Indirect exchange and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions in magnetically-doped graphene

Crystals

Volumn 3, Issue 1, 2013, Pages 49-78

  Power, Stephen R ^a,b   Ferreira, Mauro S ^a  

^a TRINITY COLLEGE DUBLIN   (Ireland)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Exchange interactions; Graphene; Magnetic impurities; Magnetic interactions; RKKY; Spintronics

Indexed keywords

EID: 84876398493     PISSN: None     EISSN: 20734352     Source Type: Journal    
DOI: 10.3390/cryst3010049     Document Type: Review

References (129)

1. Geim, A.K.; Novoselov, K.S. The rise of graphene. Nat. Mater. 2007, 6, 183-191.
2. Geim, A.K. Graphene: Status and prospects. Science 2009, 324, 1530-1534.
3. Castro Neto, A.H.; Guinea, F.; Peres, N.M.R.; Novoselov, K.S.; Geim, A.K. The electronic properties of graphene. Rev. Mod. Phys. 2009, 81, 109-162.
4. Novoselov, K.S. Nobel lecture: Graphene: Materials in the Flatland. Rev. Mod. Phys. 2011, 83, 837-849.
5. Yazyev, O.V. Emergence of magnetism in graphene materials and nanostructures. Rep. Prog. Phys. 2010, 73, doi:10.1088/0034-4885/73/5/056501.
6. Wolf, S.A.; Awschalom, D.D.; Buhrman, R.A.; Daughton, J.M.; von Molnr, S.; Roukes, M.L.; Chtchelkanova, A.Y.; Treger, D.M. Spintronics: A spin-based electronics vision for the future. Science 2001, 294, 1488-1495.
7. Awschalom, D.D.; Flatte, M.E. Challenges for semiconductor spintronics. Nat. Phys. 2007, 3, 153-159.
8. Chappert, C.; Fert, A.; van Dau, F.N. The emergence of spin electronics in data storage. Nat. Mater. 2007, 6, 813-823.
9. Fert, A. Nobel lecture: Origin, development, and future of spintronics. Rev. Mod. Phys. 2008, 80, 1517-1530.
10. Kane, C.L.; Mele, E.J. Quantum spin hall effect in graphene. Phys. Rev. Lett. 2005, 95, 226801:1-226801:4.
11. Huertas-Hernando, D.; Guinea, F.; Brataas, A. Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps. Phys. Rev. B 2006, 74, 155426:1-155426:15.
12. Min, H.; Hill, J.E.; Sinitsyn, N.A.; Sahu, B.R.; Kleinman, L.; MacDonald, A.H. Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys. Rev. B 2006, 74, 165310:1-165310:5.
13. Huertas-Hernando, D.; Guinea, F.; Brataas, A. Spin-orbit-mediated spin relaxation in graphene. Phys. Rev. Lett. 2009, 103, 146801:1-146801:4.
14. Trauzettel, B.; Bulaev, D.V.; Loss, D.; Burkard, G. Spin qubits in graphene quantum dots. Nat. Phys. 2007, 3, 192-196.
15. Yazyev, O.V. Hyperfine interactions in graphene and related carbon nanostructures. Nano Lett. 2008, 8, 1011-1015.
16. Fischer, J.; Trauzettel, B.; Loss, D. Hyperfine interaction and electron-spin decoherence in graphene and carbon nanotube quantum dots. Phys. Rev. B 2009, 80, 155401:1-155401:9.
17. Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M.S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys. Rev. B 1996, 54, 17954-17961.
18. Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. Peculiar localized state at Zigzag graphite edge. J. Phys. Soc. Jpn 1996, 65, 1920-1923.
19. Son, Y.W.; Cohen, M.L.; Louie, S.G. Half-metallic graphene nanoribbons. Nature 2006, 444, 347-349.
20. Fernández-Rossier, J. Prediction of hidden multiferroic order in graphene zigzag ribbons. Phys. Rev. B 2008, 77, 075430-075430:5.
21. Wimmer, M.; Adagideli, I.; Berber, S.; Tománek, D.; Richter, K. Spin currents in rough graphene nanoribbons: Universal fluctuations and spin injection. Phys. Rev. Lett. 2008, 100, 177207:1-177207:4.
22. Kim, W.Y.; Kim, K.S. Prediction of very large values of magnetoresistance in a graphene nanoribbon device. Nat. Nanotechnol. 2008, 3, 408-412.
