1. 韓 政勳 (成均館大) Orbital Rashba Effect & Its Implications Jung Hoon Han
(Sungkyunkwan U)
韓 政勳
(成均館大)

2. Collaboration Choong 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, (2011)
SR Park et al. PRL 108, (2012)
JH Park et al. PRB 85, (2012)
JH Park et al. arXiv: (2012)
PJ Kim & JHH, arXiv: (2012)

3. Outline
Natural consequence of inversion symmetry breaking (ISB) is emergence of chiral orbital angular momentum (OAM)
Implication for magnetic thin layer spin transfer torque
Implication in the strong Hubbard regime – orbital Dzyaloshinskii-Moriya interaction

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

5. Symmetry & Band Structure
TR symmetry:
Inversion symmetry:
TR+I:
Crystal symmetry dictates symmetry of energy dispersion

6. Symmetry & Band Structure
If certain symmetry is lost, a corresponding change
in the band dispersion takes place
When inversion symmetry is lost (ISB),
what happens to band structure?
Answer: Orbital Rashba effect

7. Tight-binding (Microscopic) View of ISB
In a p-orbital system without ISB, pz-orbital band is separated from px-py bands
π-bond
σ-bond
Symmetry-forbidden
Petersen&Hedegard, Surf. Sci. (2000); JH Park et al. PRB (2012)

8. Once inversion symmetry breaking (ISB) occurs by electric field, pz hybridizes with px, py
π-bond
σ-bond
hybridized
like spin-flip hopping in spin-orbit models

9. L=orbital angular momentum operator (OAM) in p-orbital basis
γ = a measure of ISB

10. E ~ Rashba term for OAM ! π-bond σ-bond hybridized
Exactly the same symmetry as the spin Rashba term

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

12. How to detect chiral OAM

13. Circular Dichroism ARPES
Polarized source light (RCP/LCP) in ARPES
RCP/LCP lights give different intensities
Map of D(k) = (RCP-LCP)/(RCP+LCP)

14. Theory of Circular Dichroism
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
D(k) ~ Fij(Ef) (kph)i <k| Lj |k>
True for p- and d-orbitals (presumably for any multi-orbital band structure)
SR Park et al PRL (2012); JH Park et al. PRB (2012)

15. Circular Dichroism Map

16. Testing it Out on Cu (weak SOI)
PRB (2012) Yonsei group

17. Testing it Out on Au (medium SOI)
PRB (2012) Yonsei group

18. Bi2Se3 (strong SOI) MIT group, PRL (2011) Yonsei group, PRL (2012) + -W
kx (G-M) d) + -
ky (G-K)
LCP c)
RCP b)
R - L
Yonsei group, PRL (2012)

19. 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 (?)

20. 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!)

21. Our work extends Khaliullin’s t2g superexchange calculation 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 projection to two-orbital subspace

22. Helical
Multiple Helical
(~Skyrmion crystal)

23. Application to Magnetic Band
(& Spintronics)
JH Park et al, arXiv:

24. 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!)

25. LDA calculation for different layer structure
Asymmetric case
Symmetric case
1 Co- 3 Pt
1 Co
2Pt-Co–2Pt Co Pt Pt Co Pt Pt Pt Co Pt Pt
J.-H. Park et al., arXiv (2012)

26. 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)

27. Model of Rashba Effect in Magnetic Bands
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-induced STT
J.-H. Park et al., arXiv (2012)

28. Summary Direct consequence of ISB is orbital Rashba
Orbital Rashba easily observed by CD-ARPES
Band-specific OAM implies band-specific Rashba parameter (even signs!) in magnetic and non-magnetic thin layers
OAM-carrying bands give orbital-DM under superexchange