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.     

Acoustical Experiments on Superfluid 3He-4He Mixtures in Aerogel

This report discusses our results on the superfluidity of ³ He- ⁴ He mixtures in a 98% porosity silica aerogel. We have used low frequency sound to probe helium mixtures confined to aerogel, and have observed both the slow mode of superfluid ³ He in aerogel, which is manifested only below T_c, and an additional sound mode present only in the mixture. We attribute this novel sound mode to the slow-mode in the ⁴ He rich phase of the dilute ³ He- ⁴ He mixture. This mode exhibits positive frequency shifts below T_c in aerogel, while above T_c the mode is observed at a temperature independent frequency until close to T where it shifts to zero frequency.     

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     

Positive ion mobility in normal and superfluid 3He

The mobility of positive ions has been measured in the normal and superfluid phases of ³He at several pressures. Below 100 mK the normal phase mobility increases logarithmically with decreasing temperature down to the superfluid transition temperature T _c; it shows an anomalous jump near 100 mK. At low temperatures the drift velocity is nonlinear for electric fields exceeding 30 V/cm. In the superfluid the mobility, normalized to its value at T _c, is much less than for negative ions. We have also observed the anisotropic mobility in the A phase and the Landau critical velocity for pair-breaking in both superfluid phases.Work supported by the Academy of Finland.On leave of absence from Regensburg University, Regensburg, West Germany, supported by Deutsche Forschungsgemeinschaft.     

Possible Existence of Dense Superfluid 3He-4He Mixture in Aerogel

While studying superfluid ³He of 2.4 MPa in 97.5 %-porosity aerogel with NMR/MRI techniques, we find that the T _C is reduced when more than adequate amount of ⁴He, which covers the surface of silica strands, is introduced. For a sample, whose T _C is reduced to as low as 0.9 mK, we find that the spin diffusion coefficient in the normal phase is increased by a factor of 1.56 both in high temperature region, where ³He-³He scattering dominates, and in low temperature region, where ³He-aerogel scattering dominates. This enhancement is attributed to a modification of Landau parameter $F_{0}^{a}$ from ?0.757 to ?0.62, which is a change towards less ferromagnetic direction. The modification of microscopic quantity could be explained if small amount of ⁴He has homogeneously mixed into liquid ³He in the aerogel.     

A Preliminary Heat Capacity Measurement of 3He in Aerogel near its Superfluid Transition

We report simultaneous heat capacity and torsional oscillator measurement of ³ He in aerogel near the superfluid transition. The heat capacity has a peak at the temperature T_c where the torsional oscillator shows the onset of superfluid decoupling. The coincidence of these signatures suggests that ³ He in aerogel does undergo a true thermodynamic transition.     

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.     

Enhancement of Magnetization in Liquid 3He at Aerogel Interface

A novel feature of condensate state in liquid ³He is predicted theoretically, which consists of spin triplet s-wave Cooper pairs (Higashitani et al. in J. Low. Temp. Phys. 155:83–97, 2009). Such a spin triplet s-wave state will appear inside aerogel near the surface boundary contacting with superfluid ³He-B, and the enhancement of magnetization due to s-wave state is theoretically expected (Nagato et al. in J. Phys. Soc. Jpn. 78:123603, 2009; Higashitani et al. in Phys. Rev. B 85:024524, 2012). In order to detect this proximity effect, we made the interface in columnar glass tube which coated with 2.5 layer ⁴He, and set a saddle shape NMR coil very near the interface. At 7 bar, we found that superfluidity in liquid ³He inside aerogel never occurred, even at considerably low temperatures. At 24 bar below T/T _c =0.392, we observed no decrease of magnetization with decreasing temperatures. This phenomenon might be due to spin triplet s-wave Cooper pairs.     

NMR Characterization of 3He Nanoclusters Embedded in hcp 4He

The properties of ³He nanoclusters in phase-separated solid ³He-⁴He mixture were investigated using pulse NMR. Samples of pressure between 2.64 and 3.71 MPa and NMR frequencies, 62.5, 125, and 250 kHz were used. Magnetization was measured in the temperature range between 0.6 to 10 mK. The solid-like fraction was obtained from the relative magnitudes of magnetization and it showed a sharp increase with pressure around 2.94 MPa accompanying an abrupt change in Weiss temperature. For samples of pressure between 2.94 and 3.15 MPa, the magnetization could be separated into two components with different spin-spin relaxation time T ^* ₂'s. The short and long T ^* ₂ components showed ferromagnetic and antiferromagnetic tendencies, respectively. The long component showed an anomalous decrease of magnetization below 1.05 mK.     

