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).     

Semisuperfluidity of 3He in aerogel?

According to hydrodynamic, acoustic, and NMR studies the superfluid transition temperature of 3He in aerogel ( T(a)(c)) is significantly suppressed with respect to that of bulk 3He. We have found in the range of temperatures between T(c) and T(a)(c) a large and unexpected NMR satellite line attributable to the liquid inside the aerogel. We propose that this anomalous behavior of liquid 3He corresponds to a new type of superfluid ordering related to magnetic and possibly orbital coherence.     

A1 and A2 transitions in superfluid 3He in 98% porosity aerogel

Superfluid 3He in high porosity aerogel is the system in which the effects of static impurities on a p-wave superfluid can be investigated in a systematic manner. We performed shear acoustic impedance measurements on this system (98% porosity aerogel) in the presence of magnetic fields up to 15 T at the sample pressures of 28.4 and 33.5 bars. We observed the splitting of the superfluid transition into two transitions in high fields in both bulk and liquid in aerogel. The field dependence of the splitting in aerogel resembles that of the bulk superfluid 3He caused by the presence and growth of the A1 phase. Our results provide the first evidence of the A1 phase in superfluid (3)He/aerogel.     

Elastic stiffness of the nuclear-spin system in tetragonal U2D2 nuclear-ordered solid (3)He

We have measured temperature dependences of sound velocity for both longitudinal and transverse sound in nuclear-ordered U2D2 solid 3He with several crystal orientations along the melting curve. The sound velocity change was proportional to T4 for all sound modes and crystal orientations and was attributed to the nuclear-spin part of the internal energy. We extracted six-independent elastic stiffness of the nuclear-spin part and obtained Grüneisen constants of the spin wave velocity for four-independent strains. Grüneisen constants for compressional strain were larger than those for shear strain. Using the multiple-spin-exchange model, we explain the anisotropy of Grüneisen constants in tetragonal symmetry.     

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.     

Thermal conductivity of liquid 3He in aerogel: a gapless superfluid

We have measured the thermal conductivity of liquid 3He in 98% aerogel at ultralow temperatures. Aerogel introduces disorder on a scale comparable to the superfluid coherence length. At low pressures the liquid in the aerogel shows normal-state behavior with conductivity linear in temperature. At pressures above approximately 6 bars the onset of superfluidity suppresses the conductivity and the thermal conductivity again tends towards linear behavior in the very low temperature limit, providing strong evidence that here the liquid 3He in the aerogel is behaving as a gapless superfluid.     

Sound propagation in coexistent Bose and Fermi superfluids in aerogel

We report the first observation of longitudinal sound propagation in three dimensionally distributed Bose and Fermi superfluids in an acoustic investigation of phase separated 3He-4He mixtures confined to aerogel. At mK temperatures, this inhomogeneous system exhibits simultaneous 3He and 4He superfluidity leading to two "slow modes" along with the conventional sound mode. We also infer the superfluidity of isolated bubbles of pure 3He in a large 4He concentration sample.     

Dimensional crossover of quantum critical behavior in CeCoIn5

The nature of quantum criticality in CeCoIn5 is studied by low-temperature thermal expansion alpha(T). At the field-induced quantum critical point at H = 5 T a crossover scale T* approximately 0.3 K is observed, separating alpha(T)/T proportional, variant T(-1) from a weaker T(-1/2) divergence. We ascribe this change to a crossover in the dimensionality of the critical fluctuations which may be coupled to a change from unconventional to conventional quantum criticality. Disorder, whose effect on quantum criticality is studied in CeCoIn(5-x)Sn(x) (0 < or = x < or = 0.18), shifts T* towards higher temperatures.     

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.     

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.     

Phonons, rotons, and layer modes of liquid 4He in aerogel

We report the first observation of two-dimensional layer modes in both fully filled and partially filled aerogel. Using complementary high-energy resolution and high statistical precision neutron scattering instruments, and two different 87% porous aerogel samples, we show that the three-dimensional (3D) phonon-roton excitation energies and lifetimes of liquid 4He in aerogel are the same as in bulk 4He within current precision. The layer modes are the excitations that distinguish aerogel from the bulk rather than a difference in the 3D roton energy.     

Porosity dependence of sound propagation in liquid-<Superscript>4</Superscript>He-filled aerogel

Longitudinal sound-wave propagation has been studied in an aerogel-liquid ⁴He system for various porosities of aerogel. The superfluid transition was identified as the absorption peak, whose magnitude was suppressed by aerogel. The sound velocity was analyzed within a hydrodynamic theory in both normal and superfluid phases. The absorption peak due to phonon-roton interaction around 1 K was not observed even with the most porous aerogel. The low-temperature sound velocity and attenuation show that direct collisions of phonons with aerogel strands play an important role in the acoustic properties.     

