New perspectives for Rashba spin-orbit coupling

Nature Materials

Volumn 14, Issue 9, 2015, Pages 871-882

  Manchon, A ^a   Koo, H C ^b,c   Nitta, J ^d   Frolov, S M ^e   Duine, R A ^f  

^a KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

^b Korea Institute of Science and Technology   (South Korea)

^c Korea University   (South Korea)

^d TOHOKU UNIVERSITY   (Japan)

^e UNIVERSITY OF PITTSBURGH   (United States)

^f UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

CONDENSED MATTER PHYSICS; MAGNETIC MOMENTS;

ASYMMETRIC STRUCTURES; CONDENSED MATTER; ELECTRON TRAJECTORIES; MATERIALS SCIENTIST; RASHBA SPIN-ORBIT COUPLING; SPIN ORIENTATIONS; SPIN-ORBIT COUPLINGS; TWO-DIMENSIONAL SEMICONDUCTORS;

ELECTROSPINNING;

EID: 84939811253     PISSN: 14761122     EISSN: 14764660     Source Type: Journal    
DOI: 10.1038/nmat4360     Document Type: Article

References (150)

1. Dresselhaus, G. Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580-586 (1955).
2. Rashba, E. Properties of semiconductors with an extremum loop.1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phys. Solid State 2, 1109-1122 (1960).
3. Vas'ko, F. T. Spin splitting in the spectrum of two-dimensional electrons due to the surface potential. P. Zh. Eksp. Teor. Fiz. 30, 574-577 (1979).
4. Bychkov, Y. A. & Rasbha, E. I. Properties of a 2D electron gas with lifted spectral degeneracy. P. Zh. Eksp. Teor. Fiz. 39, 66-69 (1984).
5. Fabian, J., Matos-Abiague, A., Ertler, C., Stano, P. & Zutic, I. Semiconductor spintronics. Acta Phys. Slovaca 57, 565-907 (2007).
6. Chappert, C., Fert, A. & Van Dau, F. N. The emergence of spin electronics in data storage. Nature Mater. 6, 813-823 (2007).
7. Jungwirth, T., Wunderlich, J. & Olejník, K. Spin Hall effect devices. Nature Mater. 11, 382-390 (2012).
8. Dyakonov, M. I. & Perel, V. I. Possibility of orienting electron spins with current. ZhETF Pis. Red. 13, 657-660 (1971).
9. Hirsch, J. Spin Hall effect. Phys. Rev. Lett. 83, 1834-1837 (1999).
10. Murakami, S., Nagaosa, N. & Zhang, S.-C. Dissipationless quantum spin current at room temperature. Science 301, 1348-1351 (2003).
11. Sinova, J. et al. Universal intrinsic spin Hall effect. Phys. Rev. Lett. 92, 126603 (2004).
12. Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959-2007 (2010).
13. Kato, Y. K., Mährlein, S., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910-1913 (2004).
14. Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005).
15. Wunderlich, J. et al. Spin Hall effect transistor. Science 330, 1801-1804 (2010).
16. Valenzuela, S. O. & Tinkham, M. Direct electronic measurement of the spin Hall effect. Nature 442, 176-179 (2006).
17. Hoffmann, A. Spin Hall effects in metals. IEEE Trans. Magn. 49, 5172-5193 (2013).
18. Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. http://journals.aps.org/rmp/accepted/58077E11Q8f15e01e0aa5510b2767e3da25148b87 (2015).
19. Rauch, H. et al. Verification of coherent spinor rotation of fermions. Phys. Lett. A 54, 425-427 (1975).
20. König, M. et al. Direct observation of the Aharonov-Casher Phase. Phys. Rev. Lett. 96, 076804 (2006).
21. Bergsten, T., Kobayashi, T., Sekine, Y. & Nitta, J. Experimental demonstration of the time reversal Aharonov-Casher effect. Phys. Rev. Lett. 97, 196803 (2006).
22. Aharonov, Y. & Casher, A. Topological quantum effects for neutral particles. Phys. Rev. Lett. 53, 319-321 (1984).
23. Nitta, J., Akazaki, T., Takayanagi, H. & Enoki, T. Gate control of spin-orbit interaction in an inverted InGaAs/InAlAs heterostructure. Phys. Rev. Lett. 78, 1335-1338 (1997).
24. Wunderlich, J. et al. Spin-injection Hall effect in a planar photovoltaic cell. Nature Phys. 5, 675-681 (2009).
25. Ivchenko, E. L. & Pikus, G. E. New photogalvanic effect in gyrotropic crystals. JETP Lett. 27, 604-608 (1978).
