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Spin superfluidity and magnon Bose – Spin superfluidity and magnon Bose – Einstein condensationEinstein condensation
MicroKelvin, 2013
Yuriy BunkovYuriy BunkovInstitute Neel, CNRS, Grenoble, FranceInstitute Neel, CNRS, Grenoble, France
1. Review of Magnon BEC
2. Saga de Persistent signal
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 magnonsBEC and magnons spin supercurrent, notDirectly connected with mass superfluidity
Superfluid 3HeQuantum vacuumcharacterized by
phase S (magnetization) L (orbital momentum)
Quasiparticles
Magnons
Acoustic modes
Topological defects:
Boojum
Vortex
Brane
Particles:
Fields:
Texture of orbital momentum
Holstain-Primakoff transformation
0
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0 0.1 0.2 0.3 0.4 0.5Time, s.
Signal in the time domainA
B
0 100 200 300 400 500 600
0s.0.02s0.2s0.4s0.3s
Frequency shift, Hz.
Magnons destribution
0.03 s after the pulsebroadening 0.5 Hz
0.2 s after the pulsebroadening 2 Hz
0.3 s after the pulse( 2 Hz )
0.4 s after the pulse( 2 Hz )
Grenoble, 2003
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
Ideal gas
Quantum gas
BEC, superfluidity
Paramagnetic, Fermi liquid
Magnetically ordered
Coherent precession
H
H
H
Sx + iSy = S sin e it +i
=Hloc
=
2. Thermalized magnons = 0No BEC
1. Trap. It may be space trap (as for particle BEC) or even the trap of energy of magnons interactionH
S
2. Small angle of deflection
H
S
Not enough for BEC
For superfluid 3He critical angle is about 0.20
1. Trap. It may be space trap (as for particle BEC) or even the trap of energy of magnons interaction
2. Big angle of deflection H
SEnough for BEC but
Attractive interaction leads to instability of coherent precession. NO BEC
2. Big angle of deflection
1. Trap.
H
S
Repulsive interaction !BEC ?
May be NOT! If magnons live too short timeExample – 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)
H
CW NMRrf
= 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
20
JETPh Letters, v.47, p.478, (1988).
JosephsonJosephson
HPD 2
HPD 2
AerogelStycast
F
P Hunger, Yu M Bunkov, E Collin, and H Godfrin Journal of Physics: Conference Series. 400 012019 (2012)
Superfluid 3He-A in squeezed aerogel
Hd
L
dL
-1
-0.8
-0.6
-0.4
-0.2
0
0 0.5 1 1.5 2
-Domega-Domega/2-Domega3/41/2sinb2Domega/4
Fd + F
=L
2/2L
= L - A ; A=1
A=3/4
A=1/2
A=1/4
A=0
2
In rotating frame
0
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-1 -0.5 0 0.5 1
Excit=0.1VExcit=0.5VExcit=1.5VExcit=3.0VExcit=4.0VamplSignal
f [kHz]
Am
plit
ud
e (M
)
ba
edc
P. Hunger, Y. M. Bunkov, E. Collin and H. Godfrin« Evidence for Magnon BEC in Superfluid 3He-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)
0
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1
-1 -0.5 0 0.5 1
Excit=0.1VExcit=0.5VExcit=1.5VExcit=3.0VExcit=4.0VamplSignal
f [kHz]
Am
plit
ud
e (M
)b
aedc
CsMnF33He-A in aerogel
CW NMR experiments
-1
-0,5
0
0,5
1
0 30 60 90 120 150 180
Frqlo
Angle
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).
RbMnF3 and MnCO3 OIST 2013
RbMnF3
MnCO3
Theoretical prediction for saturation
Magnon BEC
Saga de Persistent signal
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
HPD
Catastropha
PSPS
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).
2. Coherenent State, which radiates the Persistent signal
Moscow resultsYu.M.Bunkov, S.N.Fisher, A.M.Guenault, G.R.Pickett, S.R.Zakazov, Physica B, v. 194, p. 827, (1994).
Discovery, Lancaster, 1992Yu.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 conformationYu.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
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).
LA
ng
le L
-H
Before rotation During rotation After 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).
H H
H
=H+ Hz
Quantum billiard
Anne-Sophie CHEN, Ph D Thesis, Grenoble, (1999)
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).
0
20
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100
0 10 20 30 40 50Position in the cell
S
L H H
Computer simulationGrenoble 2004
H
Lz
LH
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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Grenoble, 2004
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Oscillations
Position in the cell, mm
S
L
n
L=R(n) S
1% HPD
Grenoble, 1999Off-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
pd
rf
rf
Qb
dd
