Spin-Orbit Torque in Magnetic Bilayers - Spintronics Theory Group

Spin-orbit Torques in Metallic Bilayers 

A. Manchon, X. Wang, C. Ortiz-Pauyac, S. Grytsyuk, P. Barba Gonzalez, H. Li, P. 

Birame Ndiaye, U. Schwingenschlogl 

King Abdullah University of Science and Technology, 

Physical Science and Eng., KAUST, Saudi Arabia 

External collaborators 

Rashba Torque: M. Chshiev, Spintec, France 

Spin Hall effect: Kyung-Jin Lee, Korea University;Hyun-woo Lee, Postech; 

Mark Stiles, Paul Haney, NIST 

Dzyaloshinskii-Moriya: Kyung-Jin Lee, Korea University 

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Spintronics at KAUST 

Spin Transport Theory of Low Energy Consump7on Devices 

The Spintronics Theory Group 

We are recruiOng!! 

Post-‐Doctoral PosiOon 

Theory of Polariton Lasers 

And also 

Faculty posiOons, PhDs… 

h9p://Spintronics.kaust.edu.sa 

Collaborators 

S. S. P. Parkin, IBM Almaden 

P. Bha9acharya, U. Of Michigan 

X. Waintal, CEA; U. Schwingenschlogl, KAUST 

M. Chshiev, SPINTEC; K.-‐J. Lee, Korea University 

H. Yang, NUS; M.D. SOles, NIST 

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Consider Applying! 

Spintronics at KAUST 

Spin Transport Theory of Low Energy Consump7on Devices 

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1 st International Workshop on Spin-Orbit 

Torque at KAUST (Feb. 2013) 

Before… 

AXer… 

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1 st International Workshop on Spin-Orbit 

Torque at KAUST (Feb. 2013) 

Before… 

Listen to experimentalists! 

The controversy Spin Hall versus Rashba effect is meaningless (be.er interface v.s. bulk) 

Spin Hall AND Rashba probably present (even more complex) 

Band AXer… structure is sCll to be idenCfied (experiments v.s. theory) 

Dyakonov-‐Perel and Dzyaloshinskii-‐Moriya play an important role (which one?) 

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Outline 

I. Spin-‐Orbit Coupling Strikes Back 

AMR, AHE, SHE, Anisotropy, spin relaxa;on…and Torques 

II. What the spin is going on ? Spin Hall 

Spin Hall Torque, Spin Hall AMR & AHE, Spin Swapping? 

III. What the spin is going on ? Rashba 

Rashba torque, Dyakonov-‐Perel, Dzyalshinskii-‐Moriya and more 

IV. Dzyaloshinskii-‐Moriya InteracOon 

From Rashba to Dzyaloshinskii-‐Moriya to domain wall mo;on 

V. Spin-‐orbitronics with Magnons: The Magnonic DM Torque 

Marrying spin-‐orbitronics with spin caloritronics 

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I. Spin-‐orbit Coupling Strikes Back 

a. “The Usual Old Story” 

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a. “The Usual Old Story” 

Spin-‐orbit coupling in solids 

⇒ EffecCve k-‐dependent magneCc field 

Transfer of angular momentum & coupling to the labce 

Spin relaxaOon 

Ellio.-‐Yafet 

Dyakonov-‐Perel 

Damping 

Magnon-‐magnon 

Magnon-‐phonon 

MagneOc Anisotropy 

Uniaxial, Biaxial etc. 

Dzyaloshinskii-‐Moriya 

Anomalous Transport 

Anomalous Hall effect 

Anisotropic Magnetoresistance 

Banerjee, Nano Le.ers 2011 Krivorotov, Science 2005 

McGuire, IEEE Trans. Mag 1975 

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b. A new hope… 

J. Slonczewski 

L. Berger 

J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996). 

L. Berger, Phys. Rev. B 54, 9353 (1996). 

AlOx, MgO, TaN 

Transfer of the spin angular momentum 

Need a polarizer and a free layer 

J. Hayakawa, JJAP 44, L1267 (2005) 

Co, NiFe, CoFeB 

Pt, Ta, Bi , W 

Possible Strategies 

Spin Hall effect in the Heavy Metal: spin current injecOon 

Miron et al., Nature Materials 2010, 2011, 

Pi et al., APL 2010; Suzuki et al., APL 2011 

Liu et al, PRL 2011, PRL 2012, Science 2012 

Kim et al., Nature Materials 2012 

 

J z s ∝ y ⇒ T = J z 

s 

Miron Nature 2011 Liu et al., PRL 2011 Liu Science 2012 

∝ m × ( y × m 

) 

HM /F 

Rashba effect at the Heavy Metal/Ferromagnet interface: spin density generaOon 

 

S ∝ y ⇒ T = Δm × S ∝ y × m 

 

z 

y 

x 

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Single Domain Measurements 

Methods: GHz spin-‐FMR, kHz modulaOon 

Removes effects that depends on texture 

Domain Wall Measurements 

Methods: Current-‐induced MoOon 

Averages the (SO, STT, Damping) torques 

Anatomy of Spin-‐Orbit Torques 

ˆT = T ⊥ 

( θ) ˆm × ŷ +T || ( θ) ˆm × ( ŷ × ˆm ) 

