Spin-orbit effects in graphene and graphene-like materials. Józef Barnaś

Transcription

1 Spin-orbit effects in graphene and graphene-like materials Józef Barnaś Faculty of Physics, Adam Mickiewicz University, Poznań & Institute of Molecular Physics PAN, Poznań In collaboration with: A. Dyrdał, Adam Mickiewicz University, Poznań V.Dugaev, M Inglot, Rzeszów University of Technology R. Swirkowicz, M. Wierzbicki, K. Zberecki, Warswow Univerity of Technology E Sherman, University at Bilbao, Spain T. Stobiecki and team, AGH, Kraków

2 Schedule: Introduction: 2D crystals Spin-orbit interaction Spin-Hall effect and spin Hall insulators Edge states and edge magnetism in nanoribbons Current-induced spin polarization Spin-orbital torque Resonant photo-voltaic effect

3 Atomic structure: honeycomb 2D lattice A B Two triangular sublattices: A and B Buckled hexagonal lattice * silicene (Si atoms) * germanene (Ge atoms) Unbuckled hexagonal lattice * graphene (C atoms) Atomically different sublattices * SiC (silicon carbide) * BN (boron nitride) Avramov et al, Phys Chem Lett 2012

4 Effective Hamiltonian near the Dirac points: spin-orbit interaction H H 0 H int so H R so H imp so H v 0 k x x y k y H int t so so z z Intrinsic spin-orbit coupling H R so R x y y x Rashba spinorbit coupling H imp so Spin-orbit interaction due to impurities

5 Intrinsic spin-orbit interaction Graphene (C); t so 5 ev Silicene (Si); t so 4 mev Germanene (Ge); t so 43 mev Stanene (Sn); t so 30 mev Rashba spin-orbit interaction Graphene on Ni(111) R 122 mev (Dedkov PRL 2008) Graphene on Au ) R 50 mev (Marchenko, Nat. Com. 2012) Graphene on Ir(111) R 25 mev (Marchenko PRB 2013)

6 Intrinsic spin-orbit interaction: Graphene-like materials as spin- Hall insulators:

7 Physical origin of SHE Extrinsic (spin-orbit scattering on defects)) skew scattering side jump Intrinsic (topological) contribution Intrinsic spin-orbit interaction contributing to band structure States from the whole band contribute to the effect This term can be expressed by a Berry curvature of the respective bands

8 Energy Spin-Hall insulator phase v H k Spin-orbit gap Wavevector Universal spin Hall conductivity sh 2 e 4 Kane & Mele, PRL 2005 A Dyrdał, V Dugaev, JB, PRB 2009

9 Transition between spin Hall and band insulator phase in a vertical electric field Gate voltage normal to the plane sh 2 e 4 Silicene SHE phase diagram Energy spectrum: closing of energy gap by vertical voltage sh 4 e 4 Bilayer graphene A Dyrdal & JB, PRB, pss RRL 2012

10 Graphene-like materials as 2D topological insulators Kane & Mele, PRL 2005

11 Zigzag nanoribbons: in-plane magnetic anisotropy due to spin-orbit interaction Magnetism is created by Coulomb interaction V/2 Antiparallel configuration Parallel configuration -V/2 Spin-orbit interaction favors in-plane Orientation of the edge moments (Lado et al, PRL 2014) Yazyev Rep Prog Phys 2010

12 Hamiltonian of graphene-like nanoribbons Tight-binding Spin-orbit Coulomb interaction Ezawa 2012

13 Topologically protected zero-energy edge states Zero onsite Coulomb Interaction, U=0 The edge states are spin degenerate Topological insulator phase Wierzbicki, JB, R Swirkowicz, PRB 2015

14 Topological conventional insulator phase transition in external electric field Spin-splitting of the edge states Electrical conductance at the phase transition Wierzbicki, JB, R Swirkowicz, PRB 2015

15 Topological conventional insulator phase transition in external electric field Spin-splitting of the edge states Thermoelectric powere at the phase transition Wierzbicki, JB, R Swirkowicz, PRB 2015

16 Topological conventional insulator phase transition in staggered exchange field Ezawa, PRB 12, PRL 13 Phase transition in staggered exchange field Wierzbicki, JB, R Swirkowicz, PRB 2015

17 Suppression of spin Hall insulator phase by electron-electron interaction Mathes and Bechstedt, PRB 2014 Kane & Mele, PRL 2005 Electron-electron Interaction can suppress the topological insulator phase Wierzbicki, JB, R Swirkowicz, PRB 2015

18 SHE due to Rashba interaction

19 SHE in graphene with Rashba spin-orbit interaction Rashba interaction due to substrate Nonuniversal spin Hall conductivity A Dyrdał, V Dugaev, JB, PRB 2009

20 Random Rashba field: spin relaxation and SHE For R =50 nm, λ 2 =500 ev 2 ; s of an order of 10 ns Dugaev, Sherman, JB, PRB 2011 Dyrdał,, JB, PRB 2012

21 Experiments on SHE in graphene GIANT SPIN HALL EFFECT IN GRAPHENE GROWN BY CHEMICAL VAPOUR DEPOSITION by J. Balakrishnan, et al NATURE COMMUNICATIONS, 2014 GIANT SPIN HALL EFFECT IN GRAPHENE GROWN BY CHEMICAL VAPOUR DEPOSITION by J. Balakrishnan, et al NATURE COMMUNICATIONS, 2014 SPIN-ORBIT PROXIMITY EFFECT IN GRAPHENE by A. Avsar, et al NATURE COMMUNICATIONS, 2014 Combined effects of Rashba interaction and impurities

22 Current-induced spin polarization in Rashba field

23 Current-induced spin polarization: 2DEG H k k g k x y k y x Rashba interaction m sx geey 0 2 Linear response Aronov & Lynda-Geller 1989 Yvchenko et al 1990 Edelstein 1990

24 Current-induced spin polarization in graphene with Rashba interaction

25 Current-induced spin polarization in graphene A Dyrdal & JB, 2013

26 Current-induced spin polarization and spinorbit torque in magnetized graphene Magnetized graphene H H 0 R H so H M Spin polarization has now all components that depend on magnetic moment orientation H M jm

27 Current-induced spin-orbit torque S current-induced spin density dm dt M H eff M dm dt Field torque Damping term Spin-orbit torque τ E ex jms τ jms A Dyrdal & JB, 2015

28 Photo-galvanic effect

29 Graphene in an in-plane magnetic field Inglot, Dugaev, & JB & JB, PRB 2015

30 Optical pumping of spin polarization, spin current and charge current Graphene in an electromagnetic field Optical transitions for spin polarization for charge current

31 Photo-galvanic effect Optical current injection for ky>0 when ω 1<ω< ω2. Inglot, Dugaev, & JB & JB, PRB 2015

32 Conclusions: Internal spin-orbit interaction in graphene and graphene like materials is responsible for universal spin Hall conductance and for spin Hall insulator (2D topological insulator) state Rashba spin-orbit interaction also gives rise to spin Hall effect which is not universal. Rashba spin-orbit coupling leads to spin polarization when an external electric field is applied In a magnetized system the spin polarization gives rise to a spinorbital torque Optical pumping in the presence of Rashba interaction and external in-plane magnetic field leads to enhanced photo galvanic effect

33 Acknowledgements This work was partly csupported within the Project NANOSPIN PSPB-045/2010 supported by a grant from Switzerland through the Swiss Contribution to the enlarged European Union and partly by the National Science Center in Poland as Project No. DEC-2012/04/A/ST3/00372

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