josephson and persistent spin currents in bose-einstein condensates of magnons
TRANSCRIPT
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Kouki Nakata
Josephson Effects & Persistent Spin Currents in Magnon-BEC due to Berry Phase
University of Basel, Switzerland
Based on [arXiv:1406.7004]
[Note] All the responsibility of this slide rests with Kouki Nakata; Sep. 2014.
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MAIN AIM
Persistent spin current
To CONTROL spin currents
Direct measurement
(i.e. super spin current)
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Rapid PROGRESS of experiments
BACKGROUND
Spin-wave spin current
Quasi-equilibrium magnon-BEC
Achieved even at room temperature by using microwave pumping
(Low temperature is not required.)
Ferromagnetic insulator (YIG)
[Y. Kajiwara et al., Nature 464, 262 (2010)]
[S. O. Demokritov et al., Nature 443, 430 (2006)]
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BEC
BEC
BoseEinstein condensation of quasi-equilibrium magnons at room temperature under pumping [S. O. Demokritov et al., Nature 443, 430 (2006)]
Based on
Can be semi-classically treated Canonically conjugate variables; [, ]
=
~ += +
~ Direction of spin
~ Length of macroscopic spin
Semantic issue; Y. M. Bunkov and G. E. Volovik, arXiv:1003.4889. Textbook by Leggett D. Snoke, Nature 443, 403 (2006). C. D. Batista et al., RMP. 86, 563 (2014).
Macroscopic coherent state Quantum effects Individual spins/quasi-particles
Condensed time: over a few hundred ns.
Magnon-BEC
; Phase BEC
Quasi-equilibrium Magnon-BEC
Magnon picture
Spin picture
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BEC
BEC
BoseEinstein condensation of quasi-equilibrium magnons at room temperature under pumping [S. O. Demokritov et al., Nature 443, 430 (2006)]
Based on
=
~ += +
Semantic issue; Y. M. Bunkov and G. E. Volovik, arXiv:1003.4889. Textbook by Leggett D. Snoke, Nature 443, 403 (2006). C. D. Batista et al., RMP. 86, 563 (2014).
Macroscopic Spin
BEC
Quasi-equilibrium Magnon-BEC
Magnon picture
Macroscopic coherent state Quantum effects Individual spins/quasi-particles
Condensed time: over a few hundred ns.
Magnon-BEC
; Phase
~ Direction of spin
~ Length of macroscopic spin
Can be semi-classically treated Canonically conjugate variables; [, ]
Spin picture
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HOW TO ACHIEVE
Berry phaseGeometric phase
Quasi-equilibrium magnon-BEC
Persistent magnon-BEC current
To electro-magnetically control spin currents
Macroscopic quantum effect (coherence) Spin currents; drastically ENHANCED !!
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Spin Current Persistent magnon-BEC current
Under our control Direct measurement
Electromagnet
Toward the direct measurement of spin (magnon) current
Berry Phase
Aharonov-Casher(A-C)
Magnon-BEC (Ferromagnetic insulator)
Macroscopic Effect
CONCEPT
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OUTLINE INTRODUCTION
REVIEW
SUMMARY
RESULT Josephson effects
Persistent magnon-BEC current (i.e. super spin current)
Magnon-BEC Josephson junction (MJJ)
SYSTEM
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REVIEW
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Superconductors (SC)
[Cooper pair] = [Boson]
B. D. Josephson, [Phys. Lett. 1, 251 (1962)]
1962~
=
2J
sin()
=
2()
Josephson equations in SC
dc Josephson effect;
= 0
Relative phase is time-independent;
= 0
; Josephson current charge current
Josephson current
J (tunneling) (1973) Textbook by Leggett
w.f. w.f.
Josephson Effects Universal Phenomenon of bosonic particles
(); the external voltage applied across the junction
J (> 0); the tunneling amplitude,
the relative population, ; the relative phase
Fig by [Fa Wang and Dung-Hai Lee, Science, 332 (2011) 200]
Fig by [J. Q. You and F. Nori, Nature, 474, 589 (2011)]
Picture by Google search (HP for novel prize).
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Universal Phenomenon of bosonic particles
Anderson et al., Science (95)
Atomic BEC
Atomic BEC Magnon BEC
[Magnon] = [Bosonic quasi-particle]
Josephson Effects
B. D. Josephson, [Phys. Lett. 1, 251 (1962)]
Berry Phase (Aharonov-Casher phase)
1962~ 1997~ Now
We (Our present work)
Superconductors (SC)
[Cooper pair] = [Boson]
A. Smerzi et al., [PRL. 79, 4950 (1997)] [PRA, 59, 620 (1999)] [PRL. 84, 4521 (2000)] Leggett [Rev. Mod. Phys. 73, 307 (2001)]
M. Albiez et al. [PRL. 95, 010402 (2005)] S. Levy et al. [Nature 449, 579 (2007)]
(2001) (1973)
Fig by [Fa Wang and Dung-Hai Lee, Science, 332 (2011) 200]
Picture by Google search (HP for novel prize).
