Orbital Rashba Effect&

Its Implications

Jung Hoon Han (Sungkyunkwan U)

韓 政勳( 成均館大 )

CollaborationChoong H. Kim (Cornell) Changyoung Kim (Yonsei)Hyun-Woo Lee (POSTECH)Jin-Hong Park (SKKU)Seung Ryong Park (Colorado)Jun-Won Rhim (KIAS)Jaejun Yu (SNU)

Ref: SR Park et al. PRL 107, 156803 (2011) SR Park et al. PRL 108, 046805 (2012) JH Park et al. PRB 85, 195401 (2012) JH Park et al. arXiv:1207.0089 (2012)

PJ Kim & JHH, arXiv:1212.0932 (2012)

Outline

I. Natural consequence of inversion symmetry breaking (ISB) is emergence of chiral orbital angular momentum (OAM)

II. Implication for magnetic thin layer spin trans-fer torque

III. Implication in the strong Hubbard regime – orbital Dzyaloshinskii-Moriya interaction

Throughout the first part, spin-orbit interaction will be assumed very weak, or non-existent

Symmetry & Band Structure

A. TR symmetry:

B. Inversion symmetry:

C. TR+I:

D. Crystal symmetry dictates symmetry of energy dispersion

Symmetry & Band Structure

If certain symmetry is lost, a corresponding change

in the band dispersion takes placeWhen inversion symmetry is lost (ISB),

what happens to band structure?

Answer: Orbital Rashba effect

Tight-binding (Microscopic) View of ISB

σ-bond

π-bond

Symmetry-forbidden

In a p-orbital system without ISB, pz-orbital band is sepa-rated from px-py bands

Petersen&Hedegard, Surf. Sci. (2000); JH Park et al. PRB (2012)

σ-bond

π-bond

hy-bridized

E

Once inversion symmetry breaking (ISB) occurs by elec-tric field, pz hybridizes with px, py

like spin-flip hopping in spin-orbit models

L=orbital angular momentum operator (OAM) in p-orbital basisγ = a measure of ISB

~ Rashba term for OAM !

σ-bond

π-bond

hy-bridized

E

Exactly the same symmetry as the spin Rashba term

One band with CCW OAM (m=+1), One band with CW OAM (m=-1), One band with zero OAM (m=0).

m=+1

m=-1

m=0

How to detect chiral OAM

• Polarized source light (RCP/LCP) in ARPES

• RCP/LCP lights give different intensities

• Map of D(k) = (RCP-LCP)/(RCP+LCP)

Circular Dichroism ARPES

• Matrix element ~ <F|p*A|I> ~ <F|r*A|I>• LCP/RCP lights are given by A and A*

• D(k)=(IRCP(k)-ILCP(k))/(IRCP(k)+ILCP(k))

• D(k) is proportional to OAM average of the initial state

Theory of Circular Dichroism

D(k) ~ Fij(Ef) (kph)i <k| Lj |k>

• True for p- and d-orbitals (presumably for any multi-or-bital band structure)

SR Park et al PRL (2012); JH Park et al. PRB (2012)

Circular Dichroism Map

Testing it Out on Cu (weak SOI)

• PRB (2012) Yonsei group

• PRB (2012) Yonsei group

Testing it Out on Au (medium SOI)

• MIT group, PRL (2011)

Bi2Se3 (strong SOI)

W

kx (G-M)

d)

0+

-k y

(G

-K)

LCPc)

kx (G-M)

RCPb)

kx (G-M)

R - L

• Yonsei group, PRL (2012)

Orbital Analogue of DM

PJ Kim & JHH, arXiv:1212.0932

• Logic:

• SOI + ISB leads to spin Rashba effect, but ISB alone leads to orbital Rashba effect

• SOI + ISB + strong on-site repulsion -> Dzyaloshinskii-Moriya superexchange of spin

• ISB + strong on-site repulsion -> orbital DM (?)

Three orbital superexchange Assume, as before, three orbitals per site ISB allows certain new orbital-changing

hopping Add multi-orbital Hubbard interaction Do superexchange (very complicated!)

• Our work extends Khaliullin’s t2g superexchange calcula-tion to the situation with ISB -> orbital DM, spiral orbital order

• Superexchange process conveniently expressed by Gell-Mann matrices (3-dim Hilbert space)

• First-order terms in γ reduce to orbital DM under projec-tion to two-orbital subspace

Multiple Helical(~Skyrmion crystal)

Helical

Application to Magnetic Band(& Spintronics)

JH Park et al, arXiv:1207.0089

Implication on Spintronics• Atomic magnetic layer (< 1nm) between insulating and

Pt layers (SPINTEC group, Cornell group)

• A new type of spin transfer torque due to Rashba effect proposed and detected (a blue ocean of spintronics!)

LDA calculation for different layer structure

2Pt-Co–2Pt

Asymmetric caseSymmetric case

1 Co1 Co- 3 Pt

J.-H. Park et al., arXiv1207.0089 (2012)

Co

Co

Co

PtPt

Pt

PtPt

PtPt

Band-specific Rashba parameter

• Each band has its own sign of Rashba parameter

• Rashba parameter governs the sign/magnitude of STT

• Depending on which bands cross the Fermi level, different STT will be found (lot like the problem of Hall effect in multi-band system)

Model of Rashba Effect in Magnetic Bands

J.-H. Park et al., arXiv1207.0089 (2012)

• OAM>0 has Rashba>0• OAM<0 has Rashba<0• OAM=0 has Rashba=0

• Depending on position of chemical potential, may find different sign and magnitude of Rashba-in-duced STT

Summary

• Direct consequence of ISB is orbital Rashba

• Orbital Rashba easily observed by CD-ARPES

• Band-specific OAM implies band-specific Rashba pa-rameter (even signs!) in magnetic and non-magnetic thin layers

• OAM-carrying bands give orbital-DM under superex-change