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.     

Vibrating Wire Measurements in Superfluid 3He at the Melting Curve Down to 0.53 mK

Measurements of the vibrating wire spectrum have been carried out in superfluid ³ He along the melting curve down to 0.53mK. We have observed that at temperatures below 0.3 T_c the width of the mechanical resonance of the wire decreases exponentially with 1/T, indicating the ballistic regime of collisions with quasiparticles. The value of the superfluid energy gap was found to be (1.99±0.05)T_c, in good agreement with the values obtained from heat capacity measurements. The vibrating wire was thereby calibrated for further experiments at temperatures below 0.5mK, where the sensitivity of the melting curve thermometry becomes rather poor.     

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.     

Vibrating Wire Thermometry in Superfluid 3He

We report systematic measurements of the response of a Vibrating Wire Resonator (VWR) in normal and superfluid liquid ³He. Special attention has been paid to the hydrodynamic regime of the superfluid B-phase, where the response parameters of the VWR do not follow a simple law. We show that a simple interpolation between the region where first order slip-corrections can be applied and the ballistic regime is insufficient. Measuring an empirical effective viscosity, we propose a temperature calibration method which allows the use of VWRs as a secondary thermometer at intermediate and high pressures in the temperature range 0.2 T _c < T < 50 mK.     

The Equilibrium A-B Transition in Low Density Aerogels

No Heading We have measured in detail the NMR spectra of superfluid ³ He inside two different silica aerogels, one with a porosity of 99.3% and the other 98.6%. From these spectra, we are able to determine the equilibrium A-B transition temperatures in both aerogel samples as a function of hydrostatic pressure. We find that the slope of the reduced A-B transition temperature, 1- T_AB/T_c, vs. pressure is only about one third that seen for the bulk A-B transition, despite the fact the T_c for the two samples is suppressed very modestly, by only 4% and 8% at 34 bars. We argue from this that the presence of the aerogel stabilizes an equal-spin pairing which is district from that stable in the bulk.PACS numbers: 67.57 Pq, 67.57 Lm     

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.      

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.     

3He melting pressure thermometry

High-precision measurements of the³He melting pressure versus temperature have been made from 500 K to 25 mK using a⁶⁰Co nuclear orientation primary thermometer and a Pt NMR susceptibility secondary thermometer. Temperatures for the fixed points on the melting curve are: the superfluid A transition T_A = 2.505 mK, the A-B transition T_AB = 1.948 mK, and the solid ordering temperature t_n = 0.934 mK. These fixed points and a functional form for P(T) constitute a convenient temperature scale, based on a primary thermometer, usable to well below 1 mK.     

Melting Pressure Thermometry of the Saturated Helium Mixture at Millikelvin Temperatures

The melting pressure of a ³ He–⁴He mixture has a very simple quadratic temperature dependence below some tens of mK, determined by the entropy of the ³ He component in the liquid mixture. For undersaturated mixtures, the melting pressure also depends on the ³ He concentration x, which may vary in the course of the experiment as ⁴ He transfers between the liquid and the solid phases. On the other hand, if the mixture is saturated, the system is in a univariant state with a melting pressure that depends uniquely on temperature and, thus, offers a thermometric standard. However, the univariant state includes a pure liquid ³ He phase, which complicates the temperature dependence around its superfluid transition temperature T_c. In this paper, we analyze the melting pressure of the saturated mixture in simple terms and find an expression that is in good agreement with our experimental data, and is applicable across T_c down to very low temperatures. The obtained derivatives of the melting pressure with respect to the square of temperature are 0.92 Pa·mK⁻² above T_c and 1.52 Pa·mK⁻² in the zero-temperature limit. An erratum to this article can be found at     

The onset of superfluidity in4He films adsorbed in aerogel glass

We have completed a systematic study of the superfluid density of ⁴ He films adsorbed in 91% porosity aerogel glass. We have concentrated on the low-coverage regime (T_c<200 mK) in an attempt to address recent theoretical work on the onset of superfluidity in dirty boson systems. Our data are not in agreement with the predictions of a scaling theory of the onset transition developed by Fisher et al. ¹ We discuss the extent of this disagreement and the limitations of other models of the onset transition.