Spin currents through antiferromagnets

Rembert DuineInstitute for Theoretical Physics, Utrecht University

Department of Applied Physics, Eindhoven University of Technology

Collaborators

Utrecht:Benedetta Flebus, Scott Bender

Other:Alvaro Nunez, Alejandro Roldan (Santiago)Yaroslav Tserkovnyak (UCLA)Arne Brataas (NTNU)

See Scott’s poster for more

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?

MotivationImage courtesy Ludo Cornelissen and Bart van Wees; Nat. Phys (2015)

- Pt strips on magnetic insulator Yttrium-Iron-Garnett (YIG)- Non-local (“drag”) resistance RD=V/I- Room T- Long distance: exponential decay (length scale 10 µm)- See also Goennenwein et al. (2015), Jing Shi et al. (2016) - Related talks: Baltz, Hoffmann, Goennenwein, Klaui, …

Outline• Stochastic Landau-Lifshitz-Gilbert theory for spin

currents through antiferromagnetic insulators

• Application to non-local drag and spin Seebeckeffect

• Second part: spintronic black-hole physics

Outline• Stochastic Landau-Lifshitz-Gilbert theory for spin

currents through antiferromagnetic insulators

• Application to non-local drag and spin Seebeckeffect

• Second part: spintronic black-hole physics

Other theoretical work• Brataas, et al: Heat transport between

antiferromagnetic insulators and normal metals, Phys. Rev. B 92, 180414 (2015)

• Takei, et al., Phys. Rev. B 90, 094408 (2014); Khymyn, et al., Phys. Rev. B 93, 224421 (2016); Rezende et al., Phys. Rev. B 93, 014425 (2016); Nowak, et al.; ...

• This work: field dependence below spin-flop transition, sublattice-dependent interface coupling

Set-up

( )22 212 2 2 z z

A KE dx am n n Hmæ ö+ Ñ - -ç ÷è øò

r r r:

exchange anistropy field

S. Bender, et al. (to be submitted)

Approach• Consider fields below spin-flop transition

• Stochastic Landau-Lifschitz-Gilbert equations with coloured noise for Néel and magnetization vectors

• Coupling with electrons at interface: extra Gilbert damping contributions + reciprocal spin transfer torques [Cheng, et al. (2014); Takei, et al. (2014)]

• Applicable when Gilbert damping only relaxation mechanism (clean systems at low T).

Sublattice-dependent coupling with electrons at

interfaces

NM AFM

' ' ' '

interface 2 2a b a bdn dm dn n

dt dt dta a a aé ùæ ö æ ö+ -

= - - ´ê úç ÷ ç ÷è ø è øë û

r r r rFor example:

S. Bender, et al. (to be submitted)

AFMR absorption

Dependent on sublattice-dependenceof coupling with electrons @ interface

S. Bender, et al. (to be submitted)

Outline• Stochastic Landau-Lifshitz-Gilbert theory for spin

currents through antiferromagnetic insulators

• Application to non-local drag and spin Seebeckeffect

• Second part: spintronic black-hole physics

Spin Seebeck effect• Definition:

• Symmetric and anti-symmetriccontribution:

j S T= D

( )( )

( )

aB

a bsS k TS a

a a-:

S. Bender, et al. (to be submitted)

Spin conductance• Definition:

• Divergesat spin-floptransition(spinsuperfluidity)

• Increaseswith T

• Length scale: L/a1/2

j G µ= D ( )( )

( )

a

a bsGG

a a-:

S. Bender, et al. (to be submitted)

Outline• Stochastic Landau-Lifshitz-Gilbert theory for spin

currents through antiferromagnetic insulators

• Application to non-local drag and spin Seebeckeffect

• Second part: spintronic black-hole physics

Outline• Stochastic Landau-Lifshitz-Gilbert theory for spin

currents through antiferromagnetic insulators

• Application to non-local drag and spin Seebeckeffect

• Second part: spintronic black-hole physics

Outline• Stochastic Landau-Lifshitz-Gilbert theory for spin

currents through antiferromagnetic insulators

• Application to non-local drag and spin Seebeckeffect

• Second part: spintronic black-hole physics“general-relativistic spintronics”

Hawking radiation

Quantum mechanics + general relativity: black-hole thermodynamics, information paradox, …

Hawking (1974)

Black-hole-horizon analogues

vfish > vflowvfish < vflow

• Goal: observe radiation, solve conceptual issues

• Systems: water, atomic BEC’s and other condensates,slow light, …

Unruh (1981)

Black-hole-horizon analogues

vfish > vflowvfish < vflow

• Goal: observe radiation, solve conceptual issues

• Systems: water, atomic BEC’s and other condensates,slow light, …

Unruh (1981)

• Metallic antiferromagnets (or metallic easy-plane ferromagnets)

• Spin-transfer torques give flow velocity vs ~ current density *)

• Increasing current density (can) create horizon if vs > spin-wave velocity

Our proposal (I)

*): Nunez et al. (2005), Swaving et al. (2011), Hals et al (2011)., Yamane, et al. (2016)

A. Roldan. A.S. Nunez, RD (to be submitted)

Our proposal (II)

v jrr :

22

2

1 v n nc t

d d¶æ ö+ ×Ñ = Ñç ÷¶è ør r r

v<c v>c v<c

Linearizeddynamics:

A. Roldan. A.S. Nunez, RD (to be submitted)

Our proposal (III)v j

rr :

• Black-hole horizon will radiate magnons with Hawking temperature[Hawking, 1974]:

• Estimates: c~km/s, jc~1012 Am-2, TH~1 K

horizon

( )2H

v cTnp

¶ -¶

h:

A. Roldan. A.S. Nunez, RD (to be submitted)

Possibilities for experimental detection (I)

• Classical signature in spin-wave transmission :

• Cf. measurement of spin-wave Doppler shift in ferromagnets:

( ) B Hk Tt ew

w-h

:

Science (2008)

A. Roldan. A.S. Nunez, RD (to be submitted)

Possibilities for experimental detection (II)

• Transport signature:

• For all transport quantities:

• E.g.: magnon-drag Peltier effect

( )BnG d tw ww

¶æ ö-ç ÷¶è øò:1 1 1

HT T T® +

A. Roldan. A.S. Nunez, RD (to be submitted)

Further remarks• Relatively large Hawking temperature• Experimental signatures• Anisotropy, fields and damping• Instabilities & non-linearities (domain walls)• Long term: resource for entanglement

[NY = ´ v k- - u k+ + ùû

Take home messages:• Antiferromagnetic spin

conductance becomeslarge upon approachingspin-flop transition

• Magnon black-hole horizonsare realizable, detectable, and ultimately may serve as resourcefor entanglement

S. Bender, et al. (to be submitted)

A. Roldan. A.S. Nunez, RD (to be submitted)

“black holeson a chip”