A-like Phase Research Articles

Quantum Fluid Dynamics of Rotating Superfluid 3He in Aerogel

Superfluid 3He A-like and B-like phases in 98% aerogel have been studied under rotation up to 2π rad/s by using cw-NMR and Homogeneous Pressing Domain (HPD) NMR at 29 mT and 3.0 MPa. Triplet superfluid 3He has continuous symmetries whose degeneracies are lifted by small perturbations of magnetic field, boundary condition of the sample cell, counterflow and global anisotropies of aerogel. We report NMR results of the two typical samples in aerogel under rotation, which are almost identical in the phase diagram, T c and the critical velocity of the multiplication of vortex but are very different in textures and responses to the flow with each other. One samples (S-D) is slightly compressed by squeezing and thermal stress and thus has global anisotropic deformation along the sample axis. The other cell (S-H) has randomly(not uniaxially)-oriented global anisotropy. In the S-D, we observed a large negative shift in cw-NMR and spin wave and HPD in the B-like phase. Comparing textures determined by NMR and its response to the counterflows between two samples, we discuss how the long-range order of the continuous symmetry and textures are controlled by orientation effects due to global anisotropy in aerogel.

Soliton-Like Spin State in the A-Like Phase of 3He in Anisotropic Aerogel

We have found a new stable spin state in the A-like phase of superfluid 3He confined to intrinsically anisotropic aerogel. The state can be formed by radiofrequency excitation applied while cooling through the superfluid transition temperature and its NMR properties are different from the standard A-like phase obtained in the limit of very small excitation. It is possible that this new state is formed by textural domain walls pinned by aerogel.

Magnetic Distortion of the B-like Phase of Superfluid 3He Confined in Aerogel

We present measurements of the response of the B-like phase of superfluid 3He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid 3He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.

Long-Range Order in the A-like Phase of Superfluid 3He in Aerogel

A mutual action of the random anisotropy brought in the superfluid 3He by aerogel and of the global anisotropy caused by its deformation is considered. Strong global anisotropy tends to suppress fluctuations of orientation of the order parameter and stabilizes ABM order parameter. In a limit of vanishing anisotropy fluctuations of ABM order parameter became critical. It is argued that still in a region of small fluctuations the order parameter changes its form to be less sensitive to the random anisotropy. For a favorable landscape of the free energy of superfluid 3He the fluctuations remain small even in a limit of vanishing global anisotropy and the long-range order is maintained.

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 which is suppressed in comparison with the transition temperature of the bulk liquid. With further cooling below the certain temperature T , , 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.

Orientation effect on superfluid 3He in anisotropic aerogel

The orientation of the order parameter in the A-like and B-like phases of superfluid 3He immersed in uniaxially compressed aerogel is reported. With the use of NMR methods, it is found that the orbital momentum of the A-and B-like phases is oriented along the deformation. In the A-like phase, a relatively narrow NMR line with an anomalously large negative frequency shift is observed. The Leggett frequency in the A-like phase, which shows the same energy gap suppression as in the B-like phase, is measured.

Non-linear Mechanical Response of the A-like Phase of Superfluid 3He in Aerogel

We present measurements of the response of the A-like phase of superfluid 3He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid 3He at low temperatures and relatively high magnetic fields such that the aerogel confined superfluid is in the A-like phase, while the surrounding fluid is in the bulk B-phase. We observe a variety of interesting non-linear and hysteretic effects when the resonator is driven to higher velocities. We present some of our preliminary findings and speculate on their implications.

Textures of Superfluid 3He A-like and B-like Phases in Aerogel under Rotation

Superfluid 3He A-like and B-like phases in 98% aerogel under rotation up to 2π rad/sec have been studied by cw-NMR and Homogeneous Precessing Domain (HPD) NMR at 29 mT and 3.0 MPa. In the A-like phase, a large negative frequency shift was observed in the cw-NMR spectrum and no effect of rotation on the spectrum was found. In the B-like phase, the spin wave spectrum was observed when the sample was cooled through T c under rotation and was affected by the counter flow due to the trapped vortices. The HPD was excited in a part of the aerogel sample but introduction of vortices into the sample by rotation or trapped vortices destroyed the HPD.

Fourth Sound Measurement of Superfluid 3He in Aerogel

The fourth sound resonance experiment has been done on liquid 3He in 98.5% porosity aerogel. Aerogel was grown inside the pores among the sintered silver powder to avoid the vibration of the aerogel strands by the sound experiment. The measurement was performed at zero magnetic field and 27 bar. We observed the phase transition between the A-like and B-like phases and also their coexistent state. The A-like to B-like phase transition occurs not at a temperature but within a temperature band. In this band, the A-like phase gradually converts to the B-like phase. Possible picture of the coexistent state is discussed.

Contrasting Mechanical Anisotropies of the SuperfluidHe3Phases in Aerogel

There has been much recent interest in how impurity scattering may affect the phases of the p-wave superfluid 3He. Impurities may be added to the otherwise absolutely pure superfluid by immersing it in aerogel. Some predictions suggest that impurity scattering may destroy orientational order and force all of the superfluid phases to have an isotropic superfluid density. In contrast to this, we present experimental data showing that the response of the A-like phase to superfluid flow is highly anisotropic, revealing a texture that is easily modified by flow.