Random textures of the order parameter of superfluid 3He-B in aerogel

A phenomenological scheme of the observed properties of superfluid ³He in aerogel is proposed in the spirit of the Ginzburg-Landau theory. The effect of the aerogel on the order parameter is described by the random tensor field η_jl(r). The tensor field exerts a considerable disorienting effect on the order parameter in the A phase of ³He, but virtually unaffects the orientation of the order parameter in the B phase in zero magnetic field. The change in the texture of the order parameter emerging in the B phase in aerogel in a magnetic field is considered. It is shown that the mean square of the angle between the magnetic field direction and the anisotropy axis of the B phase is proportional to the third power of the magnetic field strength. The fluctuations of the direction of the magnetic anisotropy axis of ³He-B are correlated over the familiar “healing length”, which is inversely proportional to the field strength and has a macroscopic scale.     

Modification of the 3He phase diagram by anisotropic disorder

Motivated by the recent prediction that uniaxially compressed aerogel can stabilize the anisotropic A phase over the isotropic B phase, we measure the pressure dependent superfluid fraction of (3)He entrained in 10% axially compressed, 98% porous aerogel. We observe that a broad region of the temperature-pressure phase diagram is occupied by the metastable A phase. The reappearance of the A phase on warming from the B phase, before superfluidity is extinguished at T(c), is in contrast to its absence in uncompressed aerogel. The phase diagram is modified from that of pure (3)He, with the disappearance of the polycritical point (PCP) and the appearance of a region of A phase extending below the PCP of bulk (3)He, even in zero applied magnetic field. The expected alignment of the A phase texture by compression is not observed.     

Second wind of the Dulong-Petit law at a quantum critical point

Renewed interest in ³He physics has been stimulated by experimental observation of non-Fermi-liquid behavior of dense ³He films at low temperatures. Abnormal behavior of the specific heat C(T) of two-dimensional liquid ³He is demonstrated in the occurrence of a T-independent term in C(T). To uncover the origin of this phenomenon, we have considered the group velocity of transverse zero sound propagating in a strongly correlated Fermi liquid. For the first time, it is shown that if two-dimensional liquid ³He is located in the vicinity of the quantum critical point associated with a divergent quasiparticle effective mass, the group velocity depends strongly on temperature and vanishes as T is lowered toward zero. The predicted vigorous dependence of the group velocity can be detected in experimental measurements on liquid ³He films. We have demonstrated that the contribution to the specific heat coming from the boson part of the free energy due to the transverse zero-sound mode follows the Dulong-Petit Law. In the case of two-dimensional liquid ³He, the specific heat becomes independent of temperature at some characteristic temperature of a few millikelvins.     

Splitting of the Superfluid Transition in Liquid 3He Induced by a Nematic Aerogel

JETP Letters - The effect of inhomogeneous perturbations created by a nematic aerogel in liquid 3He on the form of the order parameter arising at the transition to the superfluid state is studied....     

Sound-like Oscillations in the Polar Phase of Superfluid 3He in a Nematic Aerogel

JETP Letters - The acoustic spectrum of the polar phase of superfluid 3He in nematic aerogel has been studied. An equation determining the dispersion of sound oscillations of the system has been...     

Longitudinal NMR and spin states in the A-like phase of 3He in aerogel

It was found that two different spin states of the A-like phase can be obtained in an aerogel sample. In one of these states, we have observed the signal of the longitudinal NMR, while, in the other state, no trace of such a signal was found. The states also have different properties in transverse NMR experiments. A longitudinal NMR signal was also observed in the B-like phase of ³He in aerogel. The text was submitted by the authors in English.     

Phase diagram of superfluid 3He in 99.3% porosity aerogel

We report on continuous-wave NMR measurements of the energy gaps of the A-like and B-like superfluid phases of 3He at 28.4 mT confined to a 99.3% porosity silica aerogel. The gaps are suppressed by the presence of the aerogel in a temperature-independent manner, but the suppression is considerably stronger than expected from the suppression of T(c). We then use our measurements to calculate the free energy ratio between the A-like and B-like phases. The equilibrium AB transition temperature, derived from where this ratio reaches unity, is consistent with previous measurements of the initial displacement of the pinned AB interface on warming. On this basis, we present for the first time the equilibrium phase diagram of the A-like and B-like phases of superfluid 3He in aerogel.     

Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels

We show how the low-frequency dependence of the proton spin-lattice relaxation time T1(nu) of octylcyanobiphenyl liquid crystals confined in high-density silica gels evidences a long-range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(nu) proportional, variant nu(2/3), is interpreted within a relaxation model due to director fluctuations in nematic liquid crystals confined to mass fractal porous media. The model provides a relation T1(nu) proportional, variant nu(2-d/2), giving a reliable value of the structural fractal dimension d(f)=2.67 for all the host silica gels.