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Physical review. B, Condensed matter

Homogeneous spin precession in rotating vortex-free He3 -B: Measurement of the superfluid density anisotropy

J. S. Korhonen, Yu. M. Bunkov, Vladimir V. Dmitriev, Y. Kondo, M. Krusius, Yu. M. Mukharsky, Ülo Parts, E. V. Thuneberg

Published Dec 1, 1992• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.46.13983

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In transverse NMR at high rf excitation, it is possible to separate a 3B^{3}\mathit{B}3B 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.
Nonlinear spin precession has been observed in ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}B$ in large counterflow of the normal and superfluid fractions. The new precessing state is stabilized at a high rf excitation level and displays frequency-locked precession over a large range of frequency shifts, with the magnitude of magnetization at its equilibrium value. Comparison to analytical and numerical calculation indicates that in this state the orbital angular momentum L\mathbf{L}L of the Cooper pairs is oriented transverse to the external magnetic field in a ``non-Leggett'' configuration with broken spin-orbit coupling. The resonance shift depends on the tipping angle $\ensuremath{\theta}$ of the magnetization as $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{L}=({\ensuremath{\Omega}}_{B}^{2}/2{\ensuremath{\omega}}_{L})(\mathrm{cos}\ensuremath{\theta}\ensuremath{-}1/5).$ The phase diagram of the precessing modes with arbitrary orientation of L\mathbf{L}L is constructed.
States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid 3{}^{3}3He-BBB represent the macroscopic examples of the Bose-Einstein condensates of magnons. Once the magnons form one of these states, this many-magnon coherent quantum state is described by a ``single-magnon wave function'' (or an order parameter). A suitable external perturbation may cause the condensate to oscillate around the state of coherent precession, which demonstrates a collective rigidity of the condensate against scattering a single magnon out of it. The states corresponding to a free coherent precession of magnetization are degenerate in the phase of precession, so there exist oscillations around such states with a gapless dispersion relation, known as the Goldstone modes. Here, we present both experimental and theoretical results of the study of the spin density oscillations superposed on a homogeneously precessing domain in superfluid 3{}^{3}3He-BBB in the presence of a high-frequency excitation field Brf{B}_{\text{rf}}Brf​. We show that the presence of this field lifts the degeneracy of the precessing state with respect to the phase of precession, that is, it violates the symmetry of the magnon condensate, and former Goldstone modes become non-Goldstone ones, as they acquire the energy gap in their spectrum.
This doctoral thesis consists of experimental studies on rotating superfluid helium-3 at millikelvin temperatures. Superfluid 3He provides an example of ordered systems where quantum phenomena are visible on a macroscopic scale. The order parameter is described by a 3x3 complex matrix leading to different superfluid phases with different properties. The A and B phases support topologically different kinds of defects, most notably vortex lines. Vortex lines are most easily created and studied in uniform rotation. Because of quantum nature, the circulation around the vortices is quantized in units of κ0 = h/2m3.\n\nIn superfluid 3He nuclear magnetic resonance (NMR) provides a means to distinguish between different types of vortices and count them one by one. During the course of this work the sensitivity of the NMR spectrometer was improved by an order of magnitude, which enabled the direct measurement of the circulation of a vortex in the A phase that carries two circulation quanta (2κ0). Up to now the circulation of the known quantized vortex types in other quantum fluids, which include superfluid 4He, superconductors, and Bose-Einstein -condensates, has been singly quantized.\n\nOther NMR experiments reported in the thesis are: (1) The first qualitative measurements of vortex annihilation in the A and B phases of 3He. These measurements tell the lowest rotation velocity that stabilizes an array of vortex lines with a given number of vortices, and how it depends on the type of the defect. (2) Studies of vortex arrays with both singly and doubly quantized A phase vortex lines coexisting in the experimental container. 3He-A provides a unique system in which this kind of arrangement can be done. (3) In order to improve the vortex detection sensitivity in the B phase even further, the response of different nonlinear spin precession modes to superfluid-normal fluid counterflow was studied. A new mode, where the orbital angular momentum is oriented transverse to the external magnetic field, was found.
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.
We present experimental proof that in rotating 3B^{3}\mathit{B}3B the vortex-core transition temperature TV{\mathit{T}}_{\mathit{V}}TV​ separates axisymmetric vortices above TV{\mathit{T}}_{\mathit{V}}TV​ from vortices with spontaneously broken axial symmetry below TV{\mathit{T}}_{\mathit{V}}TV​. The nonaxisymmetry is observed in the presence of coherent spin precession as a new soft Goldstone mode, manifested as oscillations and spiral twisting of the core anisotropy axis. These are driven by the precessing spin via spin-orbit coupling and lead to magnetic relaxation from viscous losses, which depend on vortex pinning.
The polar phase of ^{3}He, which is topological spin-triplet superfluid with the Dirac nodal line in the spectrum of Bogoliubov quasiparticles, has been recently stabilized in a nanoconfined geometry. We pump magnetic excitations (magnons) into the sample of polar phase and observe how they form a Bose-Einstein condensate, revealed by coherent precession of the magnetization of the sample. Spin superfluidity, which supports this coherence, is associated with the spontaneous breaking of U(1) symmetry by the phase of precession. We observe the corresponding Nambu-Goldstone boson and measure its mass emerging when applied rf field violates the U(1) symmetry explicitly. We suggest that the magnon BEC in the polar phase is a powerful probe for topological objects such as vortices and solitons and topological nodes in the fermionic spectrum.