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Berry Phases Aharonov- Bohm phase [Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959)]
Aharonov- Casher phase [Y. Aharonov and A. Casher, PRL, 53, 319 (1984)]
Charged particle; Magnetic dipole; =
; (Magnon)
Magnetic vector potential [Electric field][Magnetic dipole];
AB =
=:
AB
AC =2
( )
AB
Special cases of Berry phase [R. Mignani, J. Phys. A: Math. Gen. 24, L421 (1991)] [X.-G. Hea and B. McKellarb, Phys. Lett. B 264, 129(1991)]
A special case of Berry phase
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Microwave Pumping
Magnon
Magnon-BEC (macroscopic state)
Magnon pumping Room temperature
[S. O. Demokritov et al., Nature 443, 430 (2006)]
Excite additional magnons. Create a gas of quasi-equilibrium magnons with a non-zero chemical potential. A Bose condensate of magnons is formed.
Microwave pumping
We can directly inject magnons so that it becomes a macroscopic number (BEC).
[K. Nakata and G. Tatara, J. Phys. Soc. Jpn. 80, 054602 (2011).] [K. Nakata, Doctoral Thesis, Kyoto University (2014).]
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Magnon
Magnon-BEC (macroscopic state)
Magnon pumping Room temperature
= +
BEC order parameter
Quasi-equilibrium Magnon-BEC
[S. O. Demokritov et al., Nature 443, 430 (2006)]
BEC~1018 1919cm3
[Y. M. Bunkov and G. E. Volovik, arXiv:1003.4889.]
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[C. D. Batista et al., Rev. Mod. Phys., 86, 563 (2014).]
[Y. M. Bunkov and G. E. Volovik, arXiv:1003.4889.]
Quasi-equilibrium Magnon-BEC [Metastable state][Ground state]
[J. Hick et al., Phys. Rev. B 86, 184417 (2012)] [T. Kloss et al., Phys. Rev. B 81, 104308 (2010)] [S. M. Rezende, Phys. Rev. B 79, 174411(2009)] [F. S. Vannucchi et al., Phys. Rev. B 82, 140404(R) (2010)] [F. S. Vannucchi et al., EPJB 86 (2013) 463] [S. M. Rezende, Phys. Rev. B 79, 174411 (2009)]
Thermalization process
= +
BEC order parameter
[K. Nakata and G. Tatara, J. Phys. Soc. Jpn. 80, 054602 (2011).] [K. Nakata, Doctoral Thesis, Kyoto University (2014).]
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OUR WORK SYSTEM
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E = E
, ,
J
J
,
,
L
R
A-C phase:
Magnon BEC Josephson Junction
Tunneling Hamiltonian (boundary spins)
Hamiltonian of each single FIs (Magnon BECs)
with Diag = J{1, 1, }, J < 0
E = E
H =(Gross-Pitaevskii Hamiltonian; GP)
Microscopic spin model
Electric field (E = E)
Magnon picture
( Jex J )
Magnon BEC (Holstein-Primakoff tr.);
~ += +
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Magnon picture
BEC
= ~ += +
, ,
CALCULATION PROCEDURE
Spin picture
Canonically conjugate variables [, ]
BEC BEC
Macroscopic Spin
Macroscopic Spin
Magnon-BEC
; Phase
T: = L +R Population imbalance; (L R)/T,
Relative phase; R L
~Two macroscopic spins interact with each other through
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EACH VALUE
E = E
Each Value Our estimation
The exchange interaction between the two FIs Jex = 1eV
The exchange interaction between the neighboring spins in a single FI J 0.1eV
The density of magnpn-BECs [S. O. Demokritov et al., Nature (2006).] nBEC = 1019cm3
The applied magnetic field 1mT
The applied electric field to the interface 5GV/m
The width of the interface 10
The lattice constant of a FI 1
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RESULTS
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Josephson Equations in MJJ
;Renormalized time = 1 = 1ns (ex. K0/ Jex = 1eV)
Josephson spin current
nL, L
E = E
nR, R
& ; renormalized magnetic field difference & mag-mag interaction in terms of K0 (K0 ; tunneling magnitude)
nT: = nL + nR
Population imbalance; z (nL nR)/nT
Relative phase; R L
A-C phase;
x; the width of the interface (~)
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[Period]~ns
ac Josephson Effect
;Renormalized time = 1 = 1ns (ex. K0/ Jex = 1eV)
No Aharonov-Casher phase;
~(Chemical potential difference)
Condensed time: over a few hundreds ns.
S. O. Demokritov et al., Nature 443, 430 (2006).
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dc Josephson Effects
=
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Time-dependent Magnetic Field i) Increasing rate; ii) Josephson equation (weak coupling)
; electric field ; magnetic field (increasing rate)
dc effect = (steady-state solution)
( = 0) = 0
E = E
R L
z (nL nR)/nT nL, L nR, R
; renormalized mag-mag interaction in terms of K0 (K0 ; tunneling magnitude)
UL UR
Jex J
-
dc Josephson Effect 0
= 1 ~1ns
= (+ small oscillation in z)
Atomic BEC; A. Smerzi et al., [PRL. 79, 4950 (1997)] [PRA, 59, 620 (1999)] [PRL. 84, 4521 (2000)]
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dc-ac Transition; = / 0
(c) dc-ac transition; .
0 = 0.10
0 = 0.724
0 = 0.726
0 = 1.1
dc-ac Transition
(d) dc-ac transition;
0 = 0.726
0 = 0.726
Recovery due to A-C phase
= 1 ~1ns = 1 ~1ns
dc effect
ac effect
dc effect
ac effect
Atomic BEC; A. Smerzi et al.,
[PRL. 79, 4950 (1997)] [PRA, 59, 620 (1999)] [PRL. 84, 4521 (2000)]
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Persistent Magnon-BEC Currents
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Magnon-BEC Ring
Electric-gradient flux
Single-valuedness of the BEC wave function
In analogy to superconducting rings
; phase winding number
Electric flux quantum
Persistent magnon-BEC current
The A-C phase in the ring
Quantized electric-gradient flux
(, ) =
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Direct Measurement
1013V
nBEC = 1019cm3
J 0.1eV
[F. Meier and D. L., PRL 90, 167204 (2003).]
[Persistent magnon-BEC current ] = [Steady flow of the magnetic dipoles] (i.e. magnons or magnetic moment
) Moving magnetic dipoles Electric dipole fields Voltage drop .
S. O. Demokri tov et al., Nature (2006).
; Spin chains
Largely enhanced due to Macroscopic coherence
[D. Loss and P. M. Goldbart, PLA 215, 197 (1996)]
0 = 1mm
0 = 1mm
Vm~1nV
= 2, = 1/2
, times!!
10mm
50 (Phase winding number; = 0 )
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REMARKS
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Analogous Phenomenon
Magnon Josephson effect Magnon Hall effect
Dzyaloshinskii-Moriya interaction
Temperature gradient
Onose et al. [Science 329, 297 (2010)]
[Josephson spin current] [Electric field] [Thermal spin current] [temperature gradient]
Key point; Transverse spin currents
Picture from [Science 329, 297 (2010)]
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SIGNIFICANCE
The Bose Josephson junction (BJJ) of atomic BEC
=
The magnon Josephson junction (MJJ)
M. Albiez et al. [PRL. 95, 010402 (2005)] S. Levy et al. [Nature 449, 579 (2007)]
Leggett [Rev. Mod. Phys. 73, 307 (2001)]
A. Smerzi et al., [PRL. 79, 4950 (1997)] [PRA, 59, 620 (1999)] [PRL. 84, 4521 (2000)]
[Theory] [Experiment]
Exact dc Josephson effect Time-dependent magnetic field Aharonov-Casher phase
ac-dc transition Persistent magnon-BEC current
Magnon-interference Aharonov-Casher phase
Cold atom
[Our work on MJJ] = [The generalization of the preceding studies on BJJ]
Picture by Google search.
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LAST MESSAGE
Phys. Lett. A, 96 (1983), p. 365
Our work [arXiv:1406.7004]
Persistent (charge) current due to the Aharonov-Bohm phase
Persistent magnon-BEC current due to the Aharonov-Casher phase
K. N., K. A. van Hoogdalem, P. Simon, and D. Loss
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SUMMARY
Josephson Effects & Persistent Spin Currents in Magnon-BEC due to Berry Phase
I). How to electromagnetically control Josephson spin currents [Period of ac Josephson effect]~10ns
III). How to directly measure the Josephson magnon-BEC currents The resulting voltage drop from the flow of the magnons (i.e. magnetic dipoles). It is largely enhanced due the macroscopic coherence of magnon-BECs; Vm~1nV 10
13V This method is applicable to Josephson junction; 0 Vm 1V due to ac or dc effects.
II). Persistent magnon-BEC current (i.e. super spin current) due to the Berry phase It is quantized in the magnon-BEC ring.
Regarding macroscopic quantum self-trapping, please see the preprint [arXiv:1406.7004].
Each Value Our estimation
The exchange interaction between the two FIs Jex = 1eV
The exchange interaction between the neighboring spins in a single FI J 0.1eV
The density of magnpn-BECs [S. O. Demokritov et al., Nature (2006).] nBEC = 1019cm3
The applied magnetic field 1mT
The applied electric field to the interface 5GV/m
The width of the interface (The lattice constant 1) 10
Based on [arXiv:1406.7004] K. N., K. A. van Hoogdalem, P. Simon, and D. Loss