Transverse and longitudinal nuclear magnetic resonance in superfluid <Superscript>3</Superscript>He in anisotropic aerogel

It is found that the properties of nuclear magnetic resonance of both superfluid phases of ³He in an anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It is also shown that, by proper squeezing, it is possible to attain a sample with isotropic NMR properties.     

Orientation effect on superfluid <Superscript>3</Superscript>He in anisotropic aerogel

The orientation of the order parameter in the A-like and B-like phases of superfluid ³He immersed in uniaxially compressed aerogel is reported. With the use of NMR methods, it is found that the orbital momentum of the A-and B-like phases is oriented along the deformation. In the A-like phase, a relatively narrow NMR line with an anomalously large negative frequency shift is observed. The Leggett frequency in the A-like phase, which shows the same energy gap suppression as in the B-like phase, is measured. The text was submitted by the authors in English.     

Interaction of two magnetic resonance modes in the polar phase of superfluid <Superscript>3</Superscript>He

We report results of low frequency nuclear magnetic resonance (NMR) experiments in the superfluid polar phase of ³He, which is stabilized by a new type of “nematic” aerogel—nafen. We have found that an interaction between transverse and longitudinal NMR modes may essentially influence the spin dynamics. Theoretical formulas for NMR resonant frequencies are derived and applied for interpretation of the experimental results.     

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.     

Superfluid 3He in Squeezed Nematic Aerogel

We present results of nuclear magnetic resonance (NMR) experiments in superfluid ³He in two samples of nematic aerogel consisting of nearly parallel mullite strands. The samples were cut from the same piece of the aerogel, but one of them was squeezed by 30% in the direction transverse to the strands. In both samples, the superfluid transition of ³He occurred into the polar phase, where no qualitative difference between NMR properties of ³He in these samples was found. The difference, however, has appeared on further cooling, after the transition to the polar-distorted A phase (PdA phase) with the orbital part of the order parameter in the 2D Larkin–Imry–Ma (LIM) state. In the squeezed sample, the 2D LIM state is anisotropic, which results in changes in the NMR, which can be used as an additional marker of the PdA phase and have allowed us to measure the value of the anisotropy.

     

Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar <Superscript>3</Superscript>He

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid ³He, experimentally observed in uniaxial aerogel ³He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.     

Transverse and longitudinal nuclear magnetic resonance in superfluid 3He in anisotropic aerogel

It is found that the properties of nuclear magnetic resonance of both superfluid phases of ³He in an anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It is also shown that, by proper squeezing, it is possible to attain a sample with isotropic NMR properties. The text was submitted by the authors in English.     

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.     

Linear NMR in the Polar Phase of <Superscript>3</Superscript>He in Aerogel

³He is an example of the system with non-trivial Cooper paring. A few different superfluid phases are known in this system. Recently the new one, the polar phase, have been observed in ³He confined in nematically ordered aerogel. A number of various topological defects including half-quantum vortices can exist the polar phase. In this work, we present theoretical and numerical studies of linear nuclear magnetic resonance in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.     

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.     

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.     

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.     

Recent results on hyperpolarized<Superscript>3</Superscript>He−<Superscript>4</Superscript>He liquid mixtures

Laser optical pumping in low magnetic field provides very high nuclear polarizations in gaseous helium mixtures, and is used to prepare polarized liquid. Wall relaxation in glass cells is effiently reduced using cesium coatings, and bulk longitudinal relaxation times are measured. In highly magnetized samples, dipolar fields control the spin dynamics in anisotropic volumes and weak external magnetic field inhomogeneities. Long lived magnetostatic modes are observed by pulsed NMR. Detailed analysis of their frequency and damping gives information on magnetization density and spin diffusion coefficient in polarized mixtures. Experiments are performed above 0.2 K on mixtures with³He concentrations of order a few percents or larger. When phase separation occurs, the³He-rich phase retains a high polarization.     

Fermi points and the Nambu sum rule in the polar phase of <Superscript>3</Superscript>He

We discuss the polar phase of ³He, which is realized in the anisotropic aerogel. We consider it in the framework of the BCS model. In the absence of the spin–orbit interaction, this model predicts the appearance of the Fermi line. However, it is topologically unstable. We demonstrate that the spin–orbit interaction gives rise to the appearance of the two Fermi points instead of the Fermi line. In addition to the gapless Nambu–Goldstone bosons in this system the collective gapped bosonic states exist. Their gaps are calculated, and the corresponding Nambu sum rule is established.     

No robust phases in aerogel: <Superscript>3</Superscript>He-<Emphasis Type="Italic">A</Emphasis> with orientational disorder in the Ginzburg-Landau model (Comment on papers by I.A. Fomin on Robust phases)

In series of papers [2, 7], Fomin introduced and discussed the so-called robust phases in a system with frozen orientational disorder (with application to superfluid ³He in aerogel). We show that his consideration is based on the erroneous overestimation of the fluctuation energy, which comes from the interaction of the Goldstone modes with the frozen disorder. This interaction leads to the Imry-Ma effect, which destroys the orientational order but is unable to destroy the local structure of ³He-A. There is no ground for the robust phases.     

Linear theory of random textures of <Superscript>3</Superscript>He-A in an aerogel

The spatial variation of the orbital part of the order parameter of ³He-A in an aerogel has been represented as random walk of a unit vector l(r) over a sphere under the action of random anisotropy created by the system of strands of the aerogel. The statistical properties of the resulting random texture have been studied. For distances at which the variation of l is much smaller than its magnitude, the average square <δl²> of variation of l has been expressed in terms of the correlation function of the component of the random anisotropy tensor. Under simplifying assumptions on the structure of this correlation function, an analytical dependence of <δl²> on r has been obtained for isotropic and axially anisotropic aerogels. The average values of the squares of the projections of l on the axes of anisotropy for an anisotropic aerogel have been represented in terms of the parameters of the aerogel. The characteristic scale at which the long-range order is broken, as well as the magnitude of global anisotropy sufficient for the recovery of the long-range order, has been numerically estimated within a simple model. The values obtained have been compared to other estimates.     

Magnon BEC in superfluid <Superscript>3</Superscript>He-A

The new mode of magnetization precession in superfluid ³He-A in a squeezed aerogel has been recently reported. We consider this mode in terms of the Bose-Einstein condensation (BEC) of magnons. The difference between magnon BEC states in ³He-A and in ³He-B is discussed. The article is published in the original.     

Low-temperature instability of uniform spin precession in the <Emphasis Type="Italic">B</Emphasis> phase of pure <Superscript>3</Superscript>He and <Superscript>3</Superscript>He in an aerogel

The magnetic-field dependences of the threshold temperature of the low-temperature instability of uniform spin precession in pure ³He-B and ³He-B in an aerogel have been determined for the bulk mechanism. These dependences appear to be different. The theoretical dependence of the threshold temperature for the pure case has been compared with the experimental dependence. The threshold temperature of the instability for ³He in the aerogel has been estimated for typical experimental conditions.