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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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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

BEC of spin waves?

Magnetically

ordered states

Superfluids,

superconductors

Universe

H

H

H

w=gHloc

Ideal gas

Paramagnetic

Magnetically ordered

Quantum gas

w=w0

Sx + iSy = Ssinbe iwt +ia

BEC, superfluidity

Coherent precession

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).

Grenoble, 2003

( 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

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

Gross-Pitaevskii equation

Spin-Orbit interaction energy in 3He-B

M II H

M I H

L II H

f

D

D

H

D

ki

Mass superflow

Spin supercurrent

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

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

RF

H

D

H

Magnetization transport by Spin Supercurrent

RF

RF

RF

H

D

H

Magnetization transport by Spin Supercurrent

RF

RF

H

D

H

Magnetization transport by Spin Supercurrent

RF

RF

H

D

H

Magnetization transport by Spin Supercurrent

RF

RF

H

D

H

Magnetization transport by Spin Supercurrent

Critical spin currebt

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

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.

Spic current vortex

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).

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).

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

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

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

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

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

Calculated by V. Golo programm.

3D axisymmetric trap.

wxy2r2 + wz2z2

Non-ground-state Bose-Einstein condensates of magnons in superfluid 3He-B

AngleL-H

3D axisymmetric trap.

wxy2r2 + wz2z2

AngleL-H

New HPD state in 3He-B in a streched aerogel

Institut NEEL, Grenoble

HPD2

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)

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).