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Physical Review Letters

Distortion of superfluid B3 as a function of magnetic field and the first-order transition to A3 at theT=0 limit

S. N. Fisher, A. M. Guénault, C. J. Kennedy, G. R. Pickett

Published Sep 2, 1991• 61 citations
Publisher

Abstract

We have observed the distortion of the gap and associated excitation spectrum in superfluid $^{3}\mathit{B}$ with increasing magnetic field up to the first-order transition to the A phase at a temperature of ${\mathit{T}}_{\mathit{c}}$/T of about 7 (\ensuremath{\le}140 \ensuremath{\mu}K at P=0). The pair-breaking critical velocity of a vibrating-wire resonator is monitored as a function of field. By plotting the critical velocity we can follow changes in the B-phase excitation spectrum with increasing magnetic field, which are in excellent agreement with the calculations of Ashida and Nagai. The sudden transition to the A phase at the critical field is clearly seen.

DOI
10.1103/physrevlett.67.1270

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We have observed the distortion of the gap and associated excitation spectrum in superfluid 3B^{3}\mathit{B}3B with increasing magnetic field up to the first-order transition to the A phase at a temperature of Tc{\mathit{T}}_{\mathit{c}}Tc​/T of about 7 (\ensuremath{\le}140 \ensuremath{\mu}K at P=0). The pair-breaking critical velocity of a vibrating-wire resonator is monitored as a function of field. By plotting the critical velocity we can follow changes in the B-phase excitation spectrum with increasing magnetic field, which are in excellent agreement with the calculations of Ashida and Nagai. The sudden transition to the A phase at the critical field is clearly seen.
We have observed that the motion of a vibrating-wire resonator in superfluid 3B^{3}\mathit{B}3B at temperatures below Tc{\mathrm{T}}_{\mathrm{c}}Tc​/8 is associated with a sharp critical velocity, vc{\mathrm{v}}_{\mathrm{c}}vc​, above which very high dissipation sets in. We identify this velocity with the Landau critical velocity for pair breaking. That the observed value of vc{\mathrm{v}}_{\mathrm{c}}vc​ is a factor of 2 lower than the critical velocity expected from the BCS value of the gap we take as evidence that the gap is suppressed by about 50% of its bulk value near a moving boundary.
The field dependence of the magnetic susceptibility and collective mode frequencies of superfluid 3B^{3}\mathit{B}3B are calculated perturbatively in (\ensuremath{\gamma}H/\ensuremath{\Delta}) using the quasiclassical theory. With the aid of this perturbation theory, we interpret the gap distortion, nonlinear susceptibility, and collective excitations of the order parameter in terms of additional correlations between Cooper pairs that are induced by a magnetic field. We also calculate the dispersion splittings of the real squashing modes in a magnetic field. In addition to the nonlinear Zeeman shifts of these modes, which occur in strong magnetic fields (\ensuremath{\gamma}H\ensuremath{\sim}0.10\ensuremath{\Delta}), there are low-field (\ensuremath{\gamma}H\ensuremath{\sim}q2{q}^{2}q2vf2{v}_{f}^{2}vf2​/\ensuremath{\Delta}) nonlinearities of the collective mode frequencies resulting from the field dependence of the quantization axis. Our results for all of these response properties of 3B^{3}\mathit{B}3B depend upon a small number of material parameters; thus measurements of these properties can provide detailed information on the quasiparticle interactions.
Systems showing resonant superfluidity, driven by an exchange coupling of strength g between uncorrelated pairs of itinerant fermions and tightly bound ones, undergo a first-order phase transition as g increases beyond some critical value gc. The superfluid phase for g<or=gc is characterized by a gap in the fermionic single-particle spectrum and an acoustic sound-wave-like collective mode of the bosonic resonating fermion pairs inside this gap. For g>gc this state gives way to a phase-uncorrelated bosonic liquid with a q2 spectrum.
Using a new quasiparticle detector and source consisting of a blackbody radiator, we have made the first measurements of the divergence of a beam of quasiparticles produced by a vibrating-wire resonator moving at supercritical velocities in superfluid 3B^{3}\mathit{B}3B at the zero-temperature limit. At velocities just above the critical velocity of \ensuremath{\Delta}/3pF{\mathit{p}}_{\mathit{F}}pF​ we see a very narrow beam directed along the direction of motion of the wire. As the maximum wire velocity increases the beam spreads to saturate at a half-angle divergence of approximately 55\ifmmode^\circ\else\textdegree\fi{} at a maximum velocity of order \ensuremath{\Delta}/pF{\mathit{p}}_{\mathit{F}}pF​.
We have investigated the behaviour of a large vibrating wire resonator in the B-phase of superfluid 3 He at zero pressure and at temperatures below 200 μK. The vibrating wire has a low resonant frequency of around 60 Hz. At low velocities the motion of the wire is impeded by its intrinsic (vacuum) damping and by the scattering of thermal quasiparticle excitations. At higher velocities we would normally expect the motion to be further damped by the creation of quasiparticles from pair-breaking. However, for a range of temperatures, as we increase the driving force we observe a sudden decrease in the damping of the wire. This results from a reduction in the thermal damping arising from the presence of quantum vortex lines generated by the wire. These vortex lines Andreev-reflect low energy excitations and thus partially shield the wire from incident thermal quasiparticles.
Measurements of the attenuation of zero sound in superfluid 3B^{3}\mathit{B}3B show coupling to a collective mode in applied magnetic fields at frequencies \ensuremath{\nu}\ensuremath{\sim}2\ensuremath{\Delta}(T), which is identified as the J${=1}^{\mathrm{\ensuremath{-}}}$ mode. The attenuation as a function of reduced temperature in zero magnetic field is subtracted from that measured in magnetic fields up to 80 mT to reveal both the Jz{J}_{z}Jz​=+1 and Jz{J}_{z}Jz​=-1 components. The measured G factor is in good agreement with theory. The Jz{J}_{z}Jz​=+1 resonance occurs in the pair excitation continuum and subtracts from the total attenuation, resulting in an antipeak.