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Yu. M. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Elbs

Cold gas of magnons, collective behavior. Yu. M. Bunkov Institute Neel, CNRS, Grenoble, France. Yu. M. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Elbs P. Hunger G. E. Volovik J. Sauls J. Parpia W. Halperin Yu. M. Mukharskiy V. V. Dmitriev

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Yu. M. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Elbs

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  1. Cold gas of magnons, collective behavior Yu. M. Bunkov Institute Neel, CNRS, Grenoble, France Yu. M. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Elbs P. Hunger G. E. Volovik J. Sauls J. Parpia W. Halperin Yu. M. Mukharskiy V. V. Dmitriev T. Mizusaki M. Kubota A. Mitsubara

  2. BEC of spin waves? Magnetically ordered states Superfluids, superconductors Universe

  3. H H H w=gHloc Ideal gas Paramagnetic Magnetically ordered Quantum gas w=w0 Sx + iSy = Ssinbe iwt +ia BEC, superfluidity Coherent precession

  4. Superfluid 3He ~100% Normal 3He Coherent spin precession in Superfluid 3He-B A.S.Borovik-Romanov, Yu.M.Bunkov, V.V.Dmitriev, Yu.M.Mukharskiy, JETP Letters v.40, p.1033, (1984). I.A.Fomin, JETP Letters v.40, p.1036, (1984).

  5. Grenoble, 2003

  6. ( h = 1; c ~ vF) Spin waves in superfluid 3He are ready to be condensed! Magnon spectrum Magnon mass Magnon density Temperature of BEC TF = 0.1K, Texp = 0.0003K G.Volovik

  7. Dipole-dipole spin-orbit energy Spectroscopic energy Gradient energy True energy at the rotating frame Spin Supercurrent m = wL(z) - w Chemical potential F = A + (B+m) lYl2 + ClYl4 C < 0 C > 0 m=0 B+m<0 B+m>0 F Gross-Pitaevskii equation lYl2

  8. Gross-Pitaevskii equation Spin-Orbit interaction energy in 3He-B M II H M I H L II H

  9. f D D H D ki Mass superflow Spin supercurrent

  10. Dipole + magnetic gradient energy E 104°+D 104° D H w = gH x Dipole energy R(n,Q) w L Osheroff – Corruchini mode S H 0° b 104° Brinkman – Smith mode Coherent state x w = gH Bunkov, ICM, Kyoto, 2006

  11. 0.2 2 Dw W w = /2 0.15 L L m = (w - wL) / Dw 0.1 w + F m=0.05 0.05 D H F D m=0 m 0 D m= - 0.05 -0.05 -0.1 0 0.5 1 1.5 2 2 Y Magnons BEC in the gradient of magnetic field for b>104° for b<104° FD = 0 FdBphasa I J Minimization of energy in the conditions of magnetization Conservation and the gradient of chemical potencial The magnetic relaxation leads to decrease of BEC region Yu.M. Bunkov and G.E. Volovik Bose-Einstein condensation of magnons in superfluid 3He J. of  Low Temp. Phys. 150, 135, (2008) It can be compensated by a small resonance RF pumping

  12. RF H D H Magnetization transport by Spin Supercurrent RF

  13. RF RF H D H Magnetization transport by Spin Supercurrent

  14. RF RF H D H Magnetization transport by Spin Supercurrent

  15. RF RF H D H Magnetization transport by Spin Supercurrent

  16. RF RF H D H Magnetization transport by Spin Supercurrent

  17. Critical spin currebt Phys.Rev.Lett v.62, p.1631, (1989).

  18. JM RF RF H D H Df 2p p 0 Josephson effect x JETPh Letters, v.47, p.478, (1988). QFS Florida 1989, AIP Conf. Proc., v.194, p.27.

  19. Spic current vortex

  20. Spin curent vortex Frequency and amplitude of the signal from pick-up coil after Homogeneous excitation Quadrupole excitation Physica B, v.165, p.649 (1990).

  21. Goldstone modes of HPD Yu.M.Bunkov, V.V.Dmitriev, Yu.M.Mukharskiy, "Twist Oscillations of Homogeneous Precession Domain in 3He-B", JETPh Letters, v.43, p.168, (1986). Yu.M.Bunkov, V.V.Dmitriev, Yu.M.Mukharskiy,"Low frequency oscillations of the homogeneously precessing domain in 3He-B",Physica B, v.178, p.196, (1992).

  22. PS Coherent, Magnetically Excited States Grenoble, 1999 Catastropha:Yu.M.Bunkov, V.V.Dmitriev, Yu.M.Mukharskiy, J.Nyeki, D.A.Sergatskov, Europhysics Letters, v.8, p.645, (1989). HPD Explanation: Yu. Bunkov, V. L’vov, G. Volovik, JETP Lett, (2006) Catastropha Persistent signal: Yu.M.Bunkov, S.N.Fisher, A.M.Guenault, G.R.Pickett, Phys, Rev, Letters, v.69, p3092, (1992). PS

  23. 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). Before rotation During rotation After rotation H

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

  25. 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). Following Landau and Lifchitz we consider an anharmonic oscillator with a third order of nonlinearity

  26. Magnons condensation in Q-balli In the orbital texturetrap CW NMR A.-S. Chen, Yu.M. Bunkov, H. Godfrin, R. Schanen, F. Scheffer. J. Low Temp. Phys, 110, 51, (1998), 113, 693 (1998). Yu.M. Bunkov “Persistent Signal; Coherent NMR state Trapped by Orbital Texture” J. Low Temp. Phys, 138, 753 (2005) Yu.M. Bunkov, G.E. Volovik, Phys. Rev. Lett., 98, 265302 (2007). 3D axisymmetric trap. wxy2r2 + wz2z2

  27. Calculated by V. Golo programm.

  28. 3D axisymmetric trap. wxy2r2 + wz2z2 Non-ground-state Bose-Einstein condensates of magnons in superfluid 3He-B AngleL-H

  29. 3D axisymmetric trap. wxy2r2 + wz2z2 AngleL-H

  30. New HPD state in 3He-B in a streched aerogel Institut NEEL, Grenoble HPD2

  31. Superfluid 3He-A in squeezed aerogel H d L L d T. Kunimatsu, T. Sato, K. Izumina, A. Matsubara,Y. Sasaki, M. Kubota, O. Ishikawa, T. Mizusaki, Yu.M.Bunkov Pisma v ZhETP, 86, 244 (2007)

  32. Conclusions The Spin Superfluidity, the magnetic counterpart of mass superfluidity and electric supercondactivity was discovered and widely studied in Moscow, Grenoble, Lancaster, Ithaca, Helsinki, Kosice, Kyoto, Tokio, Los-Alamos and by many theoreticians. There was discovered and observed: • The coherent transport of magnetization in superfluid 3He-B. • Its based only on an antiferromagnetic properties of 3He and can be found • in other magnetically ordered materials. • 3. The formation of domain with coherent precession of magnetization. • 4. This excited state correspond to a Bose-Einstein Condensation of spin waves. • 5. Josephson phenomena, critical current and phase slippage in a channel. • Different modes of HPD oscillations. • Horizontal and vertical Spin vortex. • HPD techniques was applied for studies of counterflow and mass vortices in • 3He, new types of vortex - spin-mass vortex was observed • 6 different states with coherent precession in A and B phases of 3He • Magon BEC was found recently in JYG. (Demokritov) Nature 443, 430 (2006).

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