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

The frequency spectrum of the spin fluctuations δ S(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 δ S _z (t) is erased, in contrast with what is expected for the long range Leggett orbital configuration in the ³He-A (ABM state).     

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 the 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. The spectrum of high-frequency spin fluctuations accompanying coherently precessing spin modes is constructed.     

Magnetic Susceptibility of the Balian–Werthamer Phase of 3He in Aerogel

The equilibrium superfluid phase of ³He impregnated into high-porosity (98%) silica aerogels appears to be a non-equal-spin-pairing state in zero field at all pressures, which is generally assumed to be the Balian–Werthamer (BW) phase modified by the depairing effects of the aerogel structure. The nuclear magnetic susceptibility played a key role in identifying the B-phase of pure ³He with the BW state. We report theoretical calculations of the nuclear magnetic susceptibility for the BW model of superfluid ³He in aerogel within the framework of the Fermi-liquid theory of superfluid ³He. Scattering of quasiparticles by the aerogel, in addition to Fermi-liquid exchange corrections, leads to substantial changes in the susceptibility of the BW phase. The increase in the magnetic susceptibility of ³He-aerogel compared to pure³He-B is related to the polarizability of the gapless excitations and the impurity-induced local field. The limited data that is available is in rough agreement with theoretical predictions. Future measurements could prove important for a more definitive identification of the ordered phase, as well as for refining the theoretical model for the effects of disorder and scattering on the properties of superfluid ³He.     

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, T _c ^slab , shows a suppression proportional to ξ ₀ ² , as expected theoretically, but the absolute suppression is less than expected. Below T _c ^slab , an A-like phase is stable over a significant temperature range. A transition temperature, T _AX , 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(T _AX ). In this geometry we predict that the A-phase will be stable to T=0 at zero pressure.     

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.     

Experiments on 3He–4He Mixtures in Aerogel

We describe experiments on ³ He- ⁴ He mixtures in 98% open aerogel grown by cold-deposition (T80mK) of ⁴ He followed by the deposition of ³ He or alternatively by cooling down a homogenous mixture. The two approaches led to different ⁴ He film morphologies. We will also describe the observation of migration of ⁴ He from or toward the cell below 100 mK. This migration can lead to the exclusion of ⁴ He (other than the localized surface layers) for ⁴ He concentrations between 4% and 11% in the cell.     

Simulations of Non-linear Spin Dynamics in Spin Polarized Dilute 3He–4He Mixtures

Studies of spin dynamics of highly polarized dilute mixtures of ³He in superfluid ⁴He have been performed by various researchers over the past three decades. One series of experiments performed at Cornell University in the early 1990’s revealed a novel long timescale excitation. We present the numerical solution of the non-linear Leggett spin dynamics equation in one spatial dimension subject to boundary conditions consistent with the Cornell experiments. Experimentally observed phenomena are composed of trains of bursts in the transverse magnetization lasting several seconds. The simulations capture the time evolution of the individual bursts localized in time. Preliminary results of two dimensional simulations are also presented.     

Acoustics of a “Dirty” Fermi Liquid: 3He in Aerogel

An acoustic cavity containing ³He in 98% porous silica aerogel was used to investigate the effects of impurity scattering in a Fermi liquid. The pressure and temperature dependence of the sound attenuation in the normal Fermi liquid was extracted from the cavity response. The attenuation of sound displays behavior very different from the bulk owing to strong elastic scattering of quasi-particles by the silica strands. Using a visco-elastic model of the Fermi liquid, we find a mean free path restricted to 340 nm. Information on the sound velocity is inferred from the pressure dependence of the oscillation period of the cavity response. The data can be accounted for by a Biot model of the ³He liquid in the porous aerogel.     

Polarization Induced Spin Wave Damping in Spin Polarized Liquid 3He–4He

We have measured the temperature and polarization dependence of Silin spin wave spectra in a saturated ³He–⁴He mixture with a concentration of 9.4% at a pressure of 8 bars. The mixture has been cooled and polarized by a Leiden dilution refrigerator to temperatures in the range 10–15 mK and polarizations as high as 9.2% corresponding to 3.4 times the equilibrium polarization of 2.7% in the external magnetic field of 11.36 T. The analysis takes into account the dipolar interactions and results in the relaxation time τ _⊥ and spin diffusion constant D _⊥ . We find that τ _⊥ and D _⊥ are proportional to where T is the temperature, is the polarization enhancement factor and T _a0 is the anisotropy temperature for the mixture at equilibrium in the external field. Our result T _a0=3.66±0.14 mK is 30% higher than the theoretical prediction for very dilute mixtures and is evidence for the existence of polarization induced relaxation of transverse spin currents.     

