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.      

Depressions of superfluid density and transition temperature of3he confined in small pores

Using fourth-sound techniques, the superfluid density of³He confined in three separately packed alumina powders having volume-averaged pore radius equal to 1.9, 0.44, and 0.18 µm were measured as a function of temperature at 10 pressures between 11 and 31 bar. Systematically larger depressions of superfluid density were observed as the pore size decreased. The measured pressure dependence of the depression of the superfluid transition temperature is consistent with that of the BCS expression for the coherence length. The quality factor of fourth-sound resonance was measured as a function of temperature at 20.5 and 30.9 bar. The highest quality factor measured was 40. The temperature dependence of the quality factor is in qualitative agreement with a theory by Jensen et al.     

Transverse Acoustic Spectroscopy of Superfluid 3He in Compressed Aerogel

The unique nanoporous structure of aerogel provides a rare opportunity to study the role of anisotropic disorder on an anisotropic superfluid ³He. It has been proposed that uniaxial deformation of compliant aerogel would induce global anisotropy and a few compelling effects of global anisotropy on nature of the superfluid phases have been predicted. We measured high frequency shear acoustic impedance in superfluid ³He at 32 bar in a commercially available 98% porosity aerogel under uniaxial compression. At 5% compression, we found evidence of an A-like phase stabilized in a wider temperature width than the A-like phase in uncompressed aerogel.     

Large Boundary Magnetism and Superfluidity of Liquid 3He in Nanometer-sized Porous Alumina

Continuous-wave NMR measurements were performed for liquid ³He in porous alumina with nominal pore size of 20 nm in diameter, at temperatures down to 0.3 mK. The signal is composed of two contributions: from the liquid and from the boundary solid layer of ³He on the alumina’s surface. The latter shows a well-known ferromagnetic tendency and signal intensities can be fitted to a Curie-Weiss law in the high temperature region. The obtained Weiss temperatures are 0.18 and 0.50 mK at 7.5 and 28 bar, respectively. ⁴He coverage (4 monolayers) completely eliminates boundary signal between 7.5 bar and 32.5 bar. The residual liquid signal shows frequency shift and broadening below superfluid transition temperatures depending on liquid pressures. The obtained P-T phase diagram well resembles that of bulk liquid ³He in spite of the very narrow pore-size comparable to the coherence length of superfluid ³He.      

SH-SAW Sensor for Superfluid 3He

No Heading We have developed a new technique to study the transverse acoustic properties of superfluid ³He, employing a shear horizontal surface acoustic wave (SH-SAW) sensor. The transverse acoustic impedance can be obtained from the velocity and damping of SH-SAW which acoustically couples with liquid ³He all the interface. Since ultrasonic measurements provide the information about superfluid order-parameter through the excitation of collective modes, the SH-SAW sensor is expected to be a useful tool to study the boundary effect of superfluid ³He. Preliminary measurements were carried out at pressures of 17 and 23 bar, by the pulse transmission method at a frequency of 70 MHz. At 17 bar, imaginary squashing mode was observed as the sharp drop of the imaginary part of acoustic impedance. At 23 bar, the supercooled A-B phase transition was observed, as a jump of the real part of acoustic impedance, which was not observed in the warming process.PACS numbers: 67.57.Jj, 43.58.+z     

Superfluid helium three in aerogel

We report measurements of the superfluid density and transition temperature of³He confined within 98.2% open aerogel. Both the superfluid fraction and the temperature at which the superfluid is manifested are suppressed strongly from their bulk values. The results suggest that the aerogel reduces the order parameter by a mechanism other than as a diffusely scattering surface.     

Nuclear magnetic resonance of3He superfluid confined in high porosity aerogel

We report pulsed nuclear magnetic resonance (NMR) measurements of the transverse frequency and magnetization of³ He confined in aerogel with 98.2% open volume porosity. A homogeneous superfluid phase is observed at pressures, P > 12 bar, accompanied by a sharp onset of frequency shifts showing little or no textural broadening; a result quite unexpected for³He confined in random porous media. The transition temperatures and order parameter are both significantly suppressed from their bulk values and the magnetization data indicate this low temperature phase is an equal-spin pairing superfluid. For NMR tipping angles greater than 40 ° the resonance frequency drops abruptly to the normal state value. This tip angle dependence is not consistent with either the bulk³He-A or³He-B superfluid phases.     

