3He In Aerogel Research Articles

Effect of critical fluctuations on the spin transport in liquid He3

The contribution of pair fluctuations to the spin current in liquid 3He in aerogel near the critical temperature of transition to the superfluid state is calculated.

NMR Shifts in 3He in Aerogel Induced by Demagnetizing Fields

Magnetic materials generate demagnetizing field that depends on geometry of the sample and results in a shift of magnetic resonance frequency. This phenomenon should occur in porous nanostructures as well, e.g., in globally anisotropic aerogels. Here we report results of nuclear magnetic resonance (NMR) experiments with liquid $^3$He confined in anisotropic aerogels with different types of anisotropy (nematic and planar aerogels). Strands of aerogels in pure $^3$He are covered by a few atomic layers of paramagnetic solid $^3$He which magnetization follows the Curie-Weiss law. We have found that in our samples the NMR shift in solid $^3$He is clearly seen at ultralow temperatures and depends on value and orientation of the magnetic field. The obtained results are well described by a model of a system of non-interacting paramagnetic cylinders. The shift is proportional to the magnetization of solid $^3$He and may complicate NMR experiments with superfluid $^3$He in aerogel.

Linear NMR in the Polar Phase of 3He in Aerogel

$^3$He 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 $^3$He 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 NMR in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.

Pairbreaking effect of correlated impurities in a superfluid Fermi liquid

The conventional theory of superconducting alloys does not take into account the discrete character of impurities. Experimental data for superfluid 3He in aerogel and for some high-Tc superconductors reveal a significant discrepancy between the observed temperatures, Tc, of their transitions in the superfluid or superconducting states and those predicted theoretically. Here a theoretical scheme is presented for finding corrections to the Tc originating from spatial correlations between impurities. Analysis is limited to the Ginzburg and Landau temperature region. The shift of Tc with respect to the pure material is represented as a series in concentration of the impurities, x. In the first order on x, the conventional mean-field result for lowering Tc is recovered. The contribution of correlations enters the second-order term. It is expressed via the structure factor of the ensemble of impurities. For superfluid 3He in a silica aerogel, the sign of the correction corresponds to an enhancement of the Tc, so that the resulting pair-breaking effect of impurities is weakened. When the correlation radius of the impurities, R, exceeds the coherence length of the superfluid, the contribution of correlations to the shift of Tc acquires a factor, and the weakening of the pair-breaking effect becomes appreciable. The presented scheme is applied to the superfluid 3He in aerogel.

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 aerogel from spherical to axial. As a result instead of one transition temperature in the state, characterized by the orbital moment l=1 there are two, corresponding to projections l_z=o and l_z=\pm 1. The splitting of transition has a pronounced effect on the phase diagram of superfluid 3He and on a structures of appearing phases. Possible phase diagrams, obtained phenomenologically on a basis of Landau expansion of thermodynamic potential in a vicinity of the transition temperature are presented here. The order parameters, corresponding to each phase and their temperature dependencies are found.

The superfluid glass phase of 3He-A

It is established theoretically that an ordered state with continuous symmetry is inherently unstable to arbitrarily small amounts of disorder [1, 2]. This principle is of central importance in a wide variety of condensed systems including superconducting vortices [3, 4], Ising spin models [5] and their dynamics [6], and liquid crystals in porous media [7, 8], where some degree of disorder is ubiquitous, although its experimental observation has been elusive. Based on these ideas it was predicted [9] that 3He in high porosity aerogel would become a superfluid glass. We report here our nuclear magnetic resonance measurements on 3He in aerogel demonstrating destruction of long range orientational order of the intrinsic superfluid orbital angular momentum, confirming the existence of a superfluid glass. In contrast, 3He-A generated by warming from superfluid 3He-B has perfect long-range orientational order providing a mechanism for switching off this effect.

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.

Superfluid transition in superfluid 3He in radially compressed aerogel

The Spin Supercurrent and Bose-Einstein condensation of magnons similar to an atomic BEC was observed in 1984 in superfluid 3He-B Recently we discovered 2 new types of BEC in superfluid 3He in deformed aerogel. The orbital part of the wave function orients along the deformation and changes the magnon-magnon interaction. We can do it for 3He-A by uniaxially compressing the aerogel along the magnetic field. The other BEC state was observed in 3He-B in aerogel stretched along the magnetic field. Both states show all properties of magnon BEC We have also observed a splitting of NMR lines near Tc, which seems to indicate the formation of a new phase of superfluid 3He in aerogel. The latter looks like an analog of the 3He-A1 phase with strongly enhanced magnetic field.

Drag Force on a High Porosity Aerogel in Liquid 3He

We discuss the drag force exerted on a high porosity aerogel in liquid 3He and its effect on sound propagation. The drag force is governed by distinct laws depending on the Knudsen number Kn, the ratio of the quasiparticle mean free path to a characteristic linear size of a body immersed in liquid. In the liquid 3He-aerogel system, the characteristic length scale is aerogel strand diameter and both of the Knudsen limit (Kn ≫ 1) and the hydrodynamic limit (Kn ≪ 1) can be achieved in the normal phase by varying temperature. We show that the crossover between the two limits can be found as a drastic change in the temperature dependence of sound attenuation in the normal phase of liquid 3He in aerogel.

