Acoustic Properties of Normal Liquid 3He in 98% Aerogel

We have performed longitudinal ultrasound (9.5 MHz) attenuation and sound velocity measurements in the normal state of liquid ³He in 98% aerogel. The absolute attenuation and sound velocity were determined by direct propagation of sound pulses through the medium in a wide range of temperatures, 2 mK<T<200 mK. Due to the scattering off the aerogel, the sound excitation remains as first sound over the entire range of temperatures and pressures studied. Unlike pure liquid ³He, the sound attenuation shows a minimum around 30–50 mK, depending on the pressure. We report our results of absolute sound attenuation measurements at 29 bars of sample pressure.     

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.     

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.     

Perturbative Study of Strong Coupling Correction in Superfluid 3He in Aerogel

The AB transition curve of superfluid ³He in aerogel often shows a positive slope dT _AB(P)/dP>0 over the measured pressures P, contrary to that of the bulk liquid. Bearing this behavior in mind suggestive of a unexpectedly strong reduction of the strong coupling (SC) correction due to the aerogel, we examine impurity effects on the SC contributions to the quartic term of the Ginzburg-Landau (GL) functional. Our analysis perturbative both in the repulsive interaction and the impurity scattering suggests that, in agreement with experimental data, the impurity scattering weakens the relative stability of the ABM state to the BW state and notably reduces the SC correction for the ABM phase.     

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.     

Anisotropic Aerogels for Studying Superfluid 3He

It may be possible to stabilize new superfluid phases of ³He with anisotropic silica aerogels. We discuss two methods that introduce anisotropy in the aerogel on length scales relevant to superfluid ³He. First, anisotropy can be induced with uniaxial strain. A second method generates anisotropy during the growth and drying stages. We have grown cylindrical ∼98% aerogels with anisotropy indicated by preferential radial shrinkage after supercritical drying and find that this shrinkage correlates with small angle x-ray scattering (SAXS). The growth-induced anisotropy was found to be ∼90° out of phase relative to that induced by strain. This has implications for the possible stabilization of superfluid phases with specific symmetry.     

Scaling Results for Superfluid 3He in 98% Open Aerogel

We present experimental observations of the suppressed superfluid transition temperature, T _ca , superfluid fraction, ρ _s /ρ and Leggett frequency of ³He-B in aerogel, Ω _Ba . We determine T _ca from mass decoupling and the vanishing of the frequency shift away from the Larmor frequency in our different samples and different laboratories. We find that the suppressed transition temperature for ³He in aerogel occurs at a sample dependent, but approximately pressure independent, length, , where T _c and ξ ₀(P), are the transition temperature and the pressure dependent zero temperature coherence length for bulk ³He. T _ca also occurs at a pressure independent value of the Leggett frequency of bulk ³He-B. Further, we find that when the superfluid fraction and square of the Leggett frequency are plotted against T _ca −T (and not (T _ca −T)/T _ca ), the results of each measurement nearly collapse on to a pressure independent but sample dependent plot, with no further scaling. When plotted on a log–log scale, both measurements exhibit power laws in the range 1.33–1.45.      

Analysis of Strong-Coupling Parameters for Superfluid 3He

Superfluid ³He experiments show strong deviation from the weak-coupling limit of the Ginzburg-Landau theory, and this discrepancy grows with increasing pressure. Strong-coupling contributions to the quasiparticle interactions are known to account for this effect and they are manifest in the five β-coefficients of the fourth order Ginzburg-Landau free energy terms. The Ginzburg-Landau free energy also has a coefficient g _z to include magnetic field coupling to the order parameter. From NMR susceptibility experiments, we find the deviation of g _z from its weak-coupling value to be negligible at all pressures. New results for the pressure dependence of four different combinations of β-coefficients, β ₃₄₅, β ₁₂, β ₂₄₅, and β ₅ are calculated and comparison is made with theory.     

