A-like Phase Research Articles

Superfluid phases ofHe3in nanoscale channels

Confinement of superfluid $^3$He on length scales comparable to the radial size of the p-wave Cooper pairs can greatly alter the phase diagram by stabilizing broken symmetry phases not observed in bulk $^3$He. We consider superfluid $^3$He confined within long cylindrical channels of radius $100\mbox{ nm}$, and report new theoretical predictions for the equilibrium superfluid phases under strong confinement. The results are based on the strong-coupling formulation of Ginzburg-Landau theory with precise numerical minimization of the free energy functional to identify the equilibrium phases and their regions of stability. We introduce an extension of the standard GL strong-coupling theory that accurately accounts for the phase diagram at high pressures, including the tri-crital point and $T_{AB}(p)$ line defining the region of stability for the bulk A-phase. We also introduce tuneable boundary conditions that allow us to explore boundary scattering ranging from maximal to minimal pairbreaking, and report results for the phase diagram as a function of pressure, temperature, and boundary conditions. Four stable phases are found: a polar phase stable in the vicinity of $T_c$, a strongly anisotropic, cylindrical analog of the bulk B phase stable at sufficiently low temperatures, and two chiral A-like phases with distinctly different orbital symmetry, one of which spontaneously breaks rotation symmetry about the axis of the cylindrical channel. The relative stability of these phases depends sensitively on pressure and the degree of pairbreaking by boundary scattering. The broken symmetries exhibited by these phases give rise to distinct signatures in transverse NMR resonance spectroscopy. We present theoretical results for the transverse NMR frequency shifts as functions of temperature, the r.f. pulse tipping angle and the static NMR field orientation.

Designing supramolecular liquid-crystalline hybrids from pyrenyl-containing dendrimers and arene ruthenium metallacycles.

The association of the arene ruthenium metallacycle [Ru4(p-cymene)4(bpe)2(donq)2][DOS]4 (bpe = 1,2-bis(4-pyridyl)ethylene, donq = 5,8-dioxydo-1,4-naphtoquinonato, DOS = dodecyl sulfate) with pyrenyl-functionalized poly(arylester) dendrimers bearing cyanobiphenyl end-groups is reported. The supramolecular dendritic systems display mesomorphic properties as revealed by polarized optical microscopy, differential scanning calorimetry and small-angle X-ray scattering measurements. The multicomponent nature of the dendrimers and of the corresponding host-guest supramolecules (i.e., end-group mesogens, dendritic core, pyrene unit, aliphatic spacers, and metallacycle) leads to the formation of highly segregated mesophases with a complex multilayered structure due to the tendency of the various constitutive building-blocks to separate in different organized zones. The pyrenyl dendrimers exhibit a multilayered smectic A-like phase, thereafter referred to as LamSmA phase to emphasize this unaccustomed morphology. As for the corresponding Ru4-metallacycle adducts, they self-organize into a multicontinuous thermotropic cubic phase with the Im3̅m space group symmetry. This represents a unique example of liquid-crystalline behavior observed for such large and complex supramolecular host-guest assemblies. Models of their supramolecular organizations within both mesophases are proposed.

Some comments on superfluid 3He placed in globally deformed aerogel

New experimental results focused on the behavior of the superfluid A-like phase placed in globally deformed aerogel environment are considered. We compare experimental data collected by using optically attested axially stretched silica aerogel, on the one hand, and “nematically ordered” aerogel consisting of nearly parallel Al2O3 · H2O polymer strands, on the other. In the case of axially stretched silica aerogel the point of view was adopted according to which the orbital anisotropy axis l is long-ranged. The experiments were carried out by pulsed NMR techniques in keeping the direction of an externally applied magnetic field normal to aerogel stretching axis. We have generalized the dipole-locked configuration for arbitrary angle of inclination of the magnetic field with respect to aerogel stretching axis. The experimental data collected in using “nematically ordered” aerogel cannot be reconciled with above-mentioned results.

NMR properties of 3He-A in biaxially anisotropic aerogel

Theoretical model of G.E. Volovik for A-like phase of 3He in aerogel suggests formation of Larkin-Imry-Ma state of Anderson-Brinkmann-Morel order parameter. Most of results of NMR studies of A-like phase are in a good agreement with this model in assumption of uniaxial anisotropy, except for some of experiments in weakly anisotropic aerogel samples. We demonstrate that these results can be described in frames of the same model in assumption of biaxial anisotropy. Parameters of anisotropy in these experiments can be determined from the NMR data.