3He in Aerogel – an Inhomogeneously Disordered Unconventional Superfluid

We have examined the superfluidity of ³ He in 98.2% porous silica aerogel with up to 34% ⁴ He at 21.6 bar. The mixture is phase-separated for ⁴ He fractions between 11% and 34%. The ⁴ He-rich, phase preferentially occupies the regions of highest silica density in the aerogel, thus modifying the distribution of the correlated disorder seen by superftuid ³ He. The ³ He T _c increases slightly with ⁴ He content while the superfluid fraction decreases rapidly. This behavior is inconsistent with that of ³ He in a homogeneously scattering medium and is analogous to that of a granular superconductor.     

Dispersion-Induced Splitting of the Collective Mode Spectrum in Axial and Planar Phases of Superfluid 3He

The whole collective mode spectrum in axial and planar phases of superfluid ³He with dispersion corrections is calculated for the first time. In axial A-phase the degeneracy of clapping modes depends on the direction of the collective mode momentum k with respect to the vector l (mutual orbital moment of Cooper pairs), namely: the mode degeneracy remains the same as in case of zero momentum k for k‖l only. For any other directions there is a threefold splitting of these modes, which reaches maximum for k ⊥ l. In planar 2D-phase, which exists in the magnetic field (at H>H _C ) we find that for clapping modes the degeneracy depends on the direction of the collective mode momentum k with respect to the external magnetic field H, namely: the mode degeneracy remains the same as in case of zero momentum k for k‖H only. For any other directions different from this one (for example, for k ⊥ H) there is twofold splitting of these modes. The obtained results imply that new interesting features can be observed in ultrasound experiments in axial and planar phases: the change of the number of peaks in ultrasound absorption into clapping mode. One peak, observed for these modes by Ling et al. (J. Low Temp. Phys. 78:187, 1990), will split into two peaks in a planar phase and into three peaks in an axial phase under the change of ultrasound direction with respect to the external magnetic field H in a planar phase and with respect to the vector l in an axial phase. In planar phase, some Goldstone modes in the magnetic field become massive (quasi-Goldstone) and have a similar twofold splitting under the change of ultrasound direction with respect to the external magnetic field H. The obtained results as well will be useful under interpretation of the ultrasound experiments in axial and planar phases of superfluid ³He.     

3He Correlation Energy in the Random Phase Approximation: the One-Ripplon-Exchange Potential in Thin 3He–4He Superfluid Films

A new approach to the calculation of correlation energies in the random phase approximation (RPA) is introduced. The method is applied to the system of adsorbed ³ He in thin ⁴ He superfluid films. The ³ He component interacts by means of the exchange of virtual surface interactions (ripplons) in addition to the usual atom-atom interaction. We report on a calculation of the RPA contribution to the ³ He ground-state energy of a previously introduced model for this effective interaction called the one-ripplon-exchange potential (OREP). V_OREP is manifestly frequency dependent and complex. In this paper we study the differences in the RPA contribution to the ground-state energy between the fully complex and frequency dependent V_OREP and V_OREP in the real, static limit.     

Observation of Zero-Sound at Atomic Wave-Vectors in a Monolayer of Liquid 3He

The elementary excitations of a strongly interacting two-dimensional Fermi liquid have been investigated by inelastic neutron scattering in an experimental model system: a monolayer of liquid ³He adsorbed on graphite preplated by a monolayer of solid ⁴He. We observed for the first time the particle-hole excitations characterizing the Fermi liquid state of two-dimensional liquid ³He, and we were also able to identify the highly interesting zero-sound collective mode above a particle-hole band. Contrarily to bulk ³He, at low wave-vectors this mode lies very close to the particle-hole band. At intermediate wave-vectors, the collective mode enters the particle-hole band, where it is strongly broadened by Landau damping. At high wave-vectors, where the Landau theory is not applicable, the zero-sound collective mode reappears beyond the particle-hole band as a well defined excitation, with a dispersion relation quite similar to that of superfluid ⁴He. This spectacular effect is observed for the first time in a Fermi liquid (including plasmon excitations in electronic systems).     

