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arXiv:cond-mat/9606221 · Physical Review Letters

Stable Spin Precession at One Half of Equilibrium Magnetization in Superfluid 3 He-B

Vladimir V. Dmitriev, Ivan V. Kosarev, M. Krusius, D. Ponarin, V. M. H. Ruutu, Григорий Ефимович Воловик

Published Jan 6, 1997• 64 citations

Abstract

New modes of spin precession have been observed in superfluid ${}^{3}\mathrm{He}\ensuremath{-}B$ with a precessing magnetization ${M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}pM}_{\mathrm{eq}}$, where $p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, $\frac{1}{2}$, and $\ensuremath{\approx}0$. These dynamic order parameter states are the first examples of stable precession with a magnetization different from the equilibrium value ${M}_{\mathrm{eq}}$. The $p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$ mode is the second example of a phase-coherent state of a spin superfluid. The new states can be excited close to ${T}_{c}$ 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.

DOI: 10.1103/physrevlett.78.86

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New modes of spin precession have been observed in superfluid

{}^{3}\mathrm{He}\ensuremath{-}B

with a precessing magnetization

{M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}pM}_{\mathrm{eq}}

, where

p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

,

\frac{1}{2}

, and

\ensuremath{\approx}0

. These dynamic order parameter states are the first examples of stable precession with a magnetization different from the equilibrium value

{M}_{\mathrm{eq}}

. The

p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}

mode is the second example of a phase-coherent state of a spin superfluid. The new states can be excited close to

{T}_{c}

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.

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.

On the Spin-Orbital Structure of the "Zero" Magnetization Spin-Precessing Modes of the Superfluid

^3He-B

The spin-orbital configurations of the coherently precessing spin modes characterized by a small value of the magnetization

(M\ll M_{0}=χH_{0})

is considered. Various regimes are analysed depending on the transverse rf-field strength

States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid

{}^{3}

He-

B

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}

He-

B

in the presence of a high-frequency excitation field

{B}_{\text{rf}}

. 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.

Long-lived coherent spin precession of 3He-B at low temperatures around 0.2 Tc is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulated experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.

Magnetic supercurrents are observed in superfluid

^{3}\mathit{B}

. These supercurrents transport the longitudinal magnetization from one experimental cell to another through a narrow channel, driven by gradients of the order parameter. In both cells NMR is induced by separate signal generators at the same frequency. The supercurrent arises if a phase difference of the magnetization precession is established across the narrow channel. A critical spin supercurrent is measured at which precession phase slippage takes place. Experimental values of the critical spin supercurrent are in agreement with theoretical predictions.