Nuclear Spin Relaxation in Glass States of 3He-A in Stretched Aerogel

We present results of pulse NMR investigations of superfluid A-like phase of 3He in stretched aerogel. In this case we have anisotropic orbital glass (OG) with two possible types of ordering in spin space—ordered spin nematic (OG-SN) or disordered spin glass (OG-SG) states. It was found that longitudinal relaxation of magnetization is non-exponential in both states and depends on temperature and on inhomogeneity of external steady magnetic field. At the same conditions the relaxation in OG-SG state is more rapid than in OG-SN state. For transverse orientation of the magnetic field relative to anisotropy axis the duration of free induction decay signal was longer than in normal phase. It may be explained by formation of coherently precessing spin state.

Vortex core transitions in superfluidH3ein globally anisotropic aerogels

Core structures of a single vortex in A-like and B-like phases of superfluid $^{3}\text{H}\text{e}$ in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although any uniaxial deformation leads to a wider A-like phase with the axial pairing in the pressure-temperature phase diagram, the vortex core states in the two phases in aerogel depend highly on the type of deformation. In a compressed aerogel, the first-order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in the B-like phase while no strange vortex core is expected in the corresponding A-like phase. By contrast, in a stretched aerogel, the VCT in the B-like phase is lost while another VCT is expected to occur between a nonunitary core and a polar one in the A-like phase. Experimental search for these results is hoped to understand correlation between superfluid $^{3}\text{H}\text{e}$ and aerogel structure.

NMR in Superfluid A-Like Phase of 3He Confined in Globally Deformed Aerogel in Tilted Magnetic Field

NMR spectra in superfluid A-like phases confined in axially deformed aerogel in presence of a magnetic field inclined with respect to deformation axis is considered. The characteristic features of dipole frequency shift in axially compressed and axially stretched cases are compared. In particular, it is shown that in axially stretched aerogel environment the stability region of coherently spin precessing mode is rather narrow due to the U(1)LIM effect.

Orbital glass and spin glass states of 3He-A in aerogel

Glass states of superfluid A-like phase of 3He in aerogel induced by random orientations of aerogel strands are investigated theoretically and experimentally. In anisotropic aerogel with stretching deformation two glass phases are observed. Both phases represent the anisotropic glass of the orbital ferromagnetic vector l -- the orbital glass (OG). The phases differ by the spin structure: the spin nematic vector d can be either in the ordered spin nematic (SN) state or in the disordered spin-glass (SG) state. The first phase (OG-SN) is formed under conventional cooling from normal 3He. The second phase (OG-SG) is metastable, being obtained by cooling through the superfluid transition temperature, when large enough resonant continuous radio-frequency excitation are applied. NMR signature of different phases allows us to measure the parameter of the global anisotropy of the orbital glass induced by deformation.

Ultrasound attenuation and aP−B−Tphase diagram of superfluidH3ein 98% aerogel

Longitudinal sound attenuation measurements in superfluid 3He in 98% aerogel were conducted at pressures between 14 and 33 bar and in magnetic fields up to 4.44 kG. The temperature dependence of the ultrasound attenuation in the A-like phase was determined for the entire superfluid region exploiting the field induced meta-stable A-like phase at the highest field. In the lower field, the A-B transition in aerogel was identified by a smooth jump in attenuation on both cooling and warming. Based on the transitions observed on warming, a phase diagram as a function of pressure (P), temperature (T) and magnetic field (B) is constructed. We find that the A-B phase boundary in aerogel recedes in a drastically different manner than in bulk in response to an increasing magnetic field. The implications of the observed phase diagram are discussed.

Spin Fluctuations in A-like Superfluid Phase of 3He in Aerogel

The frequency spectrum of the spin fluctuations δS(t) superimposed on the coherently precessing spin modes in the A-like superfluid phase in aerogel is analysed. It is shown that the low amplitude spin fluctuations could be most easily observed in the case of an uni-axially deformed aerogel. It is demonstrated, in particular, that for axially stretched (radially squeezed) aerogel described by the U(1)LIM model the fourth order harmonic in δSz(t) is erased, in contrast with what is expected for the long range Leggett orbital configuration in the 3He-A (ABM state).