26. Ganichev, S. D. Spin-galvanic effect and spin orientation by current in non-magnetic semiconductors. Int. J. Mod. Phys. B 22, 1-26 (2008).
27. Rojas-Sánchez, J. C. et al. Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials. Nature Commun. 4, 2944 (2013).
28. Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun. 73, 233-235 (1990).
29. Kato, Y. K., Myers, R., Gossard, A. & Awschalom, D. D. Current-induced spin polarization in strained semiconductors. Phys. Rev. Lett. 93, 176601 (2004).
30. Ganichev, S. D. et al. Electric current-induced spin orientation in quantum well structures. J. Magn. Magn. Mater. 300, 127-131 (2006).
31. Schultz, M. et al. Rashba spin splitting in a gated HgTe quantum well. Semicond. Sci. Technol. 11, 1168-1172 (1996).
32. Datta, S. & Das, B. Electronic analog of the electro-optic modulator. Appl. Phys. Lett. 56, 665-667 (1990).
33. Koo, H. C. et al. Control of spin precession in a spin-injected field effect transistor. Science 325, 1515-1518 (2009).
34. Ohe, J., Yamamoto, M., Ohtsuki, T. & Nitta, J. Mesoscopic Stern-Gerlach spin filter by nonuniform spin-orbit interaction. Phys. Rev. B 72, 041308 (2005).
35. Kohda, M. et al. Spin-orbit induced electronic spin separation in semiconductor nanostructures. Nature Commun. 3, 1082 (2012).
36. Herbert, S. T., Muhammad, M. & Johnson, M. All-electric quantum point contact spin-polarizer. Nature Nanotech. 4, 759-764 (2009).
37. Frolov, S. M. et al. Ballistic spin resonance. Nature 458, 868-871 (2009).
38. Nowack, K. C., Koppens, F. H. L., Nazarov, Y. V. & Vandersypen, L. M. K. Coherent control of a single electron spin with electric fields. Science 318, 1430-1433 (2007).
39. Nadj-Perge, S., Frolov, S. M., Bakkers, E. P. A. M. & Kouwenhoven, L. P. Spin-orbit qubit in a semiconductor nanowire. Nature 468, 1084-1087 (2010).
40. Van den Berg, J. et al. Fast spin-orbit qubit in an indium antimonide nanowire. Phys. Rev. Lett. 110, 066806 (2013).
41. Petersson, K. D. et al. Circuit quantum electrodynamics with a spin qubit. Nature 490, 380-383 (2012).
42. Dyakonov, M. & Perel, V. Spin relaxation of conduction electrons in noncentrosymmetric semiconductors. Sov. Phys. Solid State 13, 3023-3026 (1972).
43. Averkiev, N. S. & Golub, L. E. Giant spin relaxation anisotropy in zinc-blende heterostructures. Phys. Rev. B 60, 15582-15584 (1999).
44. Schliemann, J., Egues, J. C. & Loss, D. Nonballistic spin-field-effect transistor. Phys. Rev. Lett. 90, 146801 (2003).
45. Bernevig, B. A., Orenstein, J. & Zhang, S.-C. Exact SU(2) symmetry and persistent spin helix in a spin-orbit coupled system. Phys. Rev. Lett. 97, 236601 (2006).
46. Koralek, J. D. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610-613 (2009).
47. Sasaki, A. et al. Direct determination of spin-orbit interaction coefficients and realization of the persistent spin helix symmetry. Nature Nanotech. 9, 703-709 (2014).
48. Slonczewski, J. C. Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mater. 159, L1-L7 (1996).
49. Berger, L. Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev. B 54, 9353-9358 (1996).
50. Bernevig, B. A. & Vafek, O. Piezo-magnetoelectric effects in p-doped semiconductors. Phys. Rev. B 72, 033203 (2005).
51. Manchon, A. & Zhang, S. Theory of nonequilibrium intrinsic spin torque in a single nanomagnet. Phys. Rev. B 78, 212405 (2008).
52. Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189-193 (2011).
53. Chernyshov, A. et al. Evidence for reversible control of magnetization in a ferromagnetic material by means of spin-orbit magnetic field. Nature Phys. 5, 656-659 (2009).
54. Miron, I. M. et al. Current-driven spin torque induced by the Rashba effect in a ferromagnetic metal layer. Nature Mater. 9, 230-234 (2010).
55. Kurebayashi, H. et al. An antidamping spin-orbit torque originating from the Berry curvature. Nature Nanotech. 9, 211-217 (2014).
