spin currents through antiferromagnets … · interfaces nm afm '' ' '...
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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”