Magnetic Field Dependence of the A-like to B-like Transition of Superfluid 3He in Aerogel

Longitudinal ultrasound attenuation of superfluid 3He in 98% aerogel has been measured at 33 bar and 6.22 MHz in the presence of magnetic fields up to 4.44 kG. The A-like to B-like (A-B like) phase transition in aerogel was identified by a rounded jump in attenuation while sweeping the temperature at a fixed magnetic field perpendicular to the direction of sound propagation. The suppression of the B-like phase was monitored as the magnetic field increased until the A-like phase region extended below our lowest attainable temperature (0.2 mK) at the highest field. In addition, the attenuation in the metastable A-like phase that appears when cooling in zero magnetic field was almost identical to the values observed in the A-like phase in high magnetic field.

Superfluid 3He Confined to a Single 0.6 Micron Slab Stability and Properties of the A-Like Phase Near the Weak Coupling Limit

We present the first study of the phase diagram of a thick film of superfluid 3He confined within a nanofabricated slab geometry. This cryogenic microfluidic chamber provides a well-defined environment for the superfluid, in which both the regular geometry and surface roughness may be fully characterised. The chamber is designed with a slab thickness d=0.6 μm and 3 mm thick walls to allow pressure tuning of the effective confinement between 0 and 5.5 bar. Over this range the zero temperature superfluid coherence length, ξ0, decreases by approximately a factor of two from 77 to 40 nm. Samples have so far been cooled to 350 μK. We use nuclear magnetic resonance (NMR) to ‘finger-print’ the superfluid order parameter, with the static field applied perpendicular to the slab. To enable us to resolve high quality NMR signals from the tiny amount of superfluid 3He in the slab, we have developed a spectrometer using a two stage SQUID amplifier with unprecedented sensitivity. Simple NMR zeugmatography allows the slab signal to be unambiguously distinguished from that of a small bulk liquid region near the fill line. The measured slab transition temperature, Tcslab, shows a suppression proportional to ξ02, as expected theoretically, but the absolute suppression is less than expected. Below Tcslab, an A-like phase is stable over a significant temperature range. A transition temperature, TAX, is measured on warming from a so far unidentified phase, occurring at lower temperatures, into the A-phase. At the pressures investigated (3 to 5.5 bar) the transition appears to occur at an approximately fixed value of the effective confinement d/ξ(TAX). In this geometry we predict that the A-phase will be stable to T=0 at zero pressure.

Transverse Acoustic Spectroscopy of Superfluid 3He in Compressed Aerogel

The unique nanoporous structure of aerogel provides a rare opportunity to study the role of anisotropic disorder on an anisotropic superfluid 3He. It has been proposed that uniaxial deformation of compliant aerogel would induce global anisotropy and a few compelling effects of global anisotropy on nature of the superfluid phases have been predicted. We measured high frequency shear acoustic impedance in superfluid 3He at 32 bar in a commercially available 98% porosity aerogel under uniaxial compression. At 5% compression, we found evidence of an A-like phase stabilized in a wider temperature width than the A-like phase in uncompressed aerogel.

Effect of a uniaxially deformed aerogel on the orientation of the order parameter of superfluid 3He

The effect of a uniaxially deformed aerogel on the orientation of the order parameter of 3He has been analyzed with the inclusion of correlations in the positions of the particles forming the aerogel. The minimum strain for the B phase in the uniaxially stretched aerogel that can lead to the orientation of the orbital part of the order parameter different from the bulk case has been estimated. The orientational effect has been estimated for the A-like phase in the uniaxially compressed aerogel has been estimated. It has been shown that the dependence of the orientational effect on correlations in the mutual locations of the aerogel particles is stronger than that of the superconducting transition temperature.

