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Physical review. B, Condensed matter

Fivefold splitting of the squashing collective mode of superfluid B3 by a magnetic field

Roman Movshovich, Eric Varoquaux, N. Kim, D. M. Lee

Published Jul 1, 1991• 45 citations
Publisher

Abstract

We have conducted an ultrasonic pulse-time-of-flight investigation of the squashing mode of superfluid $^{3}\mathit{B}$ in a magnetic field. All five of the expected Zeeman sublevels for this J=${2}^{\mathrm{\ensuremath{-}}}$ mode were observed. The investigation was done at a very low temperature (T/${\mathit{T}}_{\mathit{c}}$0.35) to reduce the quasiparticle broadening that tends to smear the collective modes and makes resolution of the individual sublevels impossible. Variation of the pressure was used to sweep the collective-mode frequencies through the operating frequency, 137.6 MHz of the resonant-sound transducers. Both group-velocity spectroscopy and pulse-shape analysis were used for identification of different sublevels. Performing experiments at different orientations of the sound propagation with respect to magnetic-field direction (parallel, perpendicular, 55\ifmmode^\circ\else\textdegree\fi{}, and 13\ifmmode^\circ\else\textdegree\fi{}) was the key to observation of all five modes and their identification. The Land\'e g factor was obtained from the linear dependence of the ${\mathit{J}}_{\mathit{z}}$=+2 sublevel on magnetic field and compared with theory.

DOI
10.1103/physrevb.44.332

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We have conducted an ultrasonic pulse-time-of-flight investigation of the squashing mode of superfluid 3B^{3}\mathit{B}3B in a magnetic field. All five of the expected Zeeman sublevels for this J=2\ensuremath−{2}^{\mathrm{\ensuremath{-}}}2\ensuremath− mode were observed. The investigation was done at a very low temperature (T/Tc{\mathit{T}}_{\mathit{c}}Tc​0.35) to reduce the quasiparticle broadening that tends to smear the collective modes and makes resolution of the individual sublevels impossible. Variation of the pressure was used to sweep the collective-mode frequencies through the operating frequency, 137.6 MHz of the resonant-sound transducers. Both group-velocity spectroscopy and pulse-shape analysis were used for identification of different sublevels. Performing experiments at different orientations of the sound propagation with respect to magnetic-field direction (parallel, perpendicular, 55\ifmmode^\circ\else\textdegree\fi{}, and 13\ifmmode^\circ\else\textdegree\fi{}) was the key to observation of all five modes and their identification. The Land'e g factor was obtained from the linear dependence of the Jz{\mathit{J}}_{\mathit{z}}Jz​=+2 sublevel on magnetic field and compared with theory.
We have conducted an ultrasonic pulse‐time‐of‐flight investigation of the squashing mode of the superfluid 3He‐B in a magnetic field. All five of the expected Zeeman sublevels for this J=2− mode were observed. The investigation was done at very low temperature (T/Tc<0.35) to reduce the quasi‐particle broadening that tends to smear the collective modes and makes resolution of the individual sublevels impossible. Variation of the pressure was used to sweep the collective modes’ frequencies through the operating frequency, 137.6 MHz of the resonant sound transducers. Both group velocity spectroscopy and pulse‐shape analysis were used for identification of different sublevels. Performing experiment at different orientations of the sound propagation with respect to magnetic field direction (parallel, perpendicular, 55 and 13 degrees) was the key to observation of all 5 modes and their identification. The Landé g factor was obtained from the linear dependence of the Jz=+2 mode on magnetic field and compared to theory.
Rotation of superfluid 3B^{3}\mathit{B}3B in an magnetic field enhances the coupling of the nonzero mJ{\mathrm{m}}_{\mathrm{J}}mJ​ substrates of the real squashing collective mode to the zero sound, and the fivefold line splitting becomes observable even when H is parallel to \ensuremath{\Omega} and to the direction of sound propagation. Equilibrium vortex lattices and vortex-free states can be distinguished by their characteristic absorption spectra. The dependence of the sound attenuation on the angular velocity in magnetic fields up to 32 mT is reported; the data are qualitatively compared with theory.
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.
Parametric excitation yields new results, which cannot be obtained by conventional linear spectroscopy, on the collective modes in superfluid 3B^{3}\mathit{B}3B. In our ultrasonic experiments, performed in a chamber with four quartz crystals, we have excited the real squashing (J=2+{2}^{+}2+) modes by two simultaneous sound waves which are mutually either parallel, orthogonal, or antiparallel. Qualitatively these results are in agreement with the theoretical dispersion relation of the J=2+{2}^{+}2+ modes, and quantitatively we have been able to extract the collective-mode velocities from the line splittings in zero magnetic field.
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.
We have used the acoustic Faraday effect in superfluid 3He to perform high resolution spectroscopy of an excited state of the superfluid condensate, called the imaginary squashing mode. With acoustic cavity interferometry we measure the rotation of the plane of polarization of a transverse sound wave propagating in the direction of the magnetic field from which we determine the Zeeman energy of the mode. We interpret the Landé g factor, combined with the zero-field energies of this excited state, using the theory of Sauls and Serene, to calculate the strength of f-wave interactions in 3He.