The AB Interface in Superfluid 3He as a Simulated Cosmological Brane

We present measurements of the transport of superfluid ³He quasiparticle excitations in the ballistic limit at temperatures well below T _c , and an interpretation of unexpected results as an experimental simulation of cosmological processes. Using a variable magnetic field profile we stabilize a layer of A phase across a cylinder of B phase, creating both an AB and a BA interface. These highly ordered interfaces may provide an ideal laboratory analogy for the branes and anti-branes of current cosmology. It has been suggested that brane interaction and annihilation are involved in inflation in the early Universe and leave behind topological defects such as cosmic strings. In our experiments we have annihilated our AB/BA branes by ramping down the magnetic field to remove the A phase layer. We then find that the quasiparticles face an extra impedance owing to defects left behind in the B phase texture. This is the first definitive observation of such a phenomenon.     

Effect of Strong Magnetic Fields on Superfluid 3He in 98% Porosity Aerogel

No Heading We report our results of shear acoustic impedance measurements performed on superfluid ³He in 98% porosity silica aerogel. Experiments in high porosity aerogel provide unique opportunity to study the influence of disorder on a p-wave superfluid and compare the behavior with that of the well understood pure bulk. Our experiment is designed to detect acoustic signatures from both bulk liquid and liquid in aerogel. In the past, experiments on ³He in aerogel have been conducted in zero or low magnetic fields (< 1 tesla). We made measurements in magnetic fields as high as 15 tesla at 28.4 and 33.5 bars and observed a new phase in aerogel induced by magnetic fields splitting the superfluid transition into two.PACS numbers: 67.57Pq, 67.80Mg     

Spin Pumping Effect in Superfluid 3He A1

A fountain effect is a common phenomenon in both ³He and ⁴He superfluids. Unique to superfluid ³He is the magnetic fountain effect, which has been used to determine the spin direction of the condensate in ³He A₁ phase. Here we present a pressure driven fountain effect in A₁ phase. The experimental cell is composed of a large reservoir connected to a small detector chamber through superleak channels of width of 20 μm. One wall of the detector chamber houses a movable circular 6 μm thick membrane which serves as a sensitive capacitive pressure sensor and also acts as a spin pump. In A₁ phase, a DC voltage applied on the capacitor induces a simultaneous mass and spin superfluid current into the small chamber. After equilibration, removal of the DC voltage causes a sudden pressure drop followed by a slow relaxation. The sudden drop is a consequence of reversed superfluid flow through the superleak. The observed decay times during the slow relaxation agree with those obtained in magnetically induced spin flow experiment. These observations show that the slow relaxation stems from spin relaxation in the absence of applied field gradient.     

Nonlinear Transport of Wigner Solid on Superfluid 3He–A

Electrons trapped on the surface of liquid helium form the Wigner solid accompanied with the periodic surface deformation (dimple lattice). Because of the soft surface, the Wigner solid shows unique nonlinear transport properties. Here we present the results of the nonlinear transport measurements of the Wigner solid on the superfluid ³He A phase at temperatures down to 200 μK in a magnetic field of 0.363 Tesla. The transition from linear to nonlinear behavior is observed as increasing the driving voltage. This behavior is very similar to those previously observed in the B phase and normal phase, and attributable to the deformation of the dimple shape caused by the strong damping of liquid ³He.     

QCM Measurements of Superfluid Response in 4He Films up to 180 MHz

At finite frequencies, a dynamic Kosterlitz–Thouless (KT) theory predicts a frequency dependence of the superfluid transition in ⁴He films on planar surfaces. We report results of QCM measurements to study the superfluid response on planar gold surfaces for very high frequencies up to 180 MHz in the temperature range of 0.6–1.0 K. As the frequency is increased, we observed the expected KT behavior that the superfluid transition shifts to a higher temperature from the static transition temperature T _KT and the transition temperature region broadens. The frequency dependence of the dissipation peak temperature at the transition agrees with a simple equation of the frequency dependence based on the dynamic KT theory. The microscopic parameter for the dynamic transition, the ratio of the diffusion constant to the square of the vortex core radius D/r ₀ ², is estimated to be on the order of 10¹⁰ s⁻¹.     