In globally isotropic aerogel, A-B phase separation of superfluid 3He in radial direction

It is observed that the A-like phase and the B-like phase, which are superfluid phases of 3He in high porosity silica aerogel as an impurity, coexist stably [1]. In this coexisting state, we showed by NMR experiments with radial gradient magnetic field that the A-like phase is in the edge part of a cylindrical aerogel and the B-like phase is in the central part of that [2]. It is proposed that the A-like phase might be more stabilized in globally anisotropic aerogel. According to this proportion, the aerogel might be globally anisotropic in edge part. In order to study whether the aerogel is globally anisotropic, we have performed optical birefringence experiment on aerogel samples in the same batch. This optical method is a useful tool to characterize a global anisotropy of aerogel [3]. Then, we found that aerogel samples are not globally anisotropic. Therefore, there are another mechanism for the A-B phase separation in radial direction.

Structure of vortices in superfluid 3He A-like phase in uniaxially stretched aerogel

Possible vortex-core transitions in A-like phase of superfluid 3He in uniaxially stretched aerogel are investigated. Since the global anisotropy in this system induces the polar pairing state in a narrow range close to the superfluid transition in addition to the A-like and B-like phases, the polar state may occur in the core of a vortex in the A-like phase identified with the ABM pairing state, like in the case of the bulk B phase where a core including the ABM state is realized at higher pressures. We examine the core structure of a single vortex under the boundary condition compatible with the Mermin-Ho vortex in the presence of the dipole interaction. Following Salomaa and Volovik's approach, we numerically solve the Ginzburg-Landau equation for an axially symmetric vortex and, by examining its stability against nonaxisymmetric perturbations, discuss possible vortex core states. It is found that a first order transition on core states may occur on warming from an axisymmetric vortex with a nonunitary core to a singular vortex with the polar core.

Superfluid phase stability of 3He in axially anisotropic aerogel

Measurements of superfluid 3He in 98% aerogel demonstrate the existence of a metastable A-like phase and a stable B-like phase. It has been suggested that the relative stability of these two phases is controlled by anisotropic quasiparticle scattering in the aerogel. Anisotropic scattering produced by axial compression of the aerogel has been predicted to stabilize the axial state of superfluid 3He. To explore this possiblity, we used transverse acoustic impedance to map out the phase diagram of superfluid 3He in a ∼ 98% porous silica aerogel subjected to 17% axial compression. We have previously shown that axial anisotropy in aerogel leads to optical birefringence and that optical cross-polarization studies can be used to characterize such anisotropy. Consequently, we have performed optical cross-polarization experiments to verify the presence and uniformity of the axial anisotropy in our aerogel sample. We find that uniform axial anisotropy introduced by 17% compression does not stabilize the A-like phase. We also find an increase in the supercooling of the A-like phase at lower pressure, indicating a modification to B-like phase nucleation in globally anisotropic aerogels.

Ultrasound attenuation measurements in the A-like phase of superfluid 3He in aerogel

Liquid 3He impregnated in high porosity aerogel shows many interesting features: significant suppression of superfluid transition and substantial modification of the the A-like to B-like transition. Ultrasound has been found to be a sensitive tool to measure these changes. Recently, the ultrasound attenuation measurements done in the B-like phase provided strong evidence for gapless superfluidity in liquid 3He in aerogel. We conducted high frequency sound propagation measurements at 6.22 MHz in the A-like phase of superfluid 3He induced by magnetic fields up to 4.44 kG. The magnetic field is applied perpendicular to the direction of sound propagation to see the noticeable change in attenuation between the A-like and the B-like phases. We measured the sound attenuation in the A-like phase to be larger than in the B-like phase, and this observation enabled us to identify the A-like to B-like phase transition as a function of magnetic field and pressure.

Effects of magnetic impurity scattering on superfluid 3He in aerogel

We investigate impurity effects on superfluid 3He in aerogel whose surface is not coated with 4He, different from most experimental situations. In systems with no 4He coating, spins of solid 3He absorbed on the aerogel surface are active and interact with spins of quasiparticles relevant to superfluidity and, for this reason, such an aerogel is treated as magnetic scatterers. It is found that, in the ABM pairing state affected by magnetic scatterings, not only the l-vector but also the d-vector has no long-ranged orientational order, and that the strong-coupling correction due to impurity scatterings is less suppressed than that in the nonmagnetic case, implying an expansion of the A-like phase region.

On NMR Properties of Superfluid A-like Phase in Aerogel

The models proposed to describe experimentally observed NMR signature of an A-like superfluid phase in aerogel environment are considered. Some new routes to verify the ability of various approaches are proposed. The behavior of a “robust” phase in presence of a strong magnetic field is also considered.