Sound attenuation in3He-4He liquid mixtures under pressure

The attenuation of sound was measured in³He-⁴He mixtures with³He concentrations ranging from 2.89 to 8.03% at pressures of 10 and 20 bar. The quasiparticle interaction potentials were then determined at each pressure by analyzing the sound attenuation data. The superfluid transition temperature of³He and other properties in the mixtures were then estimated from the interaction potentials.     

Anisotropice superfluid fraction of3He A1 phase

The superfluid fraction of³He a₁ phase is computed from measurements of the velocity of spin/entropy waves induced in a cylindrical chamber, for two different directions of the magnetic field: parallel and perpendicular to the axis of the chamber. The ratio of the superfluid fractions in the parallel and perpendicular orientations is 1.85, and does not depend on the field between 1 and 5 Tesla. We adapt a theoretical texture model to account for the superfluid flow, and the results are consistent with the above ratio and direct estimates of superfluid velocity.     

Acoustic Resonance of Superfluid 3He in Parallel Plates

We performed an acoustic resonance experiment of superfluid ³He confined in a stack of parallel plates, and found the fourth sound resonance. From its velocity, the superfluid density fraction was calculated. No size effect was found because the gap between parallel plates were much larger than the superfluid coherence length. The energy loss of the resonance was also measured. We found that the hydrodynamic theory qualitatively described its temperature dependence, but it could not describe the gap width dependence. Possible explanations is discussed in the text. More over, we found the unidentified resonance that cannot be explained by conventional sound modes.     

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.     

Isochores in superfluid4He between 25 bar and the melting curve

Isochores in superfluid⁴He between 25 bar and the melting curve have been measured to high resolution. Together with the published results of Maynard, these results provide the self-consistent basis for establishing the equation of state in the superfluid phase for temperatures above 1 K.This work supported in part by U.S. NSF Grant No. DMR75-19546.     

Pressure dependence of the superfluid fraction in3He-A

The superfluid fraction of the A phase was measured with a torsional oscillator at 0.6 Tesla in the wide pressure range of 0–29 bar and in the whole temperature region. After a Fermi liquid correction, a strong coupling gap enhancement factor was derived in the GL region. The value of 1.02 at 0 bar is consistent with a weak coupling limit, and increases with pressure up to the value of 1.30 at 29 bar. These results are consistent with those from the specific heat measurements at pressures above a policritical point(PCP)(22 bar) and those from the field dependence of the A-B transition temperature below the PCP.     

The paramagnon model and some properties of superfluid 3He

The paramagnon model for the BCS-type state of superfluid ³He is applied to calculate the following properties in the ABM and BW states: the pressure dependence of the initial slope of the normalized superfluid mass density vs. 1 – T/T _c; the pressure dependence of the normalized specific heat jump at T _c; and the temperature dependence of the superfluid mass density at P = 20.7 and 27.6 bar. We also calculate the temperature dependence of the normalized nuclear spin susceptibility in the BW state. We compare our results with the experimental data on the A and B phases of superfluid ³He.Supported in part by grant No. A4630 of the National Research Council of Canada.For a preliminary version of this work see Ref. 1.On leave from the Institute for Solid State Physics, University of Tokyo, Roppongi, Tokyo, Japan.     

3He in Aerogel – an Inhomogeneously Disordered Unconventional Superfluid

We have examined the superfluidity of ³ He in 98.2% porous silica aerogel with up to 34% ⁴ He at 21.6 bar. The mixture is phase-separated for ⁴ He fractions between 11% and 34%. The ⁴ He-rich, phase preferentially occupies the regions of highest silica density in the aerogel, thus modifying the distribution of the correlated disorder seen by superftuid ³ He. The ³ He T _c increases slightly with ⁴ He content while the superfluid fraction decreases rapidly. This behavior is inconsistent with that of ³ He in a homogeneously scattering medium and is analogous to that of a granular superconductor.     

