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.      

Absolute Ultrasound Attenuation Measurements in Superfluid 3He in 98% Aerogel by Direct Transmission

Systematic investigations on the effect of static disorder on p-wave superfluid ³He have been made possible by utilizing the unique structure of high porosity silica aerogel. For the past 10 years, a burst of experimental efforts revealed that three distinct superfluid phases exists. We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B-phase of the superfluid ³He in 98% aerogel. The absolute attenuation was determined by direct propagation of sound pulses through the medium in a wide range of temperatures, down to 200 μK, for sample pressures of 10 and 29 bars. Our results provide direct information on the zero-energy density of states of the superfluid phase in aerogel originating from impurity scattering.     

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     

Rotating Superfluid 3He in Aerogel

Rotational effects on textures of superfluid ³He in aerogel with 98% porosity at a pressure 3.0 MPa were investigated by cw-NMR measurement at 700 kHz (H ₀=22 mT) under rotation up to 2π rad/s. At rest, the superfluidtransition to the A phase occurred at T ^aerogel _c =2.07 mK and the A phase was supercooled down to T ^aerogel _A→B==1.73～1.80 mK and became the B phase in the cooling process. In the warming process, the B phase was superheated up to T ^aerogel _c . In the B phase, a new peak appeared in the NMR spectrum by rotating the sample. The intensity of this peak increased as the rotation speed increased almost linealy to Ω and started to be saturated for Ω≥Ω _c. We attributed the new peak to the textural change caused by the counter flow and the onset of the saturation at Ω _c to the onset of vortex nucleation in aerogel. On deceleration, the peak intensity decreased and disappeared at Ω=Ω _v. Further decreasing Ω, the peak intensity increased even at Ω=0. The counterflow peak observed at Ω=0 indicates the existence of persistent current induced by pinned vortices in aerogel. In the A phase, we did not find any noticeable change in the NMR spectrum under the rotation speed up to 2π rad/s, or by cooling through T _c with or without rotation. We concluded that the ${\hat \ell }$ texture in the A phase was strongly pinned to aerogel. No spin wave satellite signal localized at a soft, core vortex was observed in contrast to the bulk A phase.     

Superfluid Phases of 3He in Aerogel

No Heading Formal derivation of criterion for selection of superfluid phases of ³He in aerogel is presented. At the strength of the derived criterion variation of the order parameter of B-like phase in magnetic field differs from that of B-phase of pure ³He. Possible observable consequence of this difference is discussed.PACS numbers: 67.57.Pq, 67.57.Bc, 67.57.De     

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.     

Sound Modes of Superfluid 3He in Aerogel

We present the results of experiments on sound propagation at audio frequencies in ³ He-filled aerogel. Sound modes were observed at temperatures of 0.8–100 mK in an aerogel sample of 98% porosity. We find that below T _c for superfluid ³ He in the aerogel matrix the speed of sound in the composite system increases by as much as 1.5%. Also below the aerogel T _c new modes appear which correspond to propagation speeds of up to 10 m/s.     

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.     

Collision Drag Effect on Two-Fluid Hydrodynamics of Superfluid 3He in Aerogel

Sound propagation in superfluid ³He in aerogel is studied on the basis of a two-fluid model taking into account the effect by the drag force due to collisions between ³He-quasiparticles and aerogel molecules. The drag force plays a role of frictional force between the aerogel and the normal-fluid component. In local equilibrium, they move together in accordance with McKenna et al.'s model. The deviation from the local equilibrium leads to the damping of sound. We give explicit expressions for the attenuation of longitudinal sounds in this system. We also discuss the sound propagation in a superfluid ³He-aerogel system embedded in a narrow pore. It is shown that the fourth sound propagates in such a system because of the clamping of the normal fluid by the aerogel.     

Robust Superfluid Phases of 3He in Aerogel

Within a phenomenological approach possible forms of the order parameter of the superfluid phases of ³He in the vicinity of the transition temperature are discussed. The effect of aerogel is described by a random tensor field interacting with the orbital part of the order parameter. With respect to their interaction with the random tensor field a group of “robust” order parameters which can maintain long-range order in the presence of the random field is specified. Robust order parameters, corresponding to Equal Spin Pairing (ESP) states are found and proposed as candidates for the observed A-like superfluid phase of liquid ³He in aerogel.     

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.     

Scaling Properties of Superfluid 3He in Aerogel

We have investigated the superfluid transition of ³He in different samples of silica aerogel. Several of these samples have been characterized using x-ray imaging, yielding information about the microstructure of the aerogel. In comparing new measurements on a 99.5% sample with previous observations on the behavior of ³He in 98% porous aerogel we have found evidence for a scaling of the superfluid transition temperature to the correlation length of the aerogel. Furthermore, the superfluid density exhibits a similar universal behaviour over a range of values of reduced temperature. We discuss these new results in the context of superfluid pairing in the presence of a correlated disorder, specifically focussing on the fractal nature of the 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.      

Fourth Sound Propagation in Superfluid 3He in Aerogel

No Heading Impurity effect on the fourth sound propagation in the superfluid ³He-aerogel system confined in a channel is discussed on the basis of a two-fluid theory in which phenomenological parameters are determined microscopically within the homogeneous scattering model.PACS numbers: 67.57.De, 67.57.Hi, 67.57.Pq.     

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.     

Sound Spectroscopy of the Superfluid Phases of 3He in Aerogel in Zero Magnetic Field

Low-frequency sound is used to study phase transitions of ³He confined in 98% open aerogel. Superfluidity is manifested by the onset of the low frequency (slow) mode whose velocity (as a function of pressure and temperature) was used to map out the phase diagram of the B-phase and the metastable A-phase of ³He in aerogel. Analysis of the slow mode's evolution with temperature allows the development of the superfluid fraction in the A and B phases to be determined. The metastable A-phase and the equilibrium B-phase can co-exist in a properly prepared sample. Both the superfluid transition and the A→B transition exhibit a finite width of ～20–25 µK.     

Acoustic Spectroscopy of Superfluid 3He in Aerogel in the Presence of a Magnetic Field

We have constructed a silver alloy cell to investigate low frequency sound propagation in ³ He-filled aerogel at various magnetic fields. In this apparatus, two sound modes were observed in the superfluid phase. We observed both the first sound-like mode (fast mode) which is a compression wave also seen in the normal state and the second sound-like mode (slow mode) which is attributed to the out-of-phase oscillation of the superfluid and normal components of ³ He clamped to the aerogel matrix. The values of T_c and _s can be extracted from the analysis of these two modes. In addition, a Helmholtz resonance provides an in-situ signature of the bulk superfluid transition and allows us to also determine the bulk _s. By measuring these quantities over a range of applied magnetic fields we hope to explore the P, T, H phase diagram of ³ He in aerogel.     

Magnetic Field Dependence of the A-like to B-like Transition of Superfluid 3He in Aerogel

Longitudinal ultrasound attenuation of superfluid ³He in 98% aerogel has been measured at 33 bar and 6.22 MHz in the presence of magnetic fields up to 4.44 kG. The A-like to B-like (A-B like) phase transition in aerogel was identified by a rounded jump in attenuation while sweeping the temperature at a fixed magnetic field perpendicular to the direction of sound propagation. The suppression of the B-like phase was monitored as the magnetic field increased until the A-like phase region extended below our lowest attainable temperature (0.2 mK) at the highest field. In addition, the attenuation in the metastable A-like phase that appears when cooling in zero magnetic field was almost identical to the values observed in the A-like phase in high magnetic field.     

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.      

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.