Analyzing Magnetic Ordering in Magnetically-Doped Topological Insulators

1. Magnetic ordering influenced by spin-orbit interaction, opening the Dirac gap and reversal magnetization induced in magnetically-doped topological insulators and Rashba systems A.M. Shikin, I.I. Klimovskikh, A.A. Rybkina St.-Petersburg State University P. Skirdkov, K.A. Zvezdin, A. K. Zvezdin Prokhorov General Physics Institute, Moscow K. Kokh, O. Tereshchenko Rzhanov Institute and Novosibirsk State University M. Otrokov, E. Chulkov Tomsk and San Sebastian University The main idea – analysis of magnetic ordering in magnetically-doped 2D systems with helical spin structure (topological insulators and Rashba systems) and to attempt to analyze a role of coupling between exchange and spin-orbit interactions in forming the magnetic ordering (It will be done by analysis of opening the gap at the Kramers (Dirac) point due the Time Reversal Symmetry breaking and the induced out-of-plane spin polarization in the region of the gap with using spin- and angle- resolved photoemission)

2. 3D topological insulators. Helical spin structure. Spin-polarized currents. Induced magnetization. C.H. Li et al., Nature Nanotechnology 9, 218 (2014)

3. Opening gap at the Dirac point in magnetically–doped TI. Time-Reversal-Symmetry breaking Sb2-xCrxTe3 J.S.Dyck et al., PRB 71, 115214 (2002) J.S.Dyck et al., PRB 65, 115212 (2002) Out-of-plane and in-plane magnetization (Bi0.88Fe 0.12 )2Se3.7 FM-doped TIs are characterized by QAH and magneto-electric effects Y.L.Chen et al., Science 329, 659 (2010)

4. Dependence of the Dirac-mass gap on the magnetic dopant concentration in magnetically–doped TIs Density of local spins Density of states at the Fermi energy J.G.Checkelsky et al., Nature Physics 8, 729 (2012) Bi2-xMnxTe3

5. Spin structure of FM-doped TIs. Out-of-plane spin polarization at the Dirac cone FM-doped topological insulators Surface Dirac electrons mediate a ferromagnetic coupling among the local moments (impurity spins) Induced out-of-plane polarization at the Dirac point with the gap is proportional to the concentration FM dopant concentration Out-of-plane polarization Hedgehog spin texture S.-Y. Xu et al., Nature Physics 8, 616 (2012)

6. Properties of FM-doped topological insulators (magnetic origin of the gap opening) • Bulk and surface magnetism. Reversal induced magnetization. • Out-of-plane spin magnetization and opening the gap at the Dirac point (due to TRS breaking) • Dependence of the gap value and Curie temperature on FM-impurity concentration and interplay between exchange and spin-orbit interactions • QAHE and magneto-electric effect Effects which can be related to the gap opening in FM–doped topological insulators • Enhancement of effective magnetization due to influence of spin-orbit coupling. Dirac-fermion-mediated ferromagnetism. • Surface-derived ferromagnetism • Resonance influence of the diluted magnetic atoms. Hybridization between the states of magnetic dopants and Dirac cone states • Influence of photoexcitation. Reversal out-of-plane spin structure induced in magnetically-doped topological insulator

7. Magnetic impurity-induced states in topological insulators. Impurity resonance influence (calculations). LDOS for out-of-plane polarized magnetic impurities With increasing the impurity concentration the resonance peak moves from the valence band and enters the bulk gap region and shifts toward the Dirac point where the peak-peak splitting takes place. As a result the formed Dirac points are located on both sides of the resonance peak. The splitting depends on strength of interaction between impurity and the surface states R.R.Biswas et al., PRB 81, 233405 (2010) A.M.Black-Schaffer et al., PRB 85, 121103 (2012)

8. Resonant photoemission Mn(8%)-doped Bi2Se3 hv=50eV J.Sanchez-Barriga et al., Nature Commyn. DOI:10.1038 (2016)

9. V-resonances in V-doped topological insulator. V-doped Bi2Se3 (calculations) No intersection between the V-resonance and the Dirac point positions TIs are characterized by enhanced SO-interaction. It influences on the polarization of electron gas and magnetic ordering formation. Y.L.Chen et al., Science 329, 659 (2010) Large Dirac gap assumes a Dirac-fermion-mediated magnetic ordering. Role of spin-orbit interaction BiTeIwith helical spin structure and Rashba-like surface states characterized by maximally known spin-orbit coupling and spin splitting of the Rashba states

10. BiTeI Enhanced SO coupling S.V. Eremeev et al., Pis’ma v ZhETF 96, 484 (2012) K. Ishizaka et al., Nature Commun,10, 521 (2011) Potential energy and electron density as function of depth

