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Register a new userSpin diffusion in liquid $^3$He confined in planar aerogel
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We report the results of theoretical and experimental investigation of spin diffusion in the normal phase of liquid $^3$He confined in planar aerogel: a material consisting of nanostrands which are almost parallel to a specific plane and randomly oriented in this plane. Using spin echo technique we measure the spin diffusion coefficients in the directions perpendicular and parallel to the plane. We see good agreement between the experiment and the theory.
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Recent advances in experiment and theory suggest that superfluid $^3$He under planar confinement may form a pair-density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wavevectors, of possibly square or hexagonal symmetry. In this work, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landaus theory of the liquid-solid transition. A soft-mode instability at finite wavevector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wavevectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.
Andreev reflection of quasiparticle excitations from quantized line vortices is reviewed in the isotropic B phase of superfluid $^3$He in the temperature regime of ballistic quasiparticle transport at $T leq 0.20,T_mathrm{c}$. The reflection from an array of rectilinear vortices in solid-body rotation is measured with a quasiparticle beam illuminating the array mainly in the orientation along the rotation axis. The result is in agreement with the calculated Andreev reflection. The Andreev signal is also used to analyze the spin down of the superfluid component after a sudden impulsive stop of rotation from an equilibrium vortex state. In a measuring setup where the rotating cylinder has a rough bottom surface, annihilation of the vortices proceeds via a leading rapid turbulent burst followed by a trailing slow laminar decay from which the mutual friction dissipation can be determined. In contrast to currently accepted theory, mutual friction is found to have a finite value in the zero temperature limit: $alpha (T rightarrow 0) = (5 pm 0.5) cdot 10^{-4}$.
The discovery of superfluid $^{3}$He in high porosity silica aerogels, and subsequent experimental and theoretical work, have led to a better general understanding of quasiparticle scattering from impurities in unconventional pairing systems. It is immensely helpful for understanding impurity effects in the case of superfluid $^{3}$He that the structure of its order parameter is well-established. An overview of impurity effects is presented with emphasis on those experiments which have a quantitative interpretation in terms of theoretical models for homogeneous and inhomogeneous scattering. The latter can account successfully for most experimental results.
We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B-phase of superfluid $^3$He in 98% porosity aerogel down to the zero temperature limit for a wide range of pressures at zero magnetic field. The absolute attenuation was determined by direct transmission of sound pulses. Compared to the bulk fluid, our results revealed a drastically different behavior in attenuation, which is consistent with theoretical accounts with gapless excitations and a collision drag effect.
In superfluid $^3$He-B externally pumped quantized spin-wave excitations or magnons spontaneously form a Bose-Einstein condensate in a 3-dimensional trap created with the order-parameter texture and a shallow minimum in the polarizing field. The condensation is manifested by coherent precession of the magnetization with a common frequency in a large volume. The trap shape is controlled by the profile of the applied magnetic field and by the condensate itself via the spin-orbit interaction. The trapping potential can be experimentally determined with the spectroscopy of the magnon levels in the trap. We have measured the decay of the ground state condensates after switching off the pumping in the temperature range $(0.14div 0.2)T_{mathrm{c}}$. Two contributions to the relaxation are identified: (1) spin-diffusion with the diffusion coefficient proportional to the density of thermal quasiparticles and (2) the approximately temperature-independent radiation damping caused by the losses in the NMR pick-up circuit. The measured dependence of the relaxation on the shape of the trapping potential is in a good agreement with our calculations based on the magnetic field profile and the magnon-modified texture. Our values for the spin diffusion coefficient at low temperatures agree with the theoretical prediction and earlier measurements at temperatures above $0.5T_{mathrm{c}}$.
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