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Ordering of the orbital momentum in superfluid 3He-B in the deformed aerogel and new modes of coherent precession of spins

Johannes Elbs, Eddy Collin, Yu. M. Bunkov, Henri Godfrin, Григорий Ефимович Воловик

Published Jul 24, 2007• 0 citations
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Abstract

Deformation of aerogel strongly modifies the orientation of the order parameter of superfluid 3He confined in aerogel. We used a radial squeezing of aerogel to keep the orbital angular momentum of the 3He Cooper pairs in the plane perpendicular to the magnetic field. We did not find strong evidence for a polar phase, with a nodal line along the equator of the Fermi surface, predicted to occur at large radial squeezing. Instead we observed 3He-A with a clear experimental evidence of the destruction of the long-range order by random anisotropy -- the Larkin-Imry-Ma effect. In 3He-B we observed and identified new modes of NMR, which are impossible to obtain in bulk 3He-B. One of these modes is characterized by a repulsive interaction between magnons, which is suitable for the magnon Bose-Einstein condensation (BEC).

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•Feb 8, 2010•0 citations
Deformation of aerogel strongly modifies the orientation of the order parameter of superfluid 3He confined in aerogel. We used a radial squeezing of aerogel to keep the orbital angular momentum of the 3He Cooper pairs in the plane perpendicular to the magnetic field. We did not find strong evidence for a polar phase, with a nodal line along the equator of the Fermi surface, predicted to occur at large radial squeezing. Instead we observed 3He-A with a clear experimental evidence of the destruction of the long-range order by random anisotropy -- the Larkin-Imry-Ma effect. In 3He-B we observed and identified new modes of NMR, which are impossible to obtain in bulk 3He-B. One of these modes is characterized by a repulsive interaction between magnons, which is suitable for the magnon Bose-Einstein condensation (BEC).
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)
3 He is an example of the system with non-trivial Cooper paring. A few different superfluid phases are known in this system. Recently the new one, the polar phase, have been observed in 3 He confined in nematically ordered aerogel. A number of various topological defects including half-quantum vortices can exist the polar phase. In this work, we present theoretical and numerical studies of linear nuclear magnetic resonance in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.
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.
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.
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.
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.