11. BiTeI In-plane spin polarization. Spin is locked perpendicular to momentum

12. Electronic and spin structure of BiTeI. Surface termination. Te-terminated surface In-plane and out-of-plane polarization I-terminated surface In-plane and out-of-plane polarization S.V. Eremeev et al., Pis’ma v ZhETF 96, 484 (2012)

13. Magnetically-doped BiTeI Opening spontaneous gap at the Kramers point for V-doped BTeI below a Curie temperature. Te-terminated surface. V(0.5%)-doped BTeI Gap (about 90 meV) is formed at temperature 20K I.I. Klimovskikh et al., sent for publication

14. V(0.5%)-doped BiTeI. Mapping and gap formation at 20K I.I. Klimovskikh et al., sent for publication Gap90 meV

15. Opening giant Dirac-mass gap in V-doped BiTeI and dependence of the gap on the V-concentration (0.5 and 2%) Bi0.985V0.015TeI Room temperature (No gap) Bi0.985V0.015TeI 20 K (90 meV) Bi0.94V0.06TeI 15 K (125 meV) The gap of 90 and 125 meV is formed for V-concentrations 0.5 and 2%

16. Dependence of the gap in V-doped BiTeI on temperature V-doped BiTeI (2%) HiSOR Japan Mn-doped BiTeI (2.5%) MAXlab Sweden 15 K 125 meV 100 K No Gap 30 K 120 meV V-doped BiTeI (2%) Elettra (Italy) 17 K 125 meV 40 K 120 meV 56 K 106 meV

17. Rashba-state-mediated surface magnetic ordering in V-doped BiTeI V-doped BiTeI as in the system with 2D electron gas and the local V+2 magnetic moments which effectively interact via Rashba states in the system with enhanced SO interaction We can consider the exchange interaction as the sum of s-d interaction between free 2D Rashba electron gas and V2+ impurities system and electron-electron exchange interaction where is the magnetization of V2+ impurities along the z-axis, - exchange constants where It allows to present the critical temperature in the form using that and Taking into account theimpurity concentration N = 2 x1013 cm-2(2 %) we can estimate the parameters as Based on theseconstants one can nd the critical temperature of surfacemagnetic ordering in considered case as TC 88.2 K A. Zvezdin group calculations

18. Out-of-plane spin polarization in Bi0.94V0.06TeI V - resonances Calc. by M. Otrokov

19. SQUID Hysteresis loop for V-doped BiTeI at temperature 4 K. V-doped BiTeI (2%) Domains with opposite out-of-plane magnetic moments Te- and I-terminated surface areas As a result a weak averaged out-of-plane spin polarization is observed with the giant gap formation at the Kramers point Assumption about surface short-range magnetic ordering. The gap value is determined by magnetic moment developed at domains

20. To study directly the interrelation between the induced magnetic moment and the gap opening one can use the magnetization and its reversal switching induced by circularly-polarized synchrotron radiation To distinguish a spontaneous and induced magnetization the experiment will be carried out above a Curie temperature (at room temperature Role of “optically”-induced uncompensated spin accumulation

21. Depopulation of the spin-oriented states at the Fermi level under photoexcitation. “Optically”- induced uncompensated spin accumulation Other possibility of induced magnetization (above a Curie temperature) By circularly polarized laser or synchrotron radiation Topological insulator BiTeI Generated uncompensated spin accumulation in 2D Rashba electron gas transfers the induced torque to the diluted V 3d-ions.

22. Bi1.37V0.03Sb0.6Te2Se Circularly polarized synchrotron radiation induce the out-of-plane spin polarization and open Dirac gap at room temperature (due to optically-generated uncompensated spin accumulation)

23. V(0.5%)-doped BiTeI EDC at the Dirac point measured with opposite circular polarization of synchrotron radiation. Cryogenic (20K) and room temperature.

24. V(0.5%)-doped BiTeI EDC at the Dirac point measured with opposite circular polarization of synchrotron radiation. Out-of-plane spin-resolved spectra. Room temperature. Out-of-plane magnetic moments at magnetic ions interact via 2D Rashba electron gas with enhanced spin-orbit coupling Induced magnetization above a Curie temperature by CPSR (that is like to magneto-electric effect) can shift the temperature region of QAHE to room temperature