56. Garello, K. et al. Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures. Nature Nanotech. 8, 587-593 (2013).
57. Liu, L. et al. Spin-torque switching with the giant spin Hall effect of tantalum. Science 336, 555-558 (2012).
58. Mellnik, A. R. et al. Spin-transfer torque generated by a topological insulator. Nature 511, 449-451 (2014).
59. Fan, Y. et al. Magnetization switching through giant spin-orbit torque in a magnetically doped topological insulator heterostructure. Nature Mater. 13, 699-704 (2014).
60. Zelezný, J. et al. Relativistic Néel-order fields induced by electrical current in antiferromagnets. Phys. Rev. Lett. 113, 157201 (2014).
61. Wadley, P. et al. Electrical switching of an antiferromagnet. Preprint at http://arxiv.org/abs/1503.03765 (2015).
62. Dzyaloshinskii, I. E. Thermodynamic theory of weak ferromagnetism in antiferromagnetic substances. Sov. Phys. JETP 5, 1259-1262 (1957).
63. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91-98 (1960).
64. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nature Nanotech. 8, 899-911 (2013).
65. Zakeri, K. et al. Asymmetric spin-wave dispersion on Fe(110): Direct evidence of the Dzyaloshinskii-Moriya interaction. Phys. Rev. Lett. 104, 137203 (2010).
66. Onose, Y. et al. Observation of the magnon Hall effect. Science 329, 297-299 (2010).
67. Matsumoto, R. & Murakami, S. Theoretical prediction of a rotating magnon wave packet in ferromagnets. Phys. Rev. Lett. 106, 197202 (2011).
68. Manchon, A., Ndiaye, P. B., Moon, J., Lee, H. & Lee, K. Magnon-mediated Dzyaloshinskii-Moriya torque in homogeneous ferromagnets. Phys. Rev. B 90, 224403 (2014).
69. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045-3067 (2010).
70. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).
71. Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757-1761 (2006).
72. König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766-770 (2007).
73. Knez, I., Du, R.-R. & Sullivan, G. Evidence for helical edge modes in inverted InAs/GaSb quantum wells. Phys. Rev. Lett. 107, 136603 (2011).
74. Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101-1105 (2009).
75. Roushan, P. et al. Topological surface states protected from backscattering by chiral spin texture. Nature 460, 1106-1109 (2009).
76. Beenakker, C. W. J. Search for Majorana fermions in superconductors. Annu. Rev. Condens. Matter Phys. 4, 113-136 (2013).
77. Fu, L. & Kane, C. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).
78. Steda, P. & ͈eba, P. Antisymmetric spin filtering in one-dimensional electron systems with uniform spin-orbit coupling. Phys. Rev. Lett. 90, 256601 (2003).
79. Lutchyn, R., Sau, J. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).
80. Oreg, Y., Refael, G. & von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).
81. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003-1007 (2012).
82. Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602-607 (2014).
83. Choy, T.-P., Edge, J. M., Akhmerov, A. R. & Beenakker, C. W. J. Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling. Phys. Rev. B 84, 195442 (2011).
84. Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362-396 (1991).
85. Nayak, C., Simon, S., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083-1159 (2008).
86. Fu, L. Topological crystalline insulators. Phys. Rev. Lett. 106, 106802 (2011).
87. Alexandradinata, A., Fang, C., Gilbert, M. J. & Bernevig, B. A. Spin-orbit-free topological insulators without time-reversal symmetry. Phys. Rev. Lett. 113, 116403 (2014).
88. Ikegami, H., Tsutsumi, Y. & Kono, K. Chiral symmetry breaking in 3He-A. Science 341, 59-62 (2013).
89. Wehling, T. O., Black-Schaffer, A. M. & Balatsky, A. V. Dirac materials. Adv. Phys. 63, 1-76 (2014).
90. Volovik, G. E. An analog of the quantum Hall effect in a superfluid 3He film. Sov. Phys. JETP 67, 1804-1811 (1988).
91. Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nature Phys. 2, 620-625 (2006).
92. Slonczewski, J. C. & Weiss, P. R. Band structure of graphite. Phys. Rev. 109, 272-279 (1958).
93. Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201-204 (2005).
94. Han, W., Kawakami, R. K., Gmitra, M. & Fabian, J. Graphene spintronics. Nature Nanotech. 9, 794-807 (2014).
95. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).
96. Roth, A. et al. Nonlocal transport in the quantum spin Hall state. Science 325, 294-297 (2009).
97. Qiao, Z. et al. Quantum anomalous Hall effect in graphene proximity coupled to an antiferromagnetic insulator. Phys. Rev. Lett. 112, 116404 (2014).
98. Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the 'parity anomaly'. Phys. Rev. Lett. 61, 2015-2018 (1988).
99. Balakrishnan, J. et al. Giant spin Hall effect in graphene grown by chemical vapour deposition. Nature Commun. 5, 4748 (2014).
100. Young, A. F. et al. Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state. Nature 505, 528-532 (2014).
101. Marchenko, D. et al. Giant Rashba splitting in graphene due to hybridization with gold. Nature Commun. 3, 1232 (2012).
102. Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: Magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).
103. Rycerz, A., Tworzydo, J. & Beenakker, C. W. J. Valley filter and valley valve in graphene. Nature Phys. 3, 172-175 (2007).
104. Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427-1430 (2013).
105. Abanin, D. A. et al. Giant nonlocality near the Dirac point in graphene. Science 332, 328-330 (2011).
106. Gorbachev, R. V. et al. Detecting topological currents in graphene superlattices. Science 346, 448-451 (2014).
107. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nature Phys. 10, 343-350 (2014).
108. Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nature Nanotech. 7, 494-498 (2012).
109. Zeng, H., Dai, J., Yao, W., Xiao, D. & Cui, X. Valley polarization in MoS2 monolayers by optical pumping. Nature Nanotech. 7, 490-493 (2012).
110. Mak, K. F., McGill, K. L., Park, J. & McEuen, P. L. Valleytronics. The valley Hall effect in MoS2 transistors. Science 344, 1489-1492 (2014).
111. Yuan, H. et al. Generation and electric control of spin-valley-coupled circular photogalvanic current in WSe2. Nature Nanotech. 9, 851-857 (2014).
112. Zhang, Y. J., Oka, T., Suzuki, R., Ye, J. T. & Iwasa, Y. Electrically switchable chiral light-emitting transistor. Science 344, 725-728 (2014).
113. Wu, S. et al. Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS2. Nature Phys. 9, 149-153 (2013).
114. Lin, Y.-J., Jimenez-Garca, K. & Spielman, I. B. Spin-orbit-coupled Bose-Einstein condensates. Nature 471, 83-86 (2011).
115. Aidelsburger, M. Experimental realization of strong effective magnetic fields in an optical lattice. Phys. Rev. Lett. 107, 255301 (2011).
116. Zhang, J.-Y. et al. Collective dipole oscillations of a spin-orbit coupled Bose-Einstein condensate. Phys. Rev. Lett. 109, 115301 (2012).
117. Qu, C., Hamner, C., Gong, M., Zhang, C. & Engels, P. Observation of zitterbewegung in a spin-orbit-coupled Bose-Einstein condensate. Phys. Rev. A 88, 021604 (2013).
118. Ji, S.-C. et al. Experimental determination of the finite-temperature phase diagram of a spin-orbit coupled Bose gas. Nature Phys. 10, 314-320 (2014).
119. Wang, P., Yu, Z., Fu, Z., Miao, J. & Huang, L. Spin-orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012).
120. Cheuk, L. W. et al. Spin-injection spectroscopy of a spin-orbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012).
121. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237-240 (2014).
122. Williams, R. A. et al. Synthetic partial waves in ultracold atomic collisions. Science 335, 314-317 (2011).