Miron, Nature Materials 2010, Nature 2011 

Pi, APL 2010; Suzuki, APL 2011 

Liu PRL 2011, PRL 2012, Science 2012; Fan Nat. Com. 2013 

Kim, Nature Materials 2012, Garello Nature Nano 2013 

New effects 

Reversed moCon (against electron flow) 

Domain wall distorCon and ClCng 

Complex Current dependence 

Miron, Nature Materials 2011 

Emori, Nature Materials 2013 

Ryu, Nature Nanotechnology 2013 

Haazen, Nature Materials 2013 

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ˆT = T ⊥ 

( θ) ˆm × ŷ +T || ( θ) ˆm × ( ŷ × ˆm ) 

Spin Hall does NOT fully explain the data 

Rashba is NOT sufficient either 

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AlOx, MgO, TaN 

Co, NiFe, CoFeB 

Pt, Ta, Bi , W 

Bulk NM 

Spin Hall 

effect 

SHE Torque 

IOnerant spins 

SHE induced AMR, AHE 

Band structure versus disorder? 

Rashba Torque 

Dy’akonov-‐Perel RelaxaOon 

Interface 

NM/F 

“Rashba” 

SOC 

local spins 


Anisotropic Damping 

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a. DriX-‐diffusion model 

F: bulk AHE, bulk AMR 

P. Gonzales Barba 

NM: bulk SHE 

Shchelushkin and Brataas, PRB (2005) 

Spin-‐Orbit Torque 

AMR & AHE 

A. Vedyayev et al., arxiv.1108.2589 (2011) 

A. Manchon, arxiv (2012); Haney PRB (2013) 

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a. DriX-‐diffusion model 

P. Gonzales Barba 

Nice comparison with Kobs et al. PRL 2011 

See also Nakayama Phys. Rev. Le.. 110, 206601 

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b. Boltzmann Approach 

CollaboraCon: M.D SCles, P. Haney (NIST); K.J. Lee (Korea U.); H.W. Lee (Postech) 

Account for the actual sca.ering in the layers: finite size effect 

Kim Nature Materials 2013 

Haney, KJ Lee, HW Lee, Manchon & SCles PRB 87, 174411 (2013) 

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c. Beyond Spin Hall effect: Spin Swapping? 

First order in SOC, second order in V 

è Captured by 1 Born ApproximaCon 

Fan Nature CommunicaCon 2013 

Field-‐effect that does NOT 

come from the interface 

Shchelushkin and Brataas, PRB (2005) 

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Metallic surfaces 

II. What the spin is going on ? Rashba 

a. Interfacial Band Structure 

Au surface Gd/GdO interface 

Bi surface 

E. Rashba 

LaShell PRL 1996 

Kuprin PRB 2005 

Ast PRL 2007 

Huge Rashba splibng at heavy metal surface!! 

What happens at heavy metal/ferromagnet interfaces? 

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CollaboraCon: U. Schwingenschlogl; S. Grytsyuk (KAUST) 

Noble Metal/Ferromagnet 

S. Grytsyuk 

M=-‐M x x 

M=+M x x 

k y 

( σ )⋅ ˆk 

Ĥ = ε ( ˆk ) ⇒ Ĥ ≈ ε ( ˆk ) +α R ẑ × ˆ 

See Park, Kim, Lee & Han, Phys. Rev. B 87, 041301(R) 2013 

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CollaboraCon: U. Schwingenschlogl; S. Grytsyuk (KAUST) 

Noble Metal/Ferromagnet 

S. Grytsyuk 

M=-‐M x x 

M=+M x x 

k y 

( σ )⋅ ˆk 

Ĥ = ε ( ˆk ) ⇒ Ĥ ≈ ε ( ˆk ) +α R ẑ × ˆ 

See Park, Kim, Lee & Han, Phys. Rev. B 87, 041301(R) 2013 

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c. Diffusive Model for Rashba Torque 

X. Wang C. OrCz Pauyac 

3 Major Consequences 

Inverse spin Galvanic effect 

(Edelstein) 

Spin Galvanic effect 

(see Sinova PRL 2004) 

Anisotropic Spin RelaxaOon 

(Dyakonov-‐Perel) 

Spin density is generated 

by the flowing current 

Produces a spin torque 

Non-‐equilibrium spin density 

generates a charge current 

Impacts the AMR+AHE 

Induces anisotropic Damping 

Induces angular dependence 

Manchon and Zhang, Phys. Rev. B 78, 212405 (2008); 79, 094422 (2009) 

X. Wang and A. Manchon, Phys. Rev. Le.. 108, 117201 (2012). 

M. Dyakonov 

I. Perel 

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c. Diffusive Model for Rashba Torque 