Longitudinal resonance and identification of the order parameter of the A-like phase of superfluid 3He in aerogel

Interpretation of the recent experiments of Dmitriev et al. on longitudinal resonance in the A-like phase based on specific properties of the “robust” order parameter is proposed.

Longitudinal NMR and spin states in the A-like phase of 3He in aerogel

It was found that two different spin states of the A-like phase can be obtained in aerogel sample. In one of these states we have observed the signal of the longitudinal NMR, while in another state no trace of such a signal was found. The states also have different properties in transverse NMR experiments. Longitudinal NMR signal was also observed in the B-like phase of 3He in aerogel.

Spin nutation in the quasi-isotropic A-like superfluid phase of 3He

The order parameter of the quasi-isotropic A-like superfluid phase of 3He has been reduced to a simple form. The frequencies of the spatially homogeneous oscillations of the spin and the spin part of the order parameter of this phase have been obtained taking into account the anisotropy of its magnetic susceptibility. It has been shown that the anisotropy of susceptibility strongly affects the low-frequency oscillation mode, which is similar to the nutation of an asymmetric top. The possibility of observing this mode using the NMR method is discussed.

Equal-spin pairing state of superfluidHe3in aerogel

The equal-spin pairing state, the so-called A-like phase, of superfluid $^{3}\mathrm{He}$ in aerogels is studied theoretically in the Ginzburg-Landau region by examining thermodynamics, and the resulting equilibrium phase diagram is mapped out. We find that the ABM pairing state with presumably quasi-long-ranged superfluid order has a lower free energy than the planar and ``robust'' states and is the best candidate of the A-like phase with a strange lowering of the polycritical point observed experimentally.

Impurity Scattering Effect on Superfluid Phases of 3He in 97.5% Porous Silica Aerogel

NMR studies of superfluid 3He in 97.5% aerogel have been performed in a magnetic field of 28.4 mT. A small-angle neutron scattering experiment on the structure of the aerogel shows that the average separation distance of silica strands is 54 nm. The aerogel strands were covered with a few layers of solid 3He whose magnetization shows Curie-Weiss behaviour. On cooling process A-like phase appeared at suppressed superfluid transition temperature TCaero and B-like phase appeared at lower temperatures although only the B-like phase was observed up to TCaero on warming process above 2.1 MPa. The superfluid transitions in aerogel always occur below the AB phase transition temperature of bulk liquid at all pressures. An isotropic inhomogeneous scattering model(IISM) proposed by Thuneberg et al. explained well the observed suppressed TCaero in 97.5% with the radius 59 nm of voids in this model. This radius is similar with the average strand separation distance of 54 nm measured in the structural analysis. This similarity of two lengths shows the connection of the suppression of TCaero with the actual average separation distance of the silica strands.

NMR Properties of a Possible Non-unitary State of Superfluid 3He in Aerogel

We discuss the NMR properties of a non-unitary state which has recently been proposed by Fomin as a candidate for the A-like phase of superfluid 3He in aerogel. The new state is robust against the anisotropic scattering by the aerogel strands. We solve Leggettt’s equation for the robust state. Two transverse resonances as well as a longitudinal resonance are obtained. We find that in the pulsed-NMR the free induction frequency depends on the tipping angle θ as (1 + cos θ).

Interfacial pinning in the superfluid 3He A-B transition in aerogel.

Continuous-wave NMR studies of 3He in the presence of 99.3% porosity silica aerogel at 34.0 bars and in a magnetic field of 28.4 mT reveal a first-order phase transition between A-like and B-like superfluid phases on both warming and cooling. NMR spectra show that the phases on warming are the same as the phases on cooling, and the interface between them is found to be strongly pinned, even close to T(c,aero). The observed behavior is consistent with spatial variation of pinning strengths within the aerogel.

Metastability and superfluid fraction of the A-like and B phases of 3He in aerogel in zero magnetic field

We report the low-frequency sound measurements of the metastable A-like (A*) phase of superfluid 3He confined within a 98% open aerogel matrix in zero magnetic field. The second soundlike (slow) mode provides an accurate determination of the superfluid fraction of (and the transition between) the A* and B phases. The A* and B phases exhibit stable coexistence in the presence of disorder, the ratio of their superfluid fractions (ρ a A* /ρ s B ) is much smaller than that of the bulk A and B phases, and argues that the A* and bulk A phases are distinct.

Order parameter of A-like 3He phase in aerogel

Phenomenological criterion of a choice of the order parameter for superfluid phases of $^3$He in aerogel in a near vicinity of the transition temperature is formulated. Except for the B-phase this criterion is met by the order parameter of axiplanar phase for a special choice of its parameters. It is proposed as a limiting at $T\to T_c$ form of the order parameter for the observed A-like phase.

NMR studies of superfluid [formula omitted] in low density silica aerogels

Continuous wave NMR studies of superfluid 3 He in 99.4%, 98.7% and 98.3% porosity silica aerogels show similar phase diagrams, with an equal spin pairing (ESP) A-like state stable near T c,a, and a B-like phase stable at lower temperatures. On cooling through T c,a, the sample magnetization and frequency shift show substantial supercooling of the A-like phase, with discontinuous changes to B-like behavior seen at about 0.64 T c,b (bulk) for all samples. On warming, both the frequency shift and magnetization change continuously as the sample enters an ESP state. This suggests that this phase transition is broadened by pinning of the A–B interface on density fluctuations in the aerogel, even very close to T c,a.