Novel Oscillating Aerogel Experiments in Superfluid 3He at Ultralow Temperatures

We present novel experiments on a disk of 98% aerogel oscillating in superfluid ³ He at ultralow temperatures. The aerogel dik is attached to a goal post shaped vibrating wire resonator and immersed in liquid ³ He cooled by a Lancaster style nuclear cooling stage. At low pressures we see no evidence for superfluidity within the aerogel down to our base temperature of below <0.11T_c. At higher pressures we observe large temperature dependent frequency shifts, reminiscent of torsional oscillator experiments. We find the transition temperature at 5 bar to be around 600K. The response of the resonator is highly non linear when the helium in the aerogel is superfluid. The resonant frequency decreases strongly with increasing wire amplitude. This offers an exciting new technique for measuring the superfluid properties of ³ He in aerogel in the ultralow temperature regime.     

Ellipsometric Study of Superfluid Onset in Thin Liquid 4Helium Films

We have developed a modulated null ellipsometer capable of measuring single layers of adsorbed ⁴He films at 1.4 K. The small optical index of liquid helium, the extreme sensitivity to temperature gradients, and the requirement of sub-monolayer stability over many hours presents significant experimental challenges, which will be briefly discussed. The main goal of our experiments is to independently measure the superfluid and normal coverage in thin adsorbed ⁴He films. This is a particularly important issue for helium films on intermediate strength substrates such as rubidium and thin cesium, where previous measurements indicate that prewetting and the Kosterlitz-Thouless transition interact strongly, and the K-T transition appears to have nonuniversal features. Independent determination of the superfluid and normal fraction can be accomplished by using the ellipsometer in conjunction with a quartz crystal micro balance (QCM). QCM measurements rely on viscous coupling of the fluid layers, and therefore respond only to the normal component of a ⁴He film. In contrast, the ellipsometer is sensitive to the total thickness, independent of the state (superfluid or normal) of the film. By combining the QCM and ellipsometric measurements we can determine the total coverage, the normal fluid component and thus the superfluid fraction.     

Simultaneous Measurements of an Ultrasound and a Torsional Oscillator for 4He in a Nanoporous Glass

Previously, we carried out ultrasonic measurements for liquid ⁴He filled in a nanoporous glass (Gelsil), and observed an increase in the sound velocity due to decoupling of the superfluid component. At zero pressure, the superfluid transition temperature T _C is suppressed to 1.4 K from the bulk lambda point, 2.17 K. This behavior is the same as torsional oscillator measurements by Yamamoto et al. (Phys. Rev. Lett. 93:075302, 2004). However, the pressure dependence of T _C and the temperature dependence of the superfluid fraction are very different from the torsional oscillator measurements. In order to clarify the origin of the difference, we have developed a new technique of simultaneous measurement of an ultrasound and a torsional oscillator, and the system successfully works for a nanoporous glass. Here, we compare decoupling of the superfluid component for ⁴He films between an ultrasound and a torsional oscillator.     

Thermal expansion coefficient of 3He near 1 mK

A measurement of the thermal expansion coefficient of ³He at 0 bar from 0.6 to 3 mK is presented. At the superfluid transition the expansion coefficient changes by 1.1 × 10^\s-6 mK^\s-1. This change is consistent with predictions based on thermodynamic arguments and existing heat capacity data.This work was supported by NSF grant DMR 79-25098.     

Superfluid Density of 4He Films Adsorbed in Porous MCM-41 Ceramic

No Heading The superfluid transition of ⁴He films adsorbed in MCM-41 ceramic with 40-Â-diameter, micron-length cylindrical channels is studied with a torsion oscillator technique. For film coverages above 1.7 layers a finite-size Kosterlitz-Thouless transition becomes apparent in the data, with considerable broadening of the KT jump of the superfluid fraction. With decreasing helium coverage the extent of the broadening increases, indicating that the vortex core size is increasing. The data is consistent with the Machta-Guyer theory of the KT transition in a cylindrical channel, but with a coverage-dependent vortex core size. At low temperatures a linear decrease of the superfluid fraction with temperature is observed, indicating a zero-dimensional excitation.PACS numbers: 67.40.Db, 67.40.Rp, 67.40.Vs, 67.40.Hf