including thek=0 dynamics relevant for NMR. It turns out that cw NMR experiments can be used to distinguish the polar phase from theA phase provided one can orient the preferred direction of the polar phase in real space parallel and perpendicular to the container walls of an experimental cell. We also examine the influence of the presence of the aerogel on the reversible and dissipative hydrodynamics generalizing earlier work on superfluid⁴He in aerogels.     

A-B Phase Conversion and Coexistence of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He at 2.4 MPa in cylindrical aerogel by NMR method. When the liquid is cooled down from the normal state, the A-like phase appears below superfluid transition temperature T _c ^a which is suppressed in comparison with the transition temperature of the bulk liquid. With further cooling below the certain temperature T _ab,c ^a , the A-like phase is converted into the B-like phase gradually. Both phases stably coexist within about 90 μK. When you keep the temperature constant in which both phases coexist, the A-B phase conversion stops. With furthermore cooling, the whole liquid becomes the B-like phase. The cwNMR spectra at the coexistence state suggest that the B-like phase is not uniformly distributed in the A-like phase like a large number of small bubbles in a liquid, but separated as a whole from the A-like phase. By applying a field gradient which changes as a function of square of radius, we found that the A-like phase is in the edge part with a cylindrical shape and the B-like phase is in the central part with a columnar shape.      

High-Pressure Phase Transitions of LaF3and CeF3

The effect of high pressure on the structure of LaF₃ (tysonite), CeF₃, and nonstoichiometric LaF₃-based solid solutions (rhombohedral system, P c1, Z = 6) is discussed. In the systems MF₂–LaF₃ with M = Pb and Sr, fluorite-like M_{1 –x} La _x F_{2 + x} solid solutions (Fm3m, Z = 4) are obtained in the composition range 0.5 x 0.75 by quenching from 1500–1700 K at p = 10 GPa. By extrapolating the composition dependences of the lattice parameter for these cubic solid solutions, the lattice parameter of cubic LaF₃ is estimated at a= 5.86 ± 0.02 Å. High-pressure x-ray diffraction studies indicate that CeF₃ undergoes a first-order phase transition similar to that revealed recently in LaF₃. At p = 20.6 GPa, the lattice parameters of orthorhombic CeF₃ (Cmma, Z= 8) are a = 8.062 ± 0.006 Å, b = 8.457 ± 0.009 Å, and c = 5.091 ± 0.006 Å. The transition is accompanied by a 7.3% decrease in volume. The high-pressures structure of LaF₃ and CeF₃ can be thought of as a distorted modification of the structure of a hypothetical fluorite-like trifluoride. The lattice parameters of the orthorhombic and cubic cells are related by a _ortho b _ortho a _cubic and c _ortho a _cubic.     

Vortex-Loops and Phase Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴ He and ³ He. A fast solidification event in the superfluid results in a local release of pressure and a velocity field in the superfluid. This in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with experiments on heterogeneous nucleation.