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

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, 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 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

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

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

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

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)

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

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

E ~ Rashba term for OAM ! π-bond σ-bond hybridized 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).

How to detect chiral OAM

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

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)

Circular Dichroism Map

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

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

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)

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 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

Helical Multiple Helical (~Skyrmion crystal)

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 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., arXiv1207.0089 (2012)

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 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., arXiv1207.0089 (2012)

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