Low temperature adsorption of 3He on silica aerogel surface and its influence on 3He spin kinetics

Significant influence of the aerogel surface heterogeneity on the processes of 3He nuclear magnetic relaxation at temperatures 1.5 − 4.2 K is discovered. This influence appears, for instance, in differences of the 3He T1 relaxation times for small portion of 3He, adsorbed at different temperatures. Binding energy data of 3He and distributions of this energy in two types of aerogel were obtained experimentally. Adsorbed 3He molecules with binding energies 60 – 250 K play supreme role in processes of nuclear magnetic relaxation of gaseous and liquid 3He in aerogel.

Magnetic Phase Transition in a Nanonetwork of SolidHe3in Aerogel

When immersed in liquid 3He, the nanometer strands of aerogel are coated with a thin layer of solid 3He, forming a network of irregular nanotubes. Owing to its high purity and weak interactions, this system is ideal for studying fundamental processes. We report the first experiments on solid 3He in aerogel at ultralow temperatures, cooled by direct adiabatic demagnetization. Simultaneous nuclear magnetic susceptibility and heat capacity measurements indicate a magnetic phase transition.

Theory of heat transport of normal liquid 3He in aerogel

The introduction of liquid 3He into a silica aerogel provides us with a model system in which to study the effects of disorder on the properties of a strongly correlated Fermi liquid. The transport of heat, mass and spin exhibits cross-over behavior from a high temperature regime, where inelastic scattering dominates, to a low temperature regime dominated by elastic scattering off the aerogel. We report exact and approximate solutions to the Boltzmann–Landau transport equation for the thermal conductivity of liquid 3He, including elastic scattering of quasi-particles by the aerogel and inelastic quasi-particle collisions. These results provide quantitative predictions on the transport properties of liquid 3He in aerogels over a wide range of pressures, temperatures and aerogel densities. In particular, we obtain a scaling function, F(T/T⋆), for the normalized thermal conductivity, , in terms of a reduced temperature, T/T⋆, where T⋆ is a cross-over temperature defined by the elastic and inelastic collision rates. Theoretical results are compared with the available experimental data for the thermal conductivity.

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.

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.

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.

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.

Pulse NMR of 3He in aerogel at temperature 1.5 K

Experimental data of 3He pulse NMR in contact with aerogel (95%) in a nuclear Larmor frequency range of 5 to 20 MHz at T=1.5 K are reported. For the first time spin kinetics of 3He (adsorbed, gaseous and liquid) has been studied systematically at temperatures higher than degeneracy temperature of this quantum liquid. It has been shown, that in all cases the nuclear spin-lattice relaxation time T1 is linearly proportional to the Larmor frequency, while the spin-spin relaxation time T2 is frequency independent. The magnetic relaxation times T1 and T2 are linearly proportional to the ratio of the magnetization of whole spin system to magnetization of the adsorbed layer of 3He.

Effect of correlated disorder on the temperature of unconventional cooper pairing: 3He in aerogel

Using liquid 3He in aerogel as an example, it is shown that correlations in positions of impurities affect the temperature $T_c$ of transition of Fermi liquid in an unconventional superfluid or superconductive state. The effect is significant if the correlation length for impurities is greater than the coherence length in the superfluid or superconductive state $\xi_0$. For 3He in aerogel the suppression of $T_c$ is expressed in terms of the structure factor of aerogel. With the account of the fractal structure of aerogel a simple expression is obtained for the decrease of $T_c$ from its clean value. This expression is in a satisfactory agreement with experimental data.

Scaling Results for Superfluid 3He in 98% Open Aerogel

We present experimental observations of the suppressed superfluid transition temperature, Tca, superfluid fraction, ρs/ρ and Leggett frequency of 3He-B in aerogel, ΩBa. We determine Tca from mass decoupling and the vanishing of the frequency shift away from the Larmor frequency in our different samples and different laboratories. We find that the suppressed transition temperature for 3He in aerogel occurs at a sample dependent, but approximately pressure independent, length, \(X=\xi_{0}(P)/\sqrt{1-T_{\mathit{ca}}/T_{c}}\) , where Tc and ξ0(P), are the transition temperature and the pressure dependent zero temperature coherence length for bulk 3He. Tca also occurs at a pressure independent value of the Leggett frequency of bulk 3He-B. Further, we find that when the superfluid fraction and square of the Leggett frequency are plotted against Tca−T (and not (Tca−T)/Tca), the results of each measurement nearly collapse on to a pressure independent but sample dependent plot, with no further scaling. When plotted on a log–log scale, both measurements exhibit power laws in the range 1.33–1.45.

Magnetic Distortion of the B-like Phase of Superfluid 3He Confined in Aerogel

We present measurements of the response of the B-like phase of superfluid 3He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid 3He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.