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 Cold gas of magnons, collective behavior Yu. M. Bunkov Institute Neel, CNRS, Grenoble, France

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

Ideal gas Quantum gas BEC, superfluidity Paramagnetic Magnetically ordered Coherent precession HHH S x + iS y = S sin  e i  t +i   =  H loc ==

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). Normal 3 He ~100% Superfluid 3 He Coherent spin precession in Superfluid 3 He-B

Grenoble, 2003

( h = 1; c ~ v F ) T F = 0.1K, T exp = K Magnon spectrum Magnon mass Magnon density Temperature of BEC Spin waves in superfluid 3 He are ready to be condensed! G.Volovik

Gross-Pitaevskii equation Gradient energy Spin Supercurrent Chemical potential  L (z  Spectroscopic energy True energy at the rotating frame Dipole-dipole spin-orbit energy F = A + (B+  l  l 2 + Cl  l 4 C < 0 ll2ll2 F C > 0  =0 B+  <0B+  >0

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

H    Mass superflow  kiki Spin supercurrent

L 104° R(n,  ) S H Dipole energy 0°  H x  =  H Dipole + magnetic gradient energy E x 104° 104°+   =  H Osheroff – Corruchini mode Brinkman – Smith mode   Bunkov, ICM, Kyoto, 2006 Coherent state

FdBphasa I J The magnetic relaxation leads to decrease of BEC region F D + F     =  L 2 /2  L  L )   =0  =0.05  = -  Yu.M. Bunkov and G.E. Volovik Bose-Einstein condensation of magnons in superfluid 3He J. of Low Temp. Phys. 150, 135, (2008)  H   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 Magnons BEC in the gradient of magnetic field F D = 0 for  <104° for  >104°

H H  RF

H H 

H H 

H H 

H H 

Phys.Rev.Lett v.62, p.1631, (1989).

H H  RF JMJM 22  0   QFS Florida 1989, AIP Conf. Proc., v.194, p.27. JETPh Letters, v.47, p.478, (1988).

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

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). 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).

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

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 rotationDuring rotationAfter rotation H

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).

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).

Magnons condensation in Q-balli In the orbital texture trap Yu.M. Bunkov, G.E. Volovik, Phys. Rev. Lett., 98, (2007). 3D axisymmetric trap.  xy 2 r 2 +  z 2 z 2 Yu.M. Bunkov “Persistent Signal; Coherent NMR state Trapped by Orbital Texture” J. Low Temp. Phys, 138, 753 (2005) CW NMR A.-S. Chen, Yu.M. Bunkov, H. Godfrin, R. Schanen, F. Scheffer. J. Low Temp. Phys, 110, 51, (1998), 113, 693 (1998).

Calculated by V. Golo programm.

3D axisymmetric trap.  xy 2 r 2 +  z 2 z 2 Angle L-H Non-ground-state Bose-Einstein condensates of magnons in superfluid 3He-B

3D axisymmetric trap.  xy 2 r 2 +  z 2 z 2 Angle L-H

HPD2 Institut NEEL, Grenoble

Superfluid 3 He-A in squeezed aerogel H d L d L 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)

1.The coherent transport of magnetization in superfluid 3He-B. 2.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. 5.Different modes of HPD oscillations. 6.Horizontal and vertical Spin vortex. 7.HPD techniques was applied for studies of counterflow and mass vortices in 3He, new types of vortex - spin-mass vortex was observed 8.6 different states with coherent precession in A and B phases of 3He 9.Magon BEC was found recently in JYG. (Demokritov) Nature 443, 430 (2006). 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: