Josephson and Persistent Spin Currents in Bose-Einstein Condensates of Magnons

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.

MAIN AIM

Persistent spin current

To CONTROL spin currents

Direct measurement

(i.e. super spin current)

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)]

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

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


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

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 !!

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

OUTLINE INTRODUCTION

REVIEW

SUMMARY

RESULT Josephson effects

Persistent magnon-BEC current (i.e. super spin current)

Magnon-BEC Josephson junction (MJJ)

SYSTEM

REVIEW

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).

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).

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

Microwave Pumping

Magnon

Magnon-BEC (macroscopic state)

Magnon pumping Room temperature


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).]

Magnon

Magnon-BEC (macroscopic state)

Magnon pumping Room temperature

= +

BEC order parameter



BEC~1018 1919cm3

[Y. M. Bunkov and G. E. Volovik, arXiv:1003.4889.]

[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).]

OUR WORK SYSTEM

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.);

~ += +

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

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

RESULTS

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 (~)

[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).

dc Josephson Effects

=

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)]

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)]

Persistent Magnon-BEC Currents

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

(, ) =

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 )

REMARKS

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)]

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.

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

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