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Spin superfluidity and magnon Bose – Einstein condensation MicroKelvin, 2013 Yuriy Bunkov Institute Neel, CNRS, Grenoble, France 1. Review of Magnon BEC 2. Saga de Persistent signal

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1.Field induced magnetic phase transition as a magnon Bose Einstein condensation No, System in thermal equilibrium can not create the BEC state 2. Magnetic transport in a superfluid vacuum No, This is the property of vacuum, the superfluid state of 3He. It is a property of texture, not particles. What we will not speak about: And we will speak about of magnons BEC and magnons spin supercurrent, not Directly connected with mass superfluidity

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Superfluid 3 He Quantum vacuum characterized by phase S (magnetization) L (orbital momentum) Quasiparticles Magnons Acoustic modes Topological defects: Boojum Vortex Brane Particles: Fields: Texture of orbital momentum

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Holstain-Primakoff transformation

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Grenoble, 2003

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Spin superfluidity and BEC of magnons was found in a 5 different states of superfluid 3He. In one of this states the induction signal can live more then one hours. Its corresponds to a 99.999% of magnons to be condensed! For an atomic BEC the 30% condensation was only achieved! Magnon BEC Atomic BEC

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Ideal gas Quantum gas BEC, superfluidity Paramagnetic, Fermi liquid Magnetically ordered Coherent precession HHH S x + iS y = S sin e i t +i = H loc ==

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2. Thermalized magnons = 0 No BEC 1. Trap. It may be space trap (as for particle BEC) or even the trap of energy of magnons interaction H S

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2. Small angle of deflection H S Not enough for BEC For superfluid 3 He critical angle is about 0.2 0 1. Trap. It may be space trap (as for particle BEC) or even the trap of energy of magnons interaction

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2. Big angle of deflection H S Enough for BEC but Attractive interaction leads to instability of coherent precession. NO BEC

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2. Big angle of deflection 1. Trap. H S Repulsive interaction ! BEC ? May be NOT! If magnons live too short time Example – stationary spin waves. The important is the spontanuos simmetry breaking. How to check? 1.Long induction decay, longer then the inhomogeneity of magnetic field 2. Non-resonance excitation (In frequency or in place)

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H CW NMR rf = 0 x Hx The magnetic relaxation leads to decrease of BEC region Minimization of energy in the conditions of magnetization Conservation and the gradient of chemical potencial It can be compensated by a small resonance RF pumping HPD1

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22 0 JETPh Letters, v.47, p.478, (1988). Josephson

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HPD 2 Aerogel Stycast F P Hunger, Yu M Bunkov, E Collin, and H Godfrin Journal of Physics: Conference Series. 400 012019 (2012)

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Superfluid 3 He-A in squeezed aerogel H d L d L 2 In rotating frame

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P. HungerP. Hunger, Y. M. Bunkov, E. Collin and H. GodfrinY. M. BunkovE. CollinH. Godfrin « Evidence for Magnon BEC in Superfluid 3 He-A »Evidence for Magnon BEC in Superfluid 3 He-A J. of Low Temp. Phys 158, 129–134 (2010) T. Kunimatsu, T. Sato, K. Izumina, A. Matsubara, Y. Sasaki, M. Kubota, O. Ishikawa, T. Mizusaki, Yu.M.Bunkov JETP Letters, 86, 244 (2007)

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CsMnF 3 3 He-A in aerogel CW NMR experiments

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Yu. M. Bunkov, E. M. Alakshin, R. R. Gazizulin, A.V. Klochkov, V.V. Kuzmin, V.S. L'vov, and M.S. Tagirov. “High Tc spin superfluidity in antiferromagnets”, Phys. Rev. Lett. 108, 177002 (2012).

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RbMnF 3 and MnCO 3 OIST 2013 RbMnF 3 MnCO 3 Theoretical prediction for saturation Magnon BEC

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Saga de Persistent signal

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Persistent Signal; Coherent NMR state assisted by orbital texture. Yuriy M. Bunko C R T B T – C N R S, Grenoble, France QFS Trento 2004

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HPD Catastropha PS Grenoble, 1999 A.S.Borovik-Romanov, Yu.M.Bunkov, V.V.Dmitriev, Yu.M.Mukharskiy, JETP Letters v.40, p.1033, (1984). Sov.Phys.JETPh, v.61, p.1199, (1985). I.A.Fomin, JETP Letters v.40, p.1036, (1984). Coherent, Magnetically Excited States Domain with Homogeneous Precession of Magnetization, 1984 Catastrophic relaxation Yu.M.Bunkov, V.V.Dmitriev, Yu.M.Mukharskiy, J.Nyeki, D.A.Sergatskov, Europhysics Letters, v.8, p.645, (1989).

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2. Coherenent State, which radiates the Persistent signal Moscow results Yu.M.Bunkov, S.N.Fisher, A.M.Guenault, G.R.Pickett, S.R.Zakazov, Physica B, v. 194, p. 827, (1994). Discovery, Lancaster, 1992 Yu.M.Bunkov, S.N.Fisher, A.M.Guenault, G.R.Pickett, Phys, Rev, Letters, v.69, p3092, (1992). ``Coherent Spin Precession and Texture in 3He-B.'' Yu.M. Bunkov, LT-21, Czechoslovak Journal of Phys. V. 46, S1, p. 231 (1996). Lancaster experimental conformation Yu.M. Bunkov, D.J. Cousins, M.P.Enrico, S.N.Fisher, G.R.Pickett, N.S.Shaw, W.Tych, LT-21, Czechoslovak Journal of Phys. V. 46, S1, p. 233 (1996). Moscow Lancaster

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Non-linear Stationary Spin Waves in Flared out texture NMR of Rotated superfluid 3He-B O.T.Ikkala, G.E.Volovik, P.Y.Hakonen, Yu.M.Bunkov, S.T.Islander, G.A.Haradze, JETP Letters v.35, p.416 (1982). L Angle L-H Before rotationDuring rotationAfter rotation H

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Grenoble experiments with Non-linear Stationary Spin Waves 0.25 Tc A.-S. Chen, Yu.M. Bunkov, H. Godfrin, R. Schanen, F. Scheffer. J. Low Temp. Phys, 110, p. 51, (1998).

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Following Landau and Lifchitz we consider an anharmonic oscillator with a third order of nonlinearity Non-linear Stationary Spin-waves A.S. Chen,Yu. M. Bunkov, H. Godfrin, R. Schanen and F. Scheffler J. of Low Temp. Phys. 113, 693 (1998).

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HH H = H+ Hz Quantum billiard Anne-Sophie CHEN, Ph D Thesis, Grenoble, (1999)

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Identity of Non-linear SSW and Persistent Signals Grenoble, 1997. A.-S. Chen, Yu.M. Bunkov, H. Godfrin, R. Schanen, F. Scheffer. J. Low Temp. Phys, 110, p. 51, (1998).

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HH Computer simulation Grenoble 2004 H Lz LHLH z Calculations of a spatial deflection of spin and orbit on basis of Poisson brackets and Takagi relaxation Follow Voislav Golo algorithm Yu.M.Bunkov, V.L.Golo, J Low Temp Phys, to be published

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Grenoble, 2004

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S L n L=R(n ) S

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1% HPD

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Grenoble, 1999 Off-resonante NMR excitation D.J.Cousins, S.N.Fisher, A.I.Gregory, G.R.Pickett, N.S.Shaw, Phys. Rev. Lett, 82, 4484, (1999) Anne-Sophie CHEN, Ph D Thesis, Grenoble, (1999) s p d rf Qb dd

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