Longitudinal resonance and identification of the order parameter of the A-like phase of superfluid 3He in aerogel

Interpretation of the recent experiments of Dmitriev et al. on longitudinal resonance in the A-like phase based on specific properties of the “robust” order parameter is proposed. The text was submitted by the author in English.     

Spin nutation in the quasi-isotropic A-like superfluid phase of 3He

The order parameter of the quasi-isotropic A-like superfluid phase of ³He has been reduced to a simple form. The frequencies of the spatially homogeneous oscillations of the spin and the spin part of the order parameter of this phase have been obtained taking into account the anisotropy of its magnetic susceptibility. It has been shown that the anisotropy of susceptibility strongly affects the low-frequency oscillation mode, which is similar to the nutation of an asymmetric top. The possibility of observing this mode using the NMR method is discussed.     

Phenomenological phase diagram of superfluid 3He in a stretched aerogel

Highly anisotropic “nematically ordered” aerogel induces global uniaxial anisotropy in superfluid ³He. The anisotropy lowers symmetry of 3He in the aerogel from spherical to axial. As a result, instead of one transition temperature in a state with an orbital moment l = 1, there are two, corresponding to projections l _z = 0 and l _z = ±1. This splitting has a pronounced effect on the phase diagram of superfluid ³He and on the structures of the appearing phases. Possible phase diagrams obtained phenomenologically on the basis of Landau expansion of the thermodynamic potential in the vicinity of the transition temperature are presented here. The order parameters corresponding to each phase and their temperature dependences are found.     

Nonlinear NMR in a superfluid B phase of <Superscript>3</Superscript>He in aerogel

The properties of liquid ³He in a low-density aerogel preliminarily covered with a few monolayers of ⁴He were studied by pulsed and nonlinear CW NMR techniques. It was found that an NMR frequency shift from the Larmor value exhibits a sharp increase at a magnetization tilting angle exceeding 104°. Nonlinear CW NMR signals related to the formation of a macroscopic region featuring homogeneous precession of the magnetization (homogeneous precession domain) were observed. The experimental results confirm that the low-temperature superfluid ³He phase in the aerogel is analogous to the B-phase in bulk ³He and indicate that the spin supercurrents play an important role in the spin dynamics of superfluid ³He in aerogel.     

NMR diffusion of hyperpolarised 3He in aerogel: a systematic pressure study.

Diffusion of hyperpolarised 3He in a silica aerogel sample with 98% porosity was measured by NMR, and systematically studied as a function of pressure P in the range 20 mbar -1 bar. Spin-echo amplitudes, recorded with pulsed gradients in the usual CMPG sequence, follow a monoexponential decay, and the decay rate varies quadratically with the gradient intensity: thus the apparent diffusion coefficient of the gas D can be evaluated. Our results show a power-law (1/D proportional to P(0.55)), which could be consistent with a fairly broad mean free path distribution, implying some inhomogeneity in the aerogel structure. We have observed a spatial non-uniformity of D, and some deviation to the quadratic dependence of the decay rate with the gradient intensity, possibly related to sample structure inhomogeneity.     

High-frequency acoustics of 3He in aerogel

High-frequency ( approximately 15 MHz) acoustics were performed on 3He in 98% porous silica aerogel using an acoustic cavity technique. Measurements of the sound attenuation in the normal Fermi liquid and superfluid display behavior quite different from the bulk owing to strong elastic scattering of quasiparticles. The transition from first-to-zero sound is completely obscured with a quasiparticle mean-free path estimated to be in the range of 200-300 nm. No collective mode attenuation peak was observed at or below the superfluid transition.     

Heat capacity of 3He in aerogel

The heat capacity of pure 3He in low density aerogel is measured at 22.5 bars. The superfluid response is simultaneously monitored with a torsional oscillator. A slightly rounded heat capacity peak, 65 microK in width, is observed at the 3He-aerogel superfluid transition, T(ca). Subtracting the bulk 3He contribution, the heat capacity shows a Fermi-liquid form above T(ca). We can fit the heat capacity attributed to superfluid within the aerogel with a rounded BCS form accounting for 0.30 of the nonbulk fluid in the aerogel, or by assuming a substantial reduction in the superfluid order parameter. Both approaches are consistent with earlier superfluid density measurements.     

