Topological proximity effect

Spin Pumping and Spin-Transfer Torque in Magnetic Tunnel Junctions and Topological

Insulators: Theory and Experiments

Branislav K. NikolićDepartment of Physics & Astronomy, University of Delaware, Newark, DE 19716, U.S.A.

1638–1655

NQS 2017, Kyoto

https://wiki.physics.udel.edu/qttg

Topological Proximity Effect in Ferromagnetic Metals:

Fundamentals and Spintronic Applications

Topological proximity effectNQS 2017, Kyoto

Collaborators Theory

Dr. Po-Hao Chang

Experiment

Prof. J. Q. Xiao Dr. Farzad Mahfouzi

Prof. N. NagaosaProf. J.-P. Wang Dr. Kurt StokbroProf. Nicholas Kioussis

J. M. Marmolejo-Tejada

Computation

Dr. Kapildeb Dolui

Topological proximity effect

Spin-Transfer Torque: Fundamentals and Applications

NQS 2017, Kyoto

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pplic

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ns{

Topological proximity effect

Quantum Transport Theory is Needed to Describe STT

NQS 2017, Kyoto

Topological proximity effect

Spin-Orbit Torque (SOT): Fundamentals and Applications

NQS 2017, Kyoto

Fund

amen

tals

App

licat

ions{

{PRL 119, 077702 (2017)

T=300 K

Nat. Mater. 12, 240 (2013)

solid-state nonvolatile analogue memory with infinite read-write endurance

Topological proximity effect

Current-Driven Nonequilibrium Spin Density as the Origin of Fieldlike SOT

NQS 2017, Kyoto

Topological proximity effect

Quantum Transport Theory (Which One?) is Needed to Describe Interfacially-Driven Antidamping SOT

NQS 2017, Kyoto

Nature 511, 449 (2014)PRB 93, 125303 (2016)

PRB 90, 174423 (2014); PRB 96, 014408 (2017) PRB 91, 134402 (2015); Nat. Nanotech. 9, 211 (2014)

SHE antidamping torque

PRB 84, 113407 (2011)PRB 86, 161406(R) (2012)arXiv:1604.07885

Berry curvature antidamping torque

MISSING INGREDIENTS: 3D geometry and switching at the boundaries

PRB 86, 014416 (2012)

PRB 95, 094401 (2017)

antidamping torque is zero in the absence of

spin-dependent scattering

missing diagrams

PRB 94, 104419 (2016) PRB 94, 104420 (2016)

Nat. Nanotech. 12, 980 (2017)

Topological proximity effect

Trouble with Simplistic Hamiltonians for Describing SOT Experiments

NQS 2017, Kyoto

Nature 511, 449 (2014)

“Our findings have potential importance for technology, in that the spin torque ratio for Bi2Se3

at room temperature is larger than that forany previously measured spin current source

material. However, as noted above, for practical applications the specific layer structure of our

devices (topological insulator/metallic magnet) does not make good use of this high intrinsic efficiency

because most of the applied current is shuntedthrough the metallic magnet and does not contribute

to spin current generation within the topological insulator. Applications will probably require coupling

topological insulators to insulating (or high-resistivity) magnets so that the majority of the

current will flow in the topological insulator.”

Topological proximity effect

Trouble with Simplistic Hamiltonians for Describing Spin-to-Charge Conversion Experiments

NQS 2017, Kyoto

Nat. Comm. 4, 2944 (2013)

Nano Lett. 15, 7126 (2015)

PRL 113, 196601 (2014)

“possibly due to inhomogeneity of kF and/or instability of the helical spin structure”

Nature Phys. 12, 1027 (2016)

Topological proximity effectNQS 2017, Kyoto

This Talk in a Nutshell: ΨTM + ΨFM

What is the electronic and spin structure of interfacial states

and how they affect SOT?

Nano Lett. 17, 5626 (2017)

Topological proximity effect

Crash Course on Rashba SO Coupling

1D:

2D:G/WS2

NQS 2017, Kyoto

Topological proximity effect

Spin Density and Torque from Nonequilibrium Green Function (NEGF) Formalism

Fundamental quantities of NEGF formalism:

NEGF for steady-state transport:

density of available quantum states: how are those states occupied:

NEGF-based expression for spin-transfer torque:

NQS 2017, Kyoto

PRB 90, 045115 (2014)

SPIN 3, 1330002 (2013)

Learn more about NEGF from:

Most general torque formula valid in the presence of SOC and other

spin-nonconserving processes

Topological proximity effect

Current-Driven Nonequilibrium Spin Texture on the Surface and in the Bulk of Bi2Se3

PRB 92, 201406(R) (2015)

NQS 2017, Kyoto

Topological proximity effect

Spectral Function and Spin Textures on the TI Side of TI/FM Heterostructures

NQS 2017, Kyoto

Nano Lett. 17, 5626 (2017)

PRB 82, 195417 (2010)arXiv:1707.06319

Topological proximity effect

Spectral Function and Spin Textures on the TI Side of NM/TI/FM Heterostructures

NQS 2017, Kyoto

Nano Lett. 17, 5626 (2017)

