Physical review. B, Condensed matter

Magnetic relaxation and He4 coverage in superfluid A13

Qiang Jiang, Haruo Kojima

Published Jun 1, 1992• 2 citations

Abstract

Measurements on spin relaxation time in superfluid $^{3}\mathit{A}_{1}$ were carried out at a pressure of 22.4 bar and a static field of 7.5 kG. The influence of surface coverage by $^{4}\mathrm{He}$ was systematically explored. The $^{4}\mathrm{He}$ coverage is used to eliminate the spin relaxation at the boundary walls and to extract the spin relaxation time in the warmer half of bulk ${\mathit{A}}_{1}$ phase. The bulk spin relaxation time is much shorter than expected from Leggett-Takagi theory applied to the ${\mathit{A}}_{1}$ phase. In the colder half of the phase, $^{4}\mathrm{He}$ coverage anomalously has no effect on the spin relaxation time.

DOI: 10.1103/physrevb.45.12616

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Physical review. B, Condensed matter

Magnetic relaxation and He4 coverage in superfluid A13

Qiang Jiang, Haruo Kojima

Published Jun 1, 1992• 2 citations

Publisher

Abstract

Measurements on spin relaxation time in superfluid

^{3}\mathit{A}_{1}

were carried out at a pressure of 22.4 bar and a static field of 7.5 kG. The influence of surface coverage by

^{4}\mathrm{He}

was systematically explored. The

^{4}\mathrm{He}

coverage is used to eliminate the spin relaxation at the boundary walls and to extract the spin relaxation time in the warmer half of bulk

{\mathit{A}}_{1}

phase. The bulk spin relaxation time is much shorter than expected from Leggett-Takagi theory applied to the

{\mathit{A}}_{1}

phase. In the colder half of the phase,

^{4}\mathrm{He}

coverage anomalously has no effect on the spin relaxation time.

DOI: 10.1103/physrevb.45.12616

Related papers

Spin Polarized Superfluid3He A1

Harry Kojima, Hidehiko Ishimoto

Under applied magnetic field, the originally single superfluid 3 He transition near 3 mK in zero field splits into two transitions between which a new A 1 phase emerges. The two second order transitions are marked by abrupt changes in viscosity, zero sound attenuation and nuclear magnetic resonance. To date, the maximum magnetic field for producing A 1 phase is 15 T. The A 1 phase has been identified with a spin-polarized (ferromagnetic) superfluid system which breaks the relative symmetry between spin, orbit and gauge spaces. A superfluid mass current in A 1 is simultaneously a spin current resulting in the propagation of spin-entropy wave. Experiments with spin-entropy wave provide measurements of anisotropic superfluid density and strong coupling parameters, spin diffusion coefficient and texture transformations. Owing to the spin-polarized nature, superflows may be generated by applied magnetic field gradients and measured from the induced magnetic fountain pressure. The mechanical spin density detector is developed to measure the spin relaxation in A 1 phase. The observed unexpected temperature dependence of the spin relaxation time gives evidence that the A 1 phase contains a small amount of the predicted minority spin condensate from dipolar interaction energy.Under applied magnetic field, the originally single superfluid 3 He transition near 3 mK in zero field splits into two transitions between which a new A 1 phase emerges. The two second order transitions are marked by abrupt changes in viscosity, zero sound attenuation and nuclear magnetic resonance. To date, the maximum magnetic field for producing A 1 phase is 15 T. The A 1 phase has been identified with a spin-polarized (ferromagnetic) superfluid system which breaks the relative symmetry between spin, orbit and gauge spaces. A superfluid mass current in A 1 is simultaneously a spin current resulting in the propagation of spin-entropy wave. Experiments with spin-entropy wave provide measurements of anisotropic superfluid density and strong coupling parameters, spin diffusion coefficient and texture transformations. Owing to the spin-polarized nature, superflows may be generated by applied magnetic field gradients and measured from the induced magnetic fountain pressure. The mechanical spin density detector is developed to measure the spin relaxation in A 1 phase. The observed unexpected temperature dependence of the spin relaxation time gives evidence that the A 1 phase contains a small amount of the predicted minority spin condensate from dipolar interaction energy.

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Physical review. B, Condensed matterDec 1, 199216 citations

Transport and relaxation processes in superfluid He3 close to the transition temperature