123. Cole, W. S., Zhang, S., Paramekanti, A. & Trivedi, N. Bose-Hubbard models with synthetic spin-orbit coupling: Mott insulators, spin textures, and superfluidity. Phys. Rev. Lett. 109, 085302 (2012).
124. Radi?, J., Di Ciolo, A., Sun, K. & Galitski, V. Exotic quantum spin models in spin-orbit-coupled Mott insulators. Phys. Rev. Lett. 109, 085303 (2012).
125. Cocks, D. et al. Time-reversal-invariant Hofstadter-Hubbard model with ultracold Fermions. Phys. Rev. Lett. 109, 205303 (2012).
126. Cai, Z., Zhou, X. & Wu, C. Magnetic phases of bosons with synthetic spin-orbit coupling in optical lattices. Phys. Rev. A 85, 061605 (2012).
127. Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604-1606 (2012).
128. Vishwanath, A. & Senthil, T. Physics of three-dimensional bosonic topological insulators: Surface-deconfined criticality and quantized magnetoelectric effect. Phys. Rev. X 3, 011016 (2013).
129. Hanson, R. & Awschalom, D. D. Coherent manipulation of single spins in semiconductors. Nature 453, 1043-1049 (2008).
130. Yang, B.-J. & Nagaosa, N. Emergent topological phenomena in thin films of pyrochlore iridates. Phys. Rev. Lett. 112, 246402 (2014).
131. Liu, Z. K. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864-867 (2014).
132. Xu, S. et al. Observation of Fermi arc surface states in a topological metal. Science 347, 294-298 (2015).
133. Witczak-Krempa, W., Chen, G., Kim, Y. B. & Balents, L. Correlated quantum phenomena in the strong spin-orbit regime. Annu. Rev. Condens. Matter Phys. 5, 57-82 (2014).
134. Naaman, R. & Waldeck, D. H. Chiral-induced spin selectivity effect. J. Phys. Chem. Lett. 3, 2178-2187 (2012).
135. Ast, C. et al. Giant spin splitting through surface alloying. Phys. Rev. Lett. 98, 186807 (2007).
136. Winkler, R. Spin-Orbit Coupling effects in Two-Dimensional Electron and Hole Systems (Springer, 2003).
137. Dyakonov, M. I. & Kachorovskii, V. Y. Spin relaxation of two-dimensional electrons in noncentrosymmetric semiconductors. Sov. Phys. Semicond. 20, 110-112 (1986).
138. Bihlmayer, G., Koroteev, Y. M., Echenique, P. M., Chulkov, E. V. & Blügel, S. The Rashba-effect at metallic surfaces. Surf. Sci. 600, 3888-3891 (2006).
139. Park, Y. H. et al. Separation of Rashba and Dresselhaus spin-orbit interactions using crystal direction dependent transport measurements. Appl. Phys. Lett. 103, 252407 (2013).
140. Nakamura, H., Koga, T. & Kimura, T. Experimental evidence of cubic Rashba effect in an inversion-symmetric oxide. Phys. Rev. Lett. 108, 206601 (2012).
141. LaShell, S., McDougall, B. & Jensen, E. Spin splitting of an Au(111) surface state band observed with angle resolved photoelectron spectroscopy. Phys. Rev. Lett. 77, 3419-3422 (1996).
142. Varykhalov, A. et al. Ir(111) surface state with giant Rashba splitting persists under graphene in air. Phys. Rev. Lett. 108, 066804 (2012).
143. King, P. D. C. et al. Large tunable Rashba spin splitting of a two-dimensional electron gas in Bi2Se3. Phys. Rev. Lett. 107, 096802 (2011).
144. Ishizaka, K. et al. Giant Rashba-type spin splitting in bulk BiTeI. Nature Mater. 10, 521-526 (2011).
145. Moser, J. et al. Tunneling anisotropic magnetoresistance and spin-orbit coupling in Fe/GaAs/Au tunnel junctions. Phys. Rev. Lett. 99, 056601 (2007).
146. Park, B. G. et al. A spin-valve-like magnetoresistance of an antiferromagnet-based tunnel junction. Nature Mater. 10, 347-351 (2011).
147. Heisenberg, W. Über den Bau der Atomkerne. I. Z. Phys. 77, 1-11 (1932).
148. Pesin, D. A. & MacDonald, A. H. Spintronics and pseudospintronics in graphene and topological insulators. Nature Mater. 11, 409-416 (2012).
149. Liu, X., Borunda, M. F., Liu, X. & Sinova, J. Effect of induced spin-orbit coupling for atoms via laser fields. Phys. Rev. Lett. 102, 046402 (2009).
150. Dalibard, J., Gerbier, F., Juzeliunas, G. & Öhberg, P. Artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523-1543 (2011).