Topological proximity effect

Spectral Function and Spin Textures on the FM Side of TI/FM Heterostructures

NQS 2017, Kyoto

Nano Lett. 17, 5626 (2017)

Topological proximity effect

Tunneling Anisotropic Magnetoresistance (TAMR) as a Probe of Interfacial Spin Texture

NQS 2017, KyotoNano Lett. 17, 5626 (2017)

Spin-orbit proximity effect

Adiabatic Expansion of NEGF Spits Out Expressions for Torque, Pumping and Gilbert Damping

NQS 2017, Kyoto

PRB 95, 113419 (2016)

charge current

charge pumping

spin torque

Gilbert damping

gives antidamping STT or field-like SOT

gives field-like STT or antidamping SOT+

+

+{ contains both equilibrium (should be

subtracted) and nonequilibrium contributions SPIN 3, 1330002 (2013)

Topological proximity effect

Spatial Profile of Antidamping SOT in TI/FI Heterostructures and the Role of Evanescent States

NQS 2017, Kyoto

PRB 95, 113419 (2016)

PRB

89, 1

9541

8 (2

014)

antidamping field-like

Topological proximity effect

xy

z

LLG Simulations of Magnetization Reversal and Switching Phase Diagram for TI/FI Bilayer

NQS 2017, Kyoto

PRB 92, 144424 (2015)APL 105, 212402 (2014)

PRB

95, 1

1341

9 (2

016)

SOT induced magnetization reversal by domain nucleation and propagation

Topological proximity effect

Exact Rotating Frame Approach to Spin Pumping in the Absence of Spin Flips

t tt

Δω

Lead Leadt

. . .. . .t

Ub

Sample

PRB 79, 054424 (2009)

NQS 2017, Kyoto

Topological proximity effect

Quantized Spin and Charge Pumping Due to Spin-Momentum Locking in 2D TIs

NQS 2017, Kyoto

PRB 82, 195440 (2010)

Topological proximity effect

How to Create 2D TI with Exposed SurfacePRB 93, 155104 (2016)

NQS 2017, Kyoto

Nano Lett. 14, 3779 (2014)

Topological proximity effect

Spin Pumping-to-Charge Conversion in TI/FM Heterostructures

PRB 90, 115432 (2014) Floquet-NEGF with ~10 exchanged photons: PRB 85, 054406 (2012)

Nan

o Le

tt. 1

5, 7

126

(201

5)Ambipolar electronic transport on the surface of an insulating bulk

Nat

ure

Phys

. 8, 4

59 (2

012)

NQS 2017, Kyoto

Topological proximity effect

Conclusions and Open Questions in Pictures

0 30 60 90 120 150 1800

1

2

HgTe: dTI=400, Ny=100, dFI=200

HgTe: dTI=200, Ny=50, dFI=100

GNR γSO=0 GNR γSO=0.03γ

Spin

Cur

rent

eIS z/Ñ

ω (e

/4π)

Precession Cone Angle θ (o)

NQS 2017, Kyoto

Spin-to-chargeconversion

Open questions: computationally

efficient ab initio calculations of SOT in

arbitrary geometry

SO torque

Spin Pumping and Spin-Transfer Torque in Magnetic Tunnel Junctions and Topological Insulators: Theory and ExperimentsCollaborators Spin-Transfer Torque: �Fundamentals and ApplicationsQuantum Transport Theory �is Needed to Describe STTSpin-Orbit Torque (SOT): �Fundamentals and ApplicationsCurrent-Driven Nonequilibrium Spin Density as the Origin of Fieldlike SOTQuantum Transport Theory (Which One?) is Needed to Describe Interfacially-Driven Antidamping SOTTrouble with Simplistic Hamiltonians �for Describing SOT ExperimentsTrouble with Simplistic Hamiltonians for Describing Spin-to-Charge Conversion Experiments This Talk in a Nutshell: ΨTM + ΨFM Crash Course on Rashba SO CouplingSpin Density and Torque from Nonequilibrium Green Function (NEGF) FormalismCurrent-Driven Nonequilibrium Spin Texture on the Surface and in the Bulk of Bi2Se3Spectral Function and Spin Textures on �the TI Side of TI/FM HeterostructuresSpectral Function and Spin Textures �on the TI Side of NM/TI/FM HeterostructuresSpectral Function and Spin Textures �on the FM Side of TI/FM HeterostructuresTunneling Anisotropic Magnetoresistance (TAMR) as a Probe of Interfacial Spin TextureAdiabatic Expansion of NEGF Spits Out Expressions for Torque, Pumping and Gilbert Damping �Spatial Profile of Antidamping SOT in TI/FI Heterostructures and the Role of Evanescent StatesLLG Simulations of Magnetization Reversal �and Switching Phase Diagram for TI/FI BilayerExact Rotating Frame Approach to �Spin Pumping in the Absence of Spin FlipsQuantized Spin and Charge Pumping �Due to Spin-Momentum Locking in 2D TIs How to Create 2D TI with Exposed SurfaceSpin Pumping-to-Charge Conversion �in TI/FM HeterostructuresConclusions and Open Questions �in Pictures