Strong Rashba spin-‐orbit coupling: Dyakonov-‐Perel relaxaOon 

X. Wang C. OrCz Pauyac 

Intermediate Rashba spin-‐orbit coupling (Δ=αk): Fermi surface breathing 

E ± 

= 2 k 2 

2m ± 

2 

" Δ % 

$ ' 

# 2 & 

C. OrCz, X. Wang, M. Chshiev, Manchon, APL 2013 

+α 2 R 

k 2 + Δα R 

k sinθ sin( ϕ −ϕ k ) 

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d. Anisotropic Damping 

Kambersky PRB 2007 

α(θ 1 ) 

α(θ 2 ) 

See also Hankiewicz PRB 2007 

Other source of anisotropic damping: Kim PRL 108, 217202 (2012) 

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Summary on Spin-‐Orbit Torques 

Spin Hall effect 

Rashba effect 

Torques 

Non-‐adiabaCc SHE Direct SHE 

Edelstein effect (ISGE) Intrinsic+non-‐adiabaCc 

D’yakonov-‐Perel anisotropic spin relaxaCon introduces angular dependence 

Transport 

Both contribute to anisotropic AMR+ AHE 

Next… 

Spin-‐pumping+SHE: anisotropic damping? 

Spin Swapping? 

Anisotropic Damping 

α ≈ α 0 

+δα sin 2 θ 

Dzyaloshinskii-‐Moriya interacOon 

Rashba Torque in Domain wall 

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V. Dzyaloshinskii-‐Moriya interacOon 

a. A short introducOon 

I. Dzyaloshinskii 

Interfacial Spin-‐orbit coupling: Dzyaloshinskii-‐Moriya interacOon 

T. Moriya 

Heisenberg exchange 

(0 th order in soc) 

I. E. Dzyaloshinskii, JETP 5, 1259 (1957) 

T. Moriya, Phys. Rev. 120, 91 (1960). 

DM interacCon 

(1 st order in soc) MC Anisotropy 

(2 nd order in soc) 

Fe/Ir 

Mn/W 

Mentzel PRL (2012) 

Bode et al. Nature 447 (2007) 

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a. A short introducOon 

Dispersion of a Neel spin spiral on Co/Ir 

FLEUR+non-‐collinear magneCsm+SOC 

Ferriani et al., PRL 101, 027201 (2008) 

M. Heide et al, PRB 78, 140403R (2008) 

F. Schubert et al. PRB 83, 165442 (2011) 

A. Belabbes 

Nature of the Noble Metal/F interface 

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b. Reversed domain wall moOon 

DM interacCon distort the Bloch wall into a Neel wall 

Chen PRL 110, 177204 (2013) 

Emori, Nature Materials 2013 

Ryu, Nature Nanotechnology 2013 

Haazen, Nature Materials 2013 

Thiaville et.al., Europhys. Le.. 100, 57002 (2012). 

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V. Spin-‐orbitronics with Magnons 

The Magnonic DM Torque 

CollaboraCon: K.J. Lee, J.H. Moon (Korea U.); H.W. Lee (Postech) 

P. Birame Ndiaye 

Rashba Hamiltonian for electrons 

Dzyaloshinskii-‐Moriya Hamiltonian for magnons 

Therefore, one expects a DM torque mediated by the magnons 

èSame direcCon as the Rashba torque: z x j 

Birame Ndiaye, Jung-‐Hwan Moon , K.-‐J. Lee, and A. Manchon, unpublished (2013) 

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V. Spin-‐orbitronics with Magnons 

The Magnonic DM Torque 

CollaboraCon: K.J. Lee, J.H. Moon (Korea U.); H.W. Lee (Postech) 

M 

(+k) 

(−k) 

H = H 0 sin(2πf 0 t)y 

P. Birame Ndiaye 

Standard RF-‐spin waves 

Thermally-‐induced magnons 

The magneCzaCon is Clted when injecCng magnons in the system 

Birame Ndiaye, Jung-‐Hwan Moon , K.-‐J. Lee, and A. Manchon, unpublished (2013) 

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Spin-‐orbitronics is not messy… 

just a li9le bit complex 

Spin-‐waves (q>0) 

Magnons Transport 

Magnon Hall effect 

Topological magnonic crystal 


Magnon-‐magnon 

Magnon-‐phonon 

Spin caloritronics 

Magnonic Torque 

Spin-‐orbit torque 

Extrinsic v.s. Intrinsic 

Bulk v.s. interfacial… 

RelaxaOon 

Spin relaxaOon Ellio.-‐Yafet 

Dyakonov-‐Perel 

MagneOc Anisotropy 

Uniaxial, Biaxial etc. 



Breathing Fermi 

Surface… 

Anomalous Transport 

Anomalous & Spin Hall effect 

Anisotropic Magnetoresistance 

Quantum Spin Hall effect 

Topological Insulators 

Skyrmion 

Chiral magnets 

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Thank you for your a9enOon! 

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Spin-Orbit Torque in Magnetic Bilayers - Spintronics Theory Group

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