P. Bhattacharyya, C. J. Pethick, H. Smith

We derive the Boltzmann equation describing long-wavelength low-frequency transport and relaxation processes in a superfluid Fermi liquid close to the transition temperature ${T}_{c}$ . In the superfluid, the quasiparticle number is not conserved and therefore one has to take into account the decay of one quasiparticle into three and the inverse process, as well as the two-quasiparticle scattering process. We calculate the collision term in the Boltzmann equation to first order in the superfluid gap $\ensuremath{\Delta}$ and show that it is related rather simply to the corresponding normal-state collision term. As applications of the Boltzmann equation, we solve it exactly to calculate the shear viscosity, and the intrinsic spin relaxation rate. The shear viscosity drops as $\ensuremath{\Delta}\ensuremath{\propto}{({T}_{c}\ensuremath{-}T)}^{\frac{1}{2}}$ for temperatures just below ${T}_{c}$ , and we determine the coefficient of $\ensuremath{\Delta}$ as a function of the normal-state collision probability. Leggett and Takagi's characteristic spin-relaxation time is shown to be equal to the relaxation time of a normal-state quasiparticle at the Fermi energy at ${T}_{c}$ . The results provide one with a useful consistency check on experimental measurements which is independent of any assumption about the normal-state collision probability.We derive the Boltzmann equation describing long-wavelength low-frequency transport and relaxation processes in a superfluid Fermi liquid close to the transition temperature ${T}_{c}$. In the superfluid, the quasiparticle number is not conserved and therefore one has to take into account the decay of one quasiparticle into three and the inverse process, as well as the two-quasiparticle scattering process. We calculate the collision term in the Boltzmann equation to first order in the superfluid gap $\ensuremath{\Delta}$ and show that it is related rather simply to the corresponding normal-state collision term. As applications of the Boltzmann equation, we solve it exactly to calculate the shear viscosity, and the intrinsic spin relaxation rate. The shear viscosity drops as $\ensuremath{\Delta}\ensuremath{\propto}{({T}_{c}\ensuremath{-}T)}^{\frac{1}{2}}$ for temperatures just below ${T}_{c}$, and we determine the coefficient of $\ensuremath{\Delta}$ as a function of the normal-state collision probability. Leggett and Takagi's characteristic spin-relaxation time is shown to be equal to the relaxation time of a normal-state quasiparticle at the Fermi energy at ${T}_{c}$. The results provide one with a useful consistency check on experimental measurements which is independent of any assumption about the normal-state collision probability.

Physical review. B, Solid stateApr 1, 197750 citations

Measurements on spin relaxation time in superfluid

^{3}\mathit{A}_{1}

were carried out at a pressure of 22.4 bar and a static field of 7.5 kG. The influence of surface coverage by

^{4}\mathrm{He}

was systematically explored. The

^{4}\mathrm{He}

coverage is used to eliminate the spin relaxation at the boundary walls and to extract the spin relaxation time in the warmer half of bulk

{\mathit{A}}_{1}

phase. The bulk spin relaxation time is much shorter than expected from Leggett-Takagi theory applied to the

{\mathit{A}}_{1}

phase. In the colder half of the phase,

^{4}\mathrm{He}

coverage anomalously has no effect on the spin relaxation time.

Mechanical pumping and filtering of spin-polarized condensate were realized in the superfluid

^{3}\text{He}

{\text{A}}_{1}

phase by the pneumatic pumping action of an electrostatically actuated diaphragm. Spin pumping increased the net spin polarization by

20--50\text{ }%

as measured by the induced pressure change during spin pumping. The observed spin relaxation time was consistent with the increased spin polarization. These observations demonstrate the feasibility of using spin pumping to substantially increase the effective magnetic field to which the

{\text{A}}_{1}

phase is exposed.

In transverse NMR at high rf excitation, it is possible to separate a

^{3}\mathit{B}

sample into two magnetic domains. In one domain the spins are precessing coherently with a large tilting angle in relation to the polarizing magnetic field while in the other they are stationary and oriented parallel to the field. We have studied the two-domain system during vortex-free rotation and found that the boundary region between the precessing and static domains is sensitive to superfluid counterflow, flowing parallel to the boundary. The volume of the precessing domain decreases and the NMR absorption, associated with spin diffusion across the boundary, increases. The shift of the domain boundary is analyzed in terms of the competition between the kinetic energy of counterflow and the gradient in the Zeeman energy. From the shift we obtain the superfluid density anisotropy, induced by the magnetic field. A calculation in the weak-coupling approximation explains only half of the measured ansiotropy at low pressures. At high pressures the discrepancy is smaller.

We derive the Boltzmann equation describing long-wavelength low-frequency transport and relaxation processes in a superfluid Fermi liquid close to the transition temperature

{T}_{c}

. In the superfluid, the quasiparticle number is not conserved and therefore one has to take into account the decay of one quasiparticle into three and the inverse process, as well as the two-quasiparticle scattering process. We calculate the collision term in the Boltzmann equation to first order in the superfluid gap $\ensuremath{\Delta}$ and show that it is related rather simply to the corresponding normal-state collision term. As applications of the Boltzmann equation, we solve it exactly to calculate the shear viscosity, and the intrinsic spin relaxation rate. The shear viscosity drops as $\ensuremath{\Delta}\ensuremath{\propto}{({T}_{c}\ensuremath{-}T)}^{\frac{1}{2}}$ for temperatures just below

{T}_{c}

, and we determine the coefficient of $\ensuremath{\Delta}$ as a function of the normal-state collision probability. Leggett and Takagi's characteristic spin-relaxation time is shown to be equal to the relaxation time of a normal-state quasiparticle at the Fermi energy at

{T}_{c}

. The results provide one with a useful consistency check on experimental measurements which is independent of any assumption about the normal-state collision probability.