23. Tao, C.; Jiao, L.; Yazyev, O.V.; Chen, Y.; Feng, J.; Zhang, X.; Capaz, R.B.; Tour, J.M.; Zettl, A.; Louie, S.G.; Dai, H.; Crommie, M.F. Spatially resolving edge states of chiral graphene nanoribbons. Nat. Phys. 2011, 7, 616-620.
24. Kunstmann, J.; Özdoǧan, C.; Quandt, A.; Fehske, H. Stability of edge states and edge magnetism in graphene nanoribbons. Phys. Rev. B 2011, 83, 045414:1-045414:8.
25. Yazyev, O.V.; Helm, L. Defect-induced magnetism in graphene. Phys. Rev. B 2007, 75, 125408:1-125408:5.
26. Palacios, J.J.; Fernández-Rossier, J.; Brey, L. Vacancy-induced magnetism in graphene and graphene ribbons. Phys. Rev. B 2008, 77, 195428:1-195428:14.
27. Pedersen, T.G.; Flindt, C.; Pedersen, J.; Mortensen, N.A.; Jauho, A.P.; Pedersen, K. Graphene antidot lattices: Designed defects and spin qubits. Phys. Rev. Lett. 2008, 100, 136804:1-136804:4.
28. Lieb, E.H. Two theorems on the Hubbard model. Phys. Rev. Lett. 1989, 62, 1201-1204.
29. Xie, L.; Wang, X.; Lu, J.; Ni, Z.; Luo, Z.; Mao, H.; Wang, R.; Wang, Y.; Huang, H.; Qi, D.; et al. Room temperature ferromagnetism in partially hydrogenated epitaxial graphene. Appl. Phys. Lett. 2011, 98, 193113:1-193113:3.
30. Soriano, D.; Leconte, N.; Ordejón, P.; Charlier, J.; Palacios, J.; Roche, S. Magnetoresistance and magnetic ordering fingerprints in hydrogenated graphene. Phys. Rev. Lett. 2011, 107, 016602:1-016602:4.
31. Krasheninnikov, A.V.; Lehtinen, P.O.; Foster, A.S.; Pyykkö, P.; Nieminen, R.M. Embedding transition-metal atoms in graphene: Structure, bonding, and magnetism. Phys. Rev. Lett. 2009, 102, 126807:1-126807:4.
32. Santos, E.J.G.; Ayuela, A.; Sánchez-Portal, D. First-principles study of substitutional metal impurities in graphene: Structural, electronic and magnetic properties. New J. Phys. 2010, 12, 053012:1-053012:32.
33. Zhang, H.; Lazo, C.; Blügel, S.; Heinze, S.; Mokrousov, Y. Electrically tunable quantum anomalous hall effect in graphene decorated by 5d transition-metal adatoms. Phys. Rev. Lett. 2012, 108, 056802:1-056802:5.
34. Weeks, C.; Hu, J.; Alicea, J.; Franz, M.; Wu, R. Engineering a robust quantum spin hall state in graphene via adatom deposition. Phys. Rev. X 2011, 1, 021001:1-021001:15.
35. Hu, J.; Alicea, J.; Wu, R.; Franz, M. Giant topological insulator gap in graphene with 5d adatoms. Phys. Rev. Lett. 2012, 109, 266801:1-266801:5.
36. Parkin, S.S.P.; More, N.; Roche, K.P. Oscillations in exchange coupling and magnetoresistance in metallic superlattice structures: Co/Ru, Co/Cr, and Fe/Cr. Phys. Rev. Lett. 1990, 64, 2304-2307.
37. Parkin, S.S.P. Systematic variation of the strength and oscillation period of indirect magnetic exchange coupling through the 3d, 4d, and 5d transition metals. Phys. Rev. Lett. 1991, 67, 3598-3601.
38. Edwards, D.M.; Mathon, J.; Muniz, R.B.; Phan, M.S. Oscillations of the exchange in magnetic multilayers as an analog of de Haas-van Alphen effect. Phys. Rev. Lett. 1991, 67, 493-496.
39. Edwards, D.M.; Mathon, J.; Muniz, R.B.; Phan, M.S. Oscillations in the exchange coupling of ferromagnetic layers separated by a nonmagnetic metallic layer. J. Phys. 1991, 3, 4941-4958.
40. Ruderman, M.A.; Kittel, C. Indirect exchange coupling of nuclear magnetic moments by conduction electrons. Phys. Rev. 1954, 96, 99-102.
41. Kasuya, T. A theory of metallic ferro-and antiferromagnetism on Zener's model. Prog. Theory Phys. 1956, 16, 45-57.
42. Yosida, K. Magnetic properties of Cu-Mn alloys. Phys. Rev. 1957, 106, 893-898.
43. Bruno, P.; Chappert, C. Oscillatory coupling between ferromagnetic layers separated by a nonmagnetic metal spacer. Phys. Rev. Lett. 1991, 67, 1602-1605.