3He Anomalously High Spin Diffusion in Solid Para-Hydrogen

NMR measurements of ³He spin diffusion coefficient in solid para-H₂ are carried out at the temperatures 0.45–1.5 K. The crystals have been grown under constant pressure 20–130 bar. The ³He concentrations in the initial para-H₂–³He gas mixtures were 0.1% and 0.3%. It is found out that the decay of echo amplitude vs both magnetic field gradient G and time interval τ between RF pulses is of non-exponential character, typical of one-dimensional diffusion in restricted geometry. The values of true spin-diffusion coefficient D _S measured are found to be ∼10⁻⁴ cm²/s at 20 bar. At 108 bar D _S value is one order of magnitude less. D _S does not depend on temperature. Such spin diffusion coefficient values seem to be anomalously high in comparison with well-known values of D _S =10⁻⁵ cm²/s for bulk liquid ³He at 27 bar and D _S =10⁻⁸ cm²/s for bulk solid ³He at 108 bar. The special experiments with the crystal annealing make it clear that the high spin diffusion here is connected with fast diffusion along dislocation lines.     

Adiabatic Melting of 4He Crystal in Superfluid 3He at Sub-millikelvin Temperatures

Adiabatic melting of ⁴He crystal to phase separated ³He–⁴He solution (at T< 2 mK) is probably the most promising method to cool the dilute phase down to temperatures substantially below 0.1 mK. When started well below the superfluid transition temperature T _c of pure ³He, this process allows, in principle, to get the final temperature (T _f ) several orders of magnitude less than the initial one (T _i ). This work is the first practical implementation of the method below the T _c of ³He. The observed cooling factor was T _i /T _f =1.4 at 0.9 mK, being mainly limited by the bad performance of the superleak filling line, by incomplete solidification of ⁴He in the cell, and by the improper thermal contact between the cell wall and the liquid.     

Thickness Dependence of Critical Current of Superfluid 3He Film

We have measured the critical current J _c , which is defined as the onset of dissipative flow, for a thickness range from 0.3 to 4 μm using inter-digitated capacitors. In the thickness dependence of J _c , two distinct dissipation regimes were observed. The crossover occurred at a thickness of ∼1 μm.     

Suhl Instability as a Mechanism of the Catastrophic Relaxation in the Superfluid 3He–B

In order to explain catastrophic relaxation, bulk mechanism based on Suhl instability (J. Phys. Chem. Solids 1, 209, 1957) is studied. It is shown, that at sufficiently low temperatures homogeneous precession of spin becomes unstable in the whole region of tipping angles of spin 0≤β≤π. In comparison with the previous publication of Surovtsev and Fomin (J. Exp. Theor. Phys. Lett. 83, 410, 2006) the leading zero temperature increments for the angles θ ₀≃104°≤β≤π are found. Estimation of the temperature of transition to the unstable state for the angle of 105°, that corresponds to the region of tipping angles in homogeneously precessing domain (HPD), is made.     

NMR Study of Superfluid Phases of 3He Confined in 97.5% Porous Silica Aerogel

We have studied the scattering effect from aerogel strands on superfluid phases of ³He by a cw NMR method at 920 kHz. Liquid ³He at a pressure of 13 bar was confined in 97.5% porous aerogel from the same batch as that of a recent 4th sound study. The NMR experiment was performed in a magnetic field of 28.4 mT down to 0.3 mK. As temperature decreased, the NMR resonant frequency increased below 0.76 mK. The temperature of 0.76 mK agrees with the superfluid transition temperature T ^aerogel _c observed in the 4th sound study at the same pressure. Below T ^aerogel _c the behavior of thefrequency shift as a function of temperature indicates that there is no phasetransition to the other superfluid phase down to about 0.4 T ^aerogel _c . Owing to a very large surface solid ³He magnetization, we could not determine the superfluid phase of ³He in the aerogel in the magnetization measurement.     

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

No Heading 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 T_C^aero and B-like phase appeared at lower temperatures although only the B-like phase was observed up to T_C^aero 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 T_C^aero 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 T_C^aero with the actual average separation distance of the silica strands.PACS numbers: 67.57.Pq, 67.80.Jd     

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.