Spin Relaxation in 3He-A1 Measured by Magnetic Fountain Pressure

No Heading Measurements of spin relaxation in superfluid ³He-A₁ phase as inferred from the decay of magnetic fountain pressure are reported in magnetic fields up to 8 testa and in pressure between 1 and 29 bars. Unlike in the previous experiment¹, the magnetic fountain pressure detector is placed in an apparatus containing A₁ phase liquid and there is no interface with any other phases of ³He. An abrupt large change in relaxation time observed in the previous experiment is now absent near the middle of A₁ phase. This observation supports the idea that the origin of the abrupt change in relaxation time is the presence of A₁/A₂ interface.PACS numbers: 67.57.–z, 67.65.+z, 72.25.–b     

Packed Powder as Superleak for Spin Pump Experiments in Superfluid 3He A1

Experimental exploration of highly spin-polarized states of liquid ³He by applying external magnetic field is limited by the availability of static magnetic field. In the “ferromagnetic” superfluid A₁ phase of liquid ³He there is an alternate method for boosting spin-polarization by the process of spin pumping without requiring such high magnetic field. The spin pumping in the A₁ phase takes advantage of a superleak (SL) acting simultaneously as a filter for both entropy and spin. The spin pump technique that uses the SL-spin filter and a mechanical actuator enables us to directly boost polarization of ³He. The amount of enhancement of spin polarization has been limited so far. We are now developing a new type of SL filter made of packed aluminum oxide powder (referred as PAP-SL), in order to achieve greater enhancement of spin polarization. Several kinds of the PAP-SL filter were constructed by pressing aluminum oxide powders into a cylinder holder. The packed structures were carefully characterized by a flow-rate-measurement, X-ray tomography, and mercury intrusion porosimetry. The preliminary result shows that the PAP-SL works as SL filter for the superfluid ³He.     

Recent Spin Pump Experiments on Superfluid 3He–A1

The superfluid ³He A₁ phase, containing a spin-polarized condensate allows us to explore the dynamics of superfluid spin current. In the mechano-spin effect (MSE), a mechanically applied pressure gradient and a superleak-spin filter enable one to directly boost spin polarization of ³He in a small chamber. We are developing new apparatus for achieving greater enhancement of spin density. A development of a new-type ³He-hydraulic actuator has been already reported. We present here the construction of new-type of superleak-spin-filter made of packed powder aluminum oxide (referred as PAP-SL). The PAP-SL is popular in the study of superfluid ⁴He, but has not been established for that of the superfluid ³He. The attempt to construct the PAP-SL for the spin pump experiment was made by using aluminum oxide powder with nominal 1 μm powder diameter and with packing fraction of 40 %. Before executing the experiment, the nuclear demagnetization cryostat of ISSP, Univ. Tokyo which has been used for this experimental activity, was heavily damaged by the 2011 Great East Japan (Higashi Nihon) Earthquake. The repair work and earthquake damage protection strengthening has just been accomplished.     

Spin relaxation phenomena in the 3He-A1 phase. Effects of magnetic field profile,spin counterflow,and 4He coverage

We report observations on the effects of the magnetic field profile and surface coverage by ⁴He on the magnetically driven superflows in the ³He-A₁ phase. When the gradient magnetic field profile is changed: (1) an unexpected reversal in the direction of superflow is observed, and (2) the relaxation time of the induced pressure increases in the warmer region of the A₁, phase but remains constant in the colder region. When the surfaces in the apparatus are covered with ⁴He: (1) the induced pressure amplitude decreases and the relaxation time increases and saturates at about twice that of pure ³He in the warmer side of the phase, and (2) the relaxation time is independent of the ⁴He coverage in the colder side. We give qualitative interpretation of the observed effects in terms of spin density relaxations; in the warmer side of the phase the spin density relaxes via processes in both bulk liquid and surface boundary and in the colder side the spin relaxation is dominated by connective spin counterflows in the A₂/A phase liquid in the fringing field of the static magnetic field.     

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.     

Superfluid density of3He measured by fourth sound

Superfluid density of³He has been measured using fourth sound in two superleaks: “confined,” packed powder and “open,” parallel channels. The superleak pore size has little effect on the superfluid density near the melting pressure, but it has surprisingly large effects at lower pressures. The open, parallel channel superleak results show an unexpected pressure dependence of “strong coupling” effects and an unexpectedly small superfluid density change at the B→A transition.     

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.     

Collisionless spin waves in normal and superfluid3He

Standing spin-wave modes in liquid³He have been studied by cw NMR at Larmor frequencies of 1, 2, and 4 MHz and pressures of 0, 6.3, and 12.3 bar. The spin waves, which produce peaks in the NMR line, are visible at temperatures below 5 mK at zero pressure. With the assumption of a slightly simplified sample shape and no transverse spin relaxation at the walls, the theory of Leggett fits the spin-wave frequencies in the normal liquid very well, giving a value of the Fermi liquid parameterF ₁ ^a =–0.6±0.2 at zero pressure. The width of some of the peaks is larger than expected from other determinations of the quasiparticle diffusion time _D . This could be due to wall relaxation or to deviations from the assumed sample geometry. In the superfluid A₁ and A phases, where the data cannot be fitted to existing theories, the spin-wave modes are shifted in frequency and suffer additional damping as the temperature is decreased. At still lower temperatures in the B phase an inversion of the spin-wave spectrum from one side of the NMR line to the other is observed, agreeing quantitatively with the predictions of the 1975 theory of Combescot.     