44. Bruno, P.; Chappert, C. Ruderman-Kittel theory of oscillatory interlayer exchange coupling. Phys. Rev. B 1992, 46, 261-270.
45. Baibich, M.N.; Broto, J.M.; Fert, A.; van Dau, F.N.; Petroff, F.; Etienne, P.; Creuzet, G.; Friederich, A.; Chazelas, J. Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices. Phys. Rev. Lett. 1988, 61, 2472-2475.
46. Binasch, G.; Grünberg, P.; Saurenbach, F.; Zinn, W. Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange. Phys. Rev. B 1989, 39, 4828-4830.
47. Costa, A.T.; Kirwan, D.F.; Ferreira, M.S. Indirect exchange coupling between magnetic adatoms in carbon nanotubes. Phys. Rev. B 2005, 72, 085402:1-085402:8.
48. Kirwan, D.F.; Rocha, C.G.; Costa, A.T.; Ferreira, M.S. Sudden decay of indirect exchange coupling between magnetic atoms on carbon nanotubes. Phys. Rev. B 2008, 77, 085432:1-085432:6.
49. Kirwan, D.F.; de Menezes, V.M.; Rocha, C.G.; Costa, A.T.; Muniz, R.B.; Fagan, S.B.; Ferreira, M.S. Enhanced spin-valve effect in magnetically doped carbon nanotubes. Carbon 2009, 47, 2533-2537.
50. Kirwan, D.F. Theoretical Studies of Carbon Nanotubes Interacting with Magnetic Atoms. Ph.D. Thesis, Trinity College Dublin, Dublin, Ireland, 2009.
51. Lloyd, P. Wave propagation through an assembly of spheres: II. The density of single-particle eigenstates. Proc. Phys. Soc. 1967, 90, 207-216.
52. The allowed electron energies are quantised in one-dimensional or multilayer systems. In higher dimensions the allowed energies are modified by the wells, but are not strictly quantised.
53. d'Albuquerque e Castro, J.; Ferreira, M.S.; Muniz, R.B. Theory of the exchange coupling in magnetic metallic multilayers. Phys. Rev. B 1994, 49, 16062-16065.
54. Ferreira, M.S.; Muniz, R.B.; d'Alberquerque e Castro, J.; Edwards, D.M. The nature and validity of the RKKY limit of exchange coupling in magnetic trilayers. J. Phys. Condens. Matter 1994, 6, L619-L623.
55. Ferreira, M.S.; d'Albuquerque e Castro, J.; Edwards, D.M.; Mathon, J. Fundamental oscillation periods of the interlayer exchange coupling beyond the RKKY approximation. J. Phys. Condens. Matter 1996, 8, 11259-11276.
56. Tung, L.; Buschow, K.; Franse, J.; Thuy, N. Magnetic coupling between rare earth moments in some antiferromagnetic Gd compounds. J. Magn. Magn. Mater. 1996, 154, 96-100.
57. Saremi, S. RKKY in half-filled bipartite lattices: Graphene as an example. Phys. Rev. B 2007, 76, 184430:1-184430:6.
58. Bunder, J.E.; Lin, H. Ruderman-Kittel-Kasuya-Yosida interactions on a bipartite lattice. Phys. Rev. B 2009, 80, 153414:1-153414:4.
59. Kogan, E. RKKY interaction in graphene. Phys. Rev. B 2011, 84, 115119:1-115119:6.
60. Lehtinen, P.O.; Foster, A.S.; Ayuela, A.; Krasheninnikov, A.; Nordlund, K.; Nieminen, R.M. Magnetic properties and diffusion of adatoms on a graphene sheet. Phys. Rev. Lett. 2003, 91, 017202:1-017202:4.
61. Pisani, L.; Montanari, B.; Harrison, N.M. A defective graphene phase predicted to be a room temperature ferromagnetic semiconductor. New J. Phys. 2008, 10, 033002:1-033002:9.
62. Santos, E.J.G.; Sánchez-Portal, D.; Ayuela, A. Magnetism of substitutional Co impurities in graphene: Realization of single π vacancies. Phys. Rev. B 2010, 81, 125433:1-125433:6.
63. Soriano, D.; Muñoz Rojas, F.; Fernández-Rossier, J.; Palacios, J.J. Hydrogenated graphene nanoribbons for spintronics. Phys. Rev. B 2010, 81, 165409:1-165409:7.
