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Journal of Experimental and Theoretical Physics Letters

Low-temperature stability limit of the coherent spin precession in 3He-B

E. V. Surovtsev, I. A. Fomin

Published Oct 1, 2009• 3 citations
Publisher

Abstract

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.

DOI
10.1134/s0021364009150119

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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.
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.
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.
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.
The B phase of superfluid 3{}^{3}3He can support regions of extremely long-lived coherent spin precession at ultralow temperatures, known as persistent precessing domains (PPD). The domains have been described in terms of a Bose-Einstein condensate of magnons and in terms of Q balls in field theory. The domains form in a magnetic field minimum along the vertical axis of a cylindrical cell. When far from the ends of the cell, the PPD lifetime grows exponentially on decreasing temperature. When the PPD is close to the horizontal end wall of the cell, an extra surface dissipation mechanism dominates at low temperatures. We present measurements of the PPD generated at various locations in the cell over a broad range of temperatures below 0.3 TC{T}_{C}TC​. We compare the measured properties with theoretical expectations for spin-wave modes. We present model calculations of different dissipation mechanisms and we compare these to the measured lifetimes.
The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter -- is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in ^3He-B. This superfluid current of spins -- spin supercurrent -- is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid ^4He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves -- magnons. We discuss different states of magnon superfluidity with different types of spin-orbit coupling: in bulk ^3He-B; magnetically traped "Q-balls" at very low temperatures; in ^3He-A and ^3He-B immerged in deformed aerogel; etc. Some effects in normal ^3He can also be treated as a magnetic BEC of fermi liquid. A very similar phenomena can be observed also in a magnetic systems with dinamical frequensy shift, like MnC03. We will discuss the main experimental signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex -- a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken U(1) symmetry -- phonons in the spin-superfluid magnon gas; etc. For recent review see Yu. M. Bunkov and G. E. Volovik J. Phys. Cond. Matter. 22, 164210 (2010)
Experiments have been performed at high B/T to try to establish the existence and value of an anisotropy temperature (Ta) for pure 3He, and for 6.2% and 0.7% 3He-4He mixtures. The anisotropy of diffusion in dilute Fermi gases as the temperature T goes to zero has been predicted, though experimental evidence for such anisotropy has not been universally accepted.\n\nFinite size effects have required careful analysis of the theory of the cell for the 6.2% mixture. This alters the result as determined by the usual Leggett-Rice formula. Further investigation, beyond the scope of this thesis, is currently underway for the case of pure 3He.\n\nThe possibility of using a quartz tuning fork as a viscometer has also been investigated. It is shown that tuning forks can be used field-inpendently above 3 mK in saturated 3He-4He mixtures, and to detect the superfluid A and B-phase transitions in pure 3He. It is strongly suggested from the data that the tuning fork has great potential as a high-field viscometer; however further experiments are required to fully appreciate its useful range, in both normal and superfluids.