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arXiv:cond-mat/9805119 · Physical review. B, Condensed matter

Superflow-stabilized nonlinear NMR in rotating 3He−B

Vladimir V. Dmitriev, V. B. Eltsov, M. Krusius, J. J. Ruohio, Григорий Ефимович Воловик

Published Jan 1, 1999• 9 citations
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Abstract

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 $\mathbf{L}$ 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 $\mathbf{L}$ is constructed.

DOI
10.1103/physrevb.59.165

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Nonlinear spin precession has been observed in 3He\ensuremath−B{}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}B3He\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 \ensuremathθ\ensuremath{\theta}\ensuremathθ of the magnetization as \ensuremathω\ensuremath−\ensuremathωL=(\ensuremathΩB2/2\ensuremathωL)(cos\ensuremathθ\ensuremath−1/5).\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{L}=({\ensuremath{\Omega}}_{B}^{2}/2{\ensuremath{\omega}}_{L})(\mathrm{cos}\ensuremath{\theta}\ensuremath{-}1/5).\ensuremathω\ensuremath−\ensuremathωL​=(\ensuremathΩB2​/2\ensuremathωL​)(cos\ensuremathθ\ensuremath−1/5). The phase diagram of the precessing modes with arbitrary orientation of L\mathbf{L}L is constructed.
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.
New modes of spin precession have been observed in superfluid ${}^{3}\mathrm{He}\ensuremath{-}B$ with a precessing magnetization M=pMeq{M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}pM}_{\mathrm{eq}}M=pMeq​, where p=1p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1p=1, 12\frac{1}{2}21​, and $\ensuremath{\approx}0$. These dynamic order parameter states are the first examples of stable precession with a magnetization different from the equilibrium value Meq{M}_{\mathrm{eq}}Meq​. The p=12p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}p=21​ mode is the second example of a phase-coherent state of a spin superfluid. The new states can be excited close to Tc{T}_{c}Tc​ in the range $1\ensuremath{-}T/{T}_{c}\ensuremath{\lesssim}0.02$ where dissipation is low and the energy barriers between the different local minima of the spin-orbit energy are small.
On the Spin-Orbital Structure of the "Zero" Magnetization Spin-Precessing Modes of the Superfluid 3He−B^3He-B3He−B
The spin-orbital configurations of the coherently precessing spin modes characterized by a small value of the magnetization (M≪M0=χH0)(M\ll M_{0}=χH_{0})(M≪M0​=χH0​) is considered. Various regimes are analysed depending on the transverse rf-field strength
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.
Bose-Einstein condensation of magnons in superfluid 3He-B is experimentally manifested by various states where coherent spin precession is established spontaneously, even in nonhomogeneous magnetic fields. Once such a condensate with coherent spin precession is created, it occupies the state with minimal energy, the ground state. The application of an additional magnetic field to that condensate may cause its deflection from the energy minimum and the condensate responds by creating collective gapless oscillations known as Goldstone modes. This Letter reports the experimental observation of a new (non-)Goldstone mode, which can be viewed as an additional NMR mode of condensed magnons in a rotating frame of reference.
It has been shown that the instability of uniform spin precession in the bulk of the 3 He-B superfluid phase is due to the joint action of the anisotropy of the velocities of spin waves and dipole interaction. In the leading approximation in the ratio of the Leggett frequency to the Larmor frequency, the growth increments of the amplitudes of spin waves for all of the possible decay channels have been found. The maximum increment has been determined for all of the angles of spin deviation from the equilibrium orientation. The minimum temperature to which precession is stable has been estimated.