64. Gerber, I.C.; Krasheninnikov, A.V.; Foster, A.S.; Nieminen, R.M. A first-principles study on magnetic coupling between carbon adatoms on graphene. New J. Phys. 2010, 12, 113021:1-113021:14.
65. Black-Schaffer, A.M. RKKY coupling in graphene. Phys. Rev. B 2010, 81, 205416:1-205416:8.
66. Black-Schaffer, A.M. Importance of electron-electron interactions in the RKKY coupling in graphene. Phys. Rev. B 2010, 82, 073409:1-073409:4.
67. Power, S.R.; Ferreira, M.S. Electronic structure of graphene beyond the linear dispersion regime. Phys. Rev. B 2011, 83, 155432:1-155432:7.
68. Vozmediano, M.A.H.; López-Sancho, M.P.; Stauber, T.; Guinea, F. Local defects and ferromagnetism in graphene layers. Phys. Rev. B 2005, 72, 155121:1-155121:5.
69. Cheianov, V.V.; Fal'ko, V.I. Friedel oscillations, impurity scattering, and temperature dependence of resistivity in graphene. Phys. Rev. Lett. 2006, 97, 226801:1-226801:4.
70. Brey, L.; Fertig, H.A.; Sarma, S.D. Diluted graphene antiferromagnet. Phys. Rev. Lett. 2007, 99, 116802:1-116802:4.
71. Sherafati, M.; Satpathy, S. RKKY interaction in graphene from the lattice Green's function. Phys. Rev. B 2011, 83, 165425:1-165425:8.
72. Lee, H.; Kim, J.; Mucciolo, E.R.; Bouzerar, G.; Kettemann, S. RKKY interaction in disordered graphene. Phys. Rev. B 2012, 85, 075420:1-075420:5.
73. Horiguchi, T. Lattice Green's functions for the triangular and honeycomb lattices. J. Math. Phys. 1972, 13, 1411-1419.
74. Weiße, A.; Wellein, G.; Alvermann, A.; Fehske, H. The kernel polynomial method. Rev. Mod. Phys. 2006, 78, 275-306.
75. Venezuela, P.; Muniz, R.B.; Costa, A.T.; Edwards, D.M.; Power, S.R.; Ferreira, M.S. Emergence of local magnetic moments in doped graphene-related materials. Phys. Rev. B 2009, 80, 241413:1-241413:4.
76. Wunsch, B.; Stauber, T.; Sols, F.; Guinea, F. Dynamical polarization of graphene at finite doping. New J. Phys. 2006, 8, doi:10.1088/1367-2630/8/12/318.
77. Kogan, E. All approaches to RKKY interaction in graphene are equal, but some approaches are more equal than others. Available online: http://arxiv.org/abs/1210.5744 (accessed on 18 January 2013).
78. Anderson, P.W. Localized magnetic states in metals. Phys. Rev. 1961, 124, 41-53.
79. Uchoa, B.; Rappoport, T.G.; Castro Neto, A.H. Kondo quantum criticality of magnetic adatoms in graphene. Phys. Rev. Lett. 2011, 106, 016801:1-016801:4.
80. Dugaev, V.K.; Litvinov, V.I.; Barnas, J. Exchange interaction of magnetic impurities in graphene. Phys. Rev. B 2006, 74, 224438:1-224438:5.
81. Zanolli, Z.; Charlier, J.C. Spin transport in carbon nanotubes with magnetic vacancy-defects. Phys. Rev. B 2010, 81, 165406:1-165406:6.
82. Costa, A.T.; Muniz, R.B.; Ferreira, M.S. Dynamic interaction between localized magnetic moments in carbon nanotubes. New J. Phys. 2008, 10, 063008:1-063008:10.
83. Bunder, J.E.; Hill, J.M. Geometric influence on Ruderman-Kittel-Kasuya-Yosida interactions in zigzag carbon nanotubes. J. Chem. Phys. 2012, 136, 154504:1-154504:6.
84. Szałowski, K. Indirect RKKY interaction in armchair graphene nanoribbons. Available online: http://arxiv.org/abs/1211.0615 (accessed on 18 January 2013).
85. Sun, J.; Hu, F.; Tang, H.; Guo, W.; Lin, H. Indirect exchange of magnetic impurities in zigzag graphene ribbon. Available online: http://arxiv.org/abs/1211.1199 (accessed on 18 January 2013).
86. Szałowski, K. RKKY coupling between impurity spins in graphene nanoflakes. Phys. Rev. B 2011, 84, 205409:1-205409:10.
87. Hwang, E.H.; Das Sarma, S. Screening, Kohn Anomaly, Friedel Oscillation, and RKKY interaction in bilayer graphene. Phys. Rev. Lett. 2008, 101, 156802:1-156802:4.