25. (A. Zvezdin group calculations) V-doped BiTeI Thespin-torquetransfer,whichleadstogapopening, occursintwosteps. Firstly,torquefromcircularlypolarizedsynchrotronradiationistransmittedtoelectronRashbasubsystem. Itleadstoappearanceofthemeanvalueoftheholespin, i.e. tothe“optically"- inducedspinaccumulation Onthesecondstep, electronstransferthistorquetothediluted d-ions. . This process can be described by modified Landau-Lifshitz equation includes anisotropy of d-ions and external magnetic field, is the magnetization of d-ions subsystem, is the exchange field of magnetic ions acting on the free electrons is the probability of the electron photoexcitation per unit time, - decoherence time the optically induced energygap can be estimated as: as4.3 x 1013 cm-2 the induced energy gap will beabout 100 meV If we estimate

26. Factors influencing the gap value: Opening the gap in magnetically-doped topological insulators due to exchange interaction between magnetic moments of diluted magnetic atoms Bi2-xMnxTe3 (x=0.18) Gap 16 meV Curie temperature 9-12K J. Henk et al., PRL 109, 076801 (2012) V-doped BiTeI Gap 1-10 meV (calculations by A. Ernst)

27. Factors influencing the gap value: V(0.5%)-BiTeI • V being embedded in the Bi layer has magnetic moment of 2.88 μB. • For V-doped BiTeI the magnetic moment are also induced on Te and I atoms in the immediate vicinity of V atoms and their p-states are hybridized with d-states of v atoms. • It opens the gap up to 10 meV. 2. Other possibility – presence of point defects in vicinity of the V atoms. Bi-vacancy located nearly the V-dopants induces more magnetization at Te atoms. It leads to opening the gap up to 34 meV I.I.Klimovskikh et al., sent for publication

28. Experimental observations testifying to interplay between exchange and SO coupling • So, we have shown that the gap at the Dirac point in V-doped BiTeI has a magnetic nature (dependence on the V-concentration and temperature below a Curie temperature which can be confirmed by calculation for 2DEG with enhanced SO coupling in framework of the Rashba-state-mediated magnetic ordering. • Reverse induced out-of-plane spin polarization (magnetization) induced by circularly polarized SR • Spin polarization is induced both for 2DEG and local FM-impurities • At Kramers point the Rashba states have out-of-plane polarization. Far from the Kramers point the Rashba states are characterized by in-plane polarization • How SO interaction can influence on the magnetic ordering? • What kind of magnetic ordering is formed?

29. Collinear and non-collinear exchange interaction. Inclusion of Rashba interaction. The RKKY interaction describes a parallel or antiparallel (collinear) exchange interaction between two localized spins via spin polarization of conduction electrons However, in the systems with enhanced SO coupling a non-collinear DM coupling can be developed that is followed by precession of spin and rotation of spin of polarized conduction electrons. It causes a spin spiral cycloid texture formation Idea of resonance interaction of collinear and non-collinear interactions RKKY J. Zhu et al., PRL 106, 097201 (2011) A. Fert et al., Nature Nanotechnology 8, 152 (2013)

30. Collinear and non-collinear exchange interaction. M.Bode et al., Nature 447, 190 (2007) S. Lounis et al., PRL 108, 207202 (2012) Fe-adatoms on Au(111) with Rashba-like structure of the surface states Enhanced SO interaction (due to DMI) leads to rotation of spin of polarized conduction electrons and causes spin spiral cycloid texture Magnetic atom induced Skirmion-like spin texture in surface electron waves For Rashba system two spin cycloid-like wave of opposite chirality are formed with the wave length related to two kF in electronic structure.

31. For Rashba system a new of spin texture induced in 2DEG subject to the Rashba (SO) effect by magnetic atoms. This structure can be understood as a kind of combination of Skirmionic-like waves of opposite chirality BiTeI+V k1 k2 =17Å R(V-V)=17Å As result of formation of two cycloids determined by k1 and k2 a beating of spin is formed which depends on the strength of the Rashba coupling S. Lounis et al., PRL 108, 207202 (2012)

32. Summary Magnetic doping of TIs and Rashba systems (BiTeI) characterized by enhanced SO-interaction by magnetic dopant (V) with anomalously low concentration (0.5 and 2%) leads to opening aanomalously large energy gap at the Kramers point at 15-20K due to influence of SO-interaction on magnetic coupling With growth of the diluted magnetic dopants in V-doped BiTeI from 0.5 till 2% the gap value is increasing from 90 till 125 meV. The use of circularly polarized synchrotron radiation leads to opening the gap (of about 90 meV) in V-doped TI and BITeI even at room temperature with opposite spin structure at the borders of the gap. As a result, a reversal induced out-of-plane magnetization is induced which can be switched by the direction of circular polarization. The formed spin texture can be described as magnetic dopant induced surface Skirmion-like texture in 2DEG Thank you very much for your attention