NMR on superfluid<Superscript>3</Superscript>He in aerogel

The transition to superfluidity of³He in high porosity (98.2%) acrogel has been observed by nuclear magnetic resonance techniques. The onset of the transition at all pressures above 13 bar is marked by a sharp increase in NMR frequency similar to that observed in bulk³He-A. This suggests that the aerogel/superfluid phase is highly homogeneous although both the transition temperature, T_c, and the amplitude of the order parameter are substantially suppressed. The acrogel strands are ≈ 50Å in diameter, much smaller than the superfluid coherence length. Consequently, we have attempted to interpret our observations as an impurity scattering problem. Based on our measurements of the magnetic field dependence of T_c it appears that both magnetic and potential scattering play important roles where the magnetic scattering can be associated with solid³He on the aerogel surface. This is determined by isotopic exchange with⁴He, a process which appears to stabilize a new superfluid state similar to the bulk B-phase.     

Quantum frustration in the "spin liquid" phase of two-dimensional 3He

We have measured the ultralow temperature and low field magnetic susceptibility of the 4/7 phase of two-dimensional 3He adsorbed on graphite preplated by one layer of 4He. The experiments are performed by progressively adding 4He to the system, thus suppressing in a controlled way the 3He atoms trapped in substrate heterogeneities. This procedure enables us to determine the intrinsic properties of this spin 1/2 model magnet in the zero field limit. The results show quantitatively that the system is strongly frustrated by multiple spin exchange interactions. A characteristic gapped spin liquid behavior is observed at ultralow temperature.     

Ultrasound attenuation of superfluid 3He in aerogel

We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B phase of superfluid 3He in 98% porosity aerogel down to the zero temperature limit for a wide range of pressures at zero magnetic field. The absolute attenuation was determined by direct transmission of sound pulses. Compared to the bulk fluid, our results revealed a drastically different behavior in attenuation, which is consistent with theoretical accounts with gapless excitations and a collision drag effect.     

Dissipation mechanisms near the superfluid 3He transition in aerogel

We have investigated the dissipation (Q-1) using the torsion pendulum technique for pure 3He and 3He-4He mixtures in silica aerogel near the 3He superfluid transition (T(c)) in aerogel. With pure 3He the Q-1 decreases at the onset of superfluidity. When phase separated 3He-4He mixtures are introduced into the aerogel, the Q-1 does not decrease as rapidly and eventually increases for the highest 4He content. We provide a model for the related attenuation of transverse sound alpha that takes into account elastic and inelastic scattering processes and exhibits a decrease in alpha at T(c).     

Metastability and superfluid fraction of the A-like and B phases of <Superscript>3</Superscript>He in aerogel in zero magnetic field

We report the low-frequency sound measurements of the metastable A-like (A*) phase of superfluid ³He confined within a 98% open aerogel matrix in zero magnetic field. The second soundlike (slow) mode provides an accurate determination of the superfluid fraction of (and the transition between) the A* and B phases. The A* and B phases exhibit stable coexistence in the presence of disorder, the ratio of their superfluid fractions (ρ _a ^A* /ρ _s ^B ) is much smaller than that of the bulk A and B phases, and argues that the A* and bulk A phases are distinct.     

Answer to the comment on “order parameter of A-like 3He phase in aerogel” by Mineev and Zhitomirsky

The reasons that are presented by Mineev and Zhitomirsky are based on the unjustified neglect of the contribution from fluctuations to the free energy of superfluid ³He in an aerogel.     

Contrasting mechanical anisotropies of the superfluid 3He phases in aerogel

There has been much recent interest in how impurity scattering may affect the phases of the p-wave superfluid 3He. Impurities may be added to the otherwise absolutely pure superfluid by immersing it in aerogel. Some predictions suggest that impurity scattering may destroy orientational order and force all of the superfluid phases to have an isotropic superfluid density. In contrast to this, we present experimental data showing that the response of the A-like phase to superfluid flow is highly anisotropic, revealing a texture that is easily modified by flow.     

Interfacial pinning in the superfluid 3He A-B transition in aerogel

Continuous-wave NMR studies of 3He in the presence of 99.3% porosity silica aerogel at 34.0 bars and in a magnetic field of 28.4 mT reveal a first-order phase transition between A-like and B-like superfluid phases on both warming and cooling. NMR spectra show that the phases on warming are the same as the phases on cooling, and the interface between them is found to be strongly pinned, even close to T(c,aero). The observed behavior is consistent with spatial variation of pinning strengths within the aerogel.     

He superfluidity in the presence of aerogel

Aerogels introduce disorder into the p-wave-paired superfluid ³He and suppress T_c. Quantifiable (by small angle X-ray scattering) differences in the long-range structure of two identical density aerogels are primarily responsible for their different transition temperatures. We also demonstrate that alteration of the short-range correlations by the addition of ⁴He does not strongly affect T_c. Acoustic measurements of the fast and slow modes of ³He in aerogel are described. These can be used to explore the superfluid component. We also outline future prospects.