superfluidity and spin superfluidity

Superfluidity and spin superfluidity

(in spinor Bose gases and magnetic insulators)Rembert Duine

Institute for Theoretical Physics, Utrecht UniversityDepartment of Applied Physics, Eindhoven University of

Technology

Nature Physics 11, 1022–1026 (2015), Phys. Rev. Lett. 116, 117201 (2016), arXiv:1603.01996 [cond-mat.quant-gas], arXiv:1604.03706 [cond-mat.mes-hall]

Collaborators

Utrecht:Benedetta FlebusKevin PetersGerrit Bauer (also Delft/Sendai)

Other:Jogundas Armaitis (Vilnius) Ludo Cornelissen, J. Liu, Bart van Wees (Groningen)Yaroslav Tserkovnyak, Scott Bender (UCLA->UU)J. Ben Youssef (Brest), Arne Brataas (NTNU)

Long-term motivation

superconductorlead lead

L

I=V/R with R independent of L

below room T

spin superfluid lead lead

L

?

above room T?

Outline• Introduction superfluidity and spin superfluidity

• Spinor gases: combining superfluidity and spin superfluidity (theory)

• Spin transport through magnetic insulators (theory and experiment)

Superfluid (mass) transport

ccjt

c c cj v

t

= ic e

+supercurrent:

Superfluid U(1) order parameter:

cJ k stiffness interactions

Wave-like excitations:

cg

If zero then 2sJ k

(ballistic transport)c

c cv J m

Im

Re

carried bycondensate

chemicalpotential

2

neigbours

; , ,

ixc i j xc

j i

xc

dS J S S J S S jdt

j J S S x y z

,xc i j

i j

H J S S

(ballistic) spin transportMagnetic insulator(exchange only)

Landau-Lifschitzequation:

spin current:

2xcJ k particle-like excitations: spin waves/magnons

Halperin/Hohenberg (1969)

2

1 1z z

xc i i i i ii i i

H J S S S K S B S

Spin superfluidity (I)Easy-plane magnetic insulator [SO(3) -> U(1)]

Halperin/Hohenberg (1969); review: Sonin (2010)

exchange anisotropy field

2 31BEC B xcT k J B K

Review: Giamarchi (2008)

†

ˆ2 Re

ˆ~ 2 Im

ˆ ˆ 1

a

S a

a a

Holstein-Primakofftrafo:

Spin superfluidity (II)

2 ˆ ˆzxc

dS J S S KS z Bzdt

Zero T dynamics governed by Landau-Lifshitz equation:

Write: 2 cos

~ 2 sin1

c

c

c

n

S nn

2cxc c s

c

n J n jt

B K Knt

Same as equationsfor mass superfluid!

Halperin/Hohenberg (1969); Koenig et al. (2001); review: Sonin (2010)

xc cJ Kn k

Spin superfluidity (III)

, ; polarization in -directions xc cj J n z

• mass current jc• phase of superfluid

order parameter • superfluid stiffness Js

• interparticleinteractions g

• spin current js• in-plane angle of

magnetization • exchange interactions

Jxc

• easy-plane anisotropy K

Mass vs. spin superfluidityHalperin/Hohenberg (1969); review: Sonin (2010)

ic e

Related work• Our work: hydrodynamic description treating spin

and mass superfluidity on equal footing

• Spin currents in spinor gases:- K. Kudo and Y. Kawaguchi, Physical Review A 84, 043607 (2011).- H. Flayac, et al., Physical Review B 88, 184503 (2013).- Q. Zhu, Q.-f. Sun, and B. Wu, Phys. Rev. A 91, 023633 (2015).

• Stability of spirals:- R. W. Cherng, et al., Phys. Rev. Lett. 100, 180404 (2008).

• Magnon condensation:- Fang, et al., Phys. Rev. Lett. 116, 095301 (2016) – tonight’s evening talk (?).

• Reviews:- Y. Kawaguchi and M. Ueda, Physics Reports 520, 253 (2012).- D. M. Stamper-Kurn and M. Ueda, Rev. Mod. Phys. 85, 1191 (2013).

• Which system is both a mass and spin superfluid?

• What is the interaction between mass and spin superfluidity in such a system?

NB: a ferromagnetic mass superfluid

Questions

spin superfluid

Ferromagnetic spinor Bose with quadratic Zeeman effect

2 2 22 2† † †

0 1ˆ ˆ ˆ ˆ ˆ ˆ ˆ

2z zH dx BF K F g g F

m

We have hamiltonian:

Deep in ferromagnetic regime, zero T linearized mean-field equations reduce to equations for uncoupled mass and spin superfluid with:

s xcJ J m

field

Superfluid and spin stiffness:

Collective modes:

g1<0, leads toferromagnetism

0 1mass c g g mk

spin

K K Bk

m

Armaitis and RD, arXiv (2016)

easy-plane anisotropy

leads to Bosecondensation

Collective (Goldstone) modesT

TFM

TBEC

Tmagnon BEC

quadratic spin modes

linear density + quadratic spin modes

linear density & spin modes

ferromagnet

superfluid ferromagnet

superfluid & spin superfluid

Coupling between spin and mass superfluid

with zv v nt t m

Occurs via hydrodynamic derivative:

Influence of spin polarizedmass current on magnetizationdynamics: “spin transfer” Current driven by

magnetic texture


Stationary solutions

' '2 '

z

s

n KJ

Stationary solutionspossible if:


• Dipolar interactions (lower critical current)• Upper critical current• Quasi-equilbrium magnon condensation• Magnon kinetics• Coupling to nematic/antiferromagnetic

order

Discussion

Long-term motivation

superconductorlead lead

L

I=V/R with R independent of L

below room T

spin superfluid lead lead

L

?

above room T?

Experiment (I)

- Pt strips on magnetic insulator Yttrium-Iron-Garnett (YIG)- Non-local (“drag”) resistance RD=V/I- Room T

Experiment (II)

- Short distance: 1/distance- Long distance: exponential decay (length scale 10 m)

IdeaElectron charge current

Electron spin current

Magnon spin current

Electron spin current

Electron charge current

Magnon spintronics: electical control over magnon spin currents

Magnonic many-body physics

Route to spin currents with low dissipation

Image courtesy Ludo Cornelissenand Bart van Wees

Interfacial spin current

R=V/I 2cos cos cos= *

Model

22

s m

m

j

magnon diffusion & relaxation: signal ~

/ mLe

For spin superfluid this would be ~ 1

1 C LTakei and Tserkovnyak (2014); Flebus, Bender, Tserkovnyak, RD (2016)

Take home messages• Spin superfluidity is not ferromagnetic superfluidity

• Spinor Bose gas can be spin and/or mass superfluid

• Recent developments of spintronics pave the way for integration electronic and magnonic (eventually superfluid) low-dissipation spin currents & bosonic many-body physics

superfluidity and spin superfluidity

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