Effect of Interfacial Roughness Configuration on the Exchange-Bias Field in NiO Based Spin Valves

Two series of NiO-Co-Cu-Co based spin valves with the same nominal structure were grown by the magneton sputtering technique with different deposition parameters. Texture, surface and interfacial microstructures and the magnetic properties have been investigated in detail. X-ray diffraction, grazing incident X-ray reflectivity and transverse X-ray diffuse scattering were combined to analyze the microstructure of the multilayers. The results show that the texture of the multilayers is not a prerequisite factor for an exchange-bias (EB) field in NiO/Co/Cu/Co spin valves. And the EB effect is also independent of the average roughness at the interfaces. Large correlation lengths and two dimensions of the roughness at the interface are more advantageous for the EB effect.     

Suppression of π/2−π Spin Echo in Solid 3He in High Fields

High demagnetizing field in solid ³ He leads to rich interesting phenomena such as multiple spin echoes. On the other hand, it has a severe influence on the appearance of the ordinary spin echo using /2– RF pulse sequence. We have observed spin echoes in solid ³ He in 7.4 Tesla, which appeared to decay on a much shorter time scale than T ₂ estimated from theories. This can be explained as follows. The angle made by the magnetization with the field after the -pulse differs a little from that before the pulse, because the -pulse employed in the experiment is inevitably not ideal. Since due to the demagnetizing field, the frequency of the precession motion depends on the angle between the magnetization and the field, the frequencies before and after the -pulse are different, which smeared out the spin echo. We have computed the damping time in various conditions, and found good agreement with experimental results.     

Effect of Boron Substitution for Bi on Superconductivity of the Bi-2212 Phase in the Bi-Sr-Ca-Cu-O System

Possibility of boron substitution for Bi and the substitution effect on superconductivity is investigated for the Bi-2212 phase of Bi-Sr-Ca-Cu-O. From X-ray diffraction study, it is found that samples in the (Bi_2?x B _x )Sr₂CaCu₂O _z system are mainly of the single 2212 phase in a composition range of 0.0≤x≤0.6, and both of the lattice parameters a and c change with increasing x up to 0.6. From measurements of the magnetic susceptibility and the electrical resistivity, the superconducting transition temperature is found to increase up to 0.6 with increasing x. These results are considered to show that boron is substitutable for Bi up to x=0.6 in the (Bi_2?x B _x )Sr₂CaCu₂O _z system and that the boron substitution causes the number of hole-carriers to decrease in this system.     

Phase Transitions of Superfluid 3He in 0.8-μm Slab Geometry

We have studied superfluid ³ He in 0.8 m slab geometry by cw-NMR method. The static magnetic field for NMR was 22 mT and was perpendicularly applied to the surface. At pressures from 5 bar to 27 bar, we observed the negative shifts of NMR frequencies below the transition temperatures. Moreover we observed the fast order phase transition with the supercooling phenomena at lower temperatures, but NMR frequencies did not show a jump as they do at the A-B transition in the bulk liquid. Although the phase at low temperatures seemed to be B-phase, NMR frequencies still had the negative shifts.     

Anisotropic second sound in superfluid 4He near T λ in the presence of a heat current

In the presence of a homogeneous heat current the isotropy of superfluid ⁴He is broken and the propagation of second-sound waves becomes anisotropic. We calculate the angular dependence of the velocity and damping of second sound near T within model F of Halperin, Hohenberg and Siggia to leading order in the renormalized couplings. The critical behavior is incorporated using results of the renormalization-group theory. Second-sound waves propagating parallel to the heat current become unstable if the heat current exceeds some critical value. The theory agrees with recent experiments.     

Superfluid State of 4He on Graphane and Graphene–Fluoride: Anisotropic Roton States

We explore the phase behavior of Helium films on two variants of graphene: graphane (graphene coated with H, denoted GH) and graphene–fluoride (GF). A semiempirical interaction with these substrates is used in T=0 K Path Integral Ground State and finite temperature Path Integral Monte Carlo simulations. We predict that ⁴He forms anisotropic fluid states at low coverage. This behavior differs qualitatively from that on graphite because of the different surface composition, symmetry and spacing of the adsorption sites. The ⁴He ground state on both substrates is thus a self-bound anisotropic superfluid with a superfluid fraction ρ _s /ρ lower than 1 due to the corrugation of the adsorption potential. In the case of GF such corrugation is so large that ρ _s /ρ=0.6 at T=0 K and the superfluid is essentially restricted to move in a multiconnected space, along the bonds of a honeycomb lattice. We predict a superfluid transition temperature T? 0.25 (1.1) K for ⁴He on GF (GH). We have studied the elementary excitation spectrum of ⁴He on GF at equilibrium density finding a phonon–maxon–roton dispersion relation that is strongly anisotropic in the roton region. We conclude that these new platforms for adsorption studies offer the possibility of studying novel superfluid phases of quantum condensed matter.