An oscillating superleak sound transducer

A resonator has been constructed in which a rigid superleak, fixed at one point across an annular cavity filled with liquid ⁴He, behaves as a differential filter for superfluid flow. The boundary conditions which obtain at the superleak determine the motion of the total fluid in the annulus and, by its reaction force on the superleak, the motion of the resonator as a whole. The condition for resonance motion of the resonator when driven (externally) by a periodic torque has given information about the temperature dependence of the superfluid density in the superleak which, in these experiments, was porous vycor glass.     

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.     

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.     

Negative Ion Mobility in Superfluid 3He Under High Magnetic Field

The negative ion mobility has been measured in superfluid ³He at pressures above 20 bar under high magnetic field up to 14 Tesla. It does not depend on the temperature in the normal phase, followed by a rapid increase below the superfluid transition in both A ₁ and A ₂ phase. The isothermal mobility is found to be independent of the magnetic field in the normal and A ₂ phase, while it decreases with increasing magnetic field in the A ₁ phase. This field dependence is explained by taking account of the field dependence of the transition temperature (T _{A 1}) between the normal and the A ₁ phase. Therefore the scattering cross section between, the negative ion and the ³He quasiparticles has no magnetic field dependence both in the superfluid and the normal phase.     

Spin-Entropy Wave Propagation in 3He A1 in Magnetic Fields up to 12 Tesla

The propagation of spin-entropy wave has been studied in ³ He A ₁ in magnetic fields up to 12 tesla and at a pressure of 22.9 bar. The superfluid fraction at T _c2 extracted from the propagation velocity increases linearly with magnetic field and reduced temperature. The anomalous attenuation previously found near T _c2 in lower magnetic fields was also observed in the present maximum field. The pore size in the oscillating superleak transducer does not affect the anomalous attenuation. Outside the anomalous attenuation region, the dissipation coefficient is found to vary linearly with frequency. This frequency dependence is contrary to that of dissipations owing to viscous losses at walls and to bulk losses.     

Superfluid 3He in Presence of Spin-Polarized Scattering Centers

The influence of spin-exchange scattering centers on triplet Cooper pairing is considered by exploring the behavior of superfluid ³He in high porosity aerogel, containing ³He atoms localized on the surface of silica strands. The homogeneously distributed isotropic scattering system of spin-polarized impurity centers is adopted as a simple model to investigate the contribution of the spin-exchange scattering channel for quasiparticles to the formation of non-unitary superfluid A₁-phase in the aerogel environment. It is demonstrated that an interference between the potential and exchange parts of quasiparticle scattering from spin-polarized impurity centers can change considerably the temperature width and the spin structure of the A₁-phase in aerogel. PACS numbers: 05.70 Ln, 05.70 Jk, 64.     

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.     

Study of Bulk Longitudinal Spin Relaxation in 3He-4He Liquid Mixtures

Longitudinal spin relaxation has been investigated in spin polarised liquid ³ He- ⁴ He mixtures in cesium-coated glass cells. The contribution of wall relaxation is found to be either negligible or easy to separate, and bulk relaxation times can be derived from systematic studies. We report on relaxation measurements at saturated vapour pressure, for temperatures ranging from 1.1 to 3K. ³ He densities vary from 0.07 to 11 mmol.cm^–3 ( ³ He concentrations between x ₃ 0.3 and 34%), so that both normal and superfluid ³ He- ⁴ He solutions are studied. At fixed temperature, the longitudinal relaxation time is inversely proportional to the ³ He number density over the whole range of investigated concentrations. In contrast, it is almost independent of temperature (changes do not exceed 10%). Comparison with published data and expected behaviours is discussed.     

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.     

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.     

Transverse Acoustic Impedance Measurements for Surface States of Superfluid 3He A1 and A2 Phases

We measured the complex transverse acoustic impedance in both superfluid ³He A₁ and A₂ phases. This impedance is sensitive to surface states. In our preliminary results, the temperature dependence of the impedance in the A₁ phase is similar to that in A phase, and the imaginary part shows an anomaly in the A₂ phase. These anomalies occurred at the temperature defined as T _k , which is lower as the frequency gets higher. The similar frequency dependence of T _k in each phase suggests that the anomaly is attributed to the same origin. The frequency dependence of the T _k /T _c indicates that the shape of the surface density of each spin pair state did not greatly change in the present experimental temperature range.     

4He in Nano-porous Media: Superfluidity and Quantum Phase Transition

This paper reviews recent findings of novel phenomena in ⁴He confined to a nano-porous glass. We examined pressure–temperature (P-T) phase diagram of ⁴He confined in a porous Gelsil glass that had nanopores 2.5 nm in diameter, by torsional oscillator and pressure studies. The obtained phase diagram is fairly unprecedented the superfluid transition temperature approaches zero at 3.4 MPa, and a novel nonsuperfluid phase exists between the superfluid and solid phase. These observations indicate that the confined ⁴He undergoes a superfluid-nonsuperfluid-solid quantum phase transition at zero temperature. We propose that the nonsuperfluid phase may be a localized Bose-condensed state in which global phase coherence is destroyed by a strong correlation between the ⁴He atoms or by a random potential. ⁴He in nanospace is an excellent model system for studying a strongly correlated Bose liquid and solid in a confinement potential.