88. Killi, M.; Heidarian, D.; Paramekanti, A. Controlling local moment formation and local moment interactions in bilayer graphene. New J. Phys. 2011, 13, doi:10.1088/1367-2630/13/5/053043.
89. Belonenko, M.; Lebedev, N.; Pak, A. Study of the indirect interaction in the quantum dots of the graphene bilayer in the framework of the s-d model. Tech. Phys. Lett. 2011, 37, 724-727.
90. Jiang, L.; Lü, X.; Gao, W.; Yu, G.; Liu, Z.; Zheng, Y. RKKY interaction in AB-stacked multilayer graphene. J. Phys. Condens. Matter 2012, 24, doi: 10.1088/0953-8984/24/20/206003.
91. Power, S.R.; de Menezes, V.M.; Fagan, S.B.; Ferreira, M.S. Model of impurity segregation in graphene nanoribbons. Phys. Rev. B 2009, 80, 235424:1-235424:5.
92. Mucciolo, E.R.; Castro Neto, A.H.; Lewenkopf, C.H. Conductance quantization and transport gaps in disordered graphene nanoribbons. Phys. Rev. B 2009, 79, 075407:1-075407:5.
93. Gorjizadeh, N.; Farajian, A.A.; Kawazoe, Y. The effects of defects on the conductance of graphene nanoribbons. Nanotechnology 2009, 20, 015201:1-015201:6.
94. Power, S.R.; de Menezes, V.M.; Fagan, S.B.; Ferreira, M.S. Magnetization profile for impurities in graphene nanoribbons. Phys. Rev. B 2011, 84, 195431:1-195431:8.
95. Klinovaja, J.; Loss, D. RKKY interaction in carbon nanotubes and graphene nanoribbons Available online: http://arxiv.org/abs/1211.3067 (accessed on 18 January 2013).
96. Sherafati, M.; Satpathy, S. Analytical expression for the RKKY interaction in doped graphene. Phys. Rev. B 2011, 84, 125416:1-125416:5.
97. Lee, H.; Mucciolo, E.R.; Bouzerar, G.; Kettemann, S. RKKY interactions in graphene: Dependence on disorder and Fermi energy. Phys. Rev. B 2012, 86, 205427:1-205427:7.
98. Pereira, V.M.; Castro Neto, A.H.; Peres, N.M.R. Tight-binding approach to uniaxial strain in graphene. Phys. Rev. B 2009, 80, 045401:1-045401:8.
99. Pereira, V.M.; Castro Neto, A.H. Strain engineering of graphene's electronic structure. Phys. Rev. Lett. 2009, 103, 046801:1-046801:4.
100. Ribeiro, R.M.; Pereira, V.M.; Peres, N.M.R.; Briddon, P.R.; Neto, A.H.C. Strained graphene: Tight-binding and density functional calculations. New J. Phys. 2009, 11, doi:10.1088/1367-2630/11/11/115002.
101. Pereira, V.M.; Castro Neto, A.H.; Liang, H.Y.; Mahadevan, L. Geometry, mechanics, and electronics of singular structures and wrinkles in graphene. Phys. Rev. Lett. 2010, 105, 156603:1-156603:4.
102. Guinea, F.; Katsnelson, M.I.; Geim, A.K. Energy gaps and a zero-field quantum hall effect in graphene by strain engineering. Nat. Phys. 2010, 6, 30-33.
103. Pellegrino, F.M.D.; Angilella, G.G.N.; Pucci, R. Transport properties of graphene across strain-induced nonuniform velocity profiles. Phys. Rev. B 2011, 84, 195404:1-195404:11.
104. Klimov, N.N.; Jung, S.; Zhu, S.; Li, T.; Wright, C.A.; Solares, S.D.; Newell, D.B.; Zhitenev, N.B.; Stroscio, J.A. Electromechanical properties of graphene drumheads. Science 2012, 336, 1557-1561.
105. Mohiuddin, T.M.G.; Lombardo, A.; Nair, R.R.; Bonetti, A.; Savini, G.; Jalil, R.; Bonini, N.; Basko, D.M.; Galiotis, C.; Marzari, N.; Novoselov, K.S.; Geim, A.K.; Ferrari, A.C. Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation. Phys. Rev. B 2009, 79, 205433:1-205433:8.
106. Levy, N.; Burke, S.A.; Meaker, K.L.; Panlasigui, M.; Zettl, A.; Guinea, F.; Neto, A.H.C.; Crommie, M.F. Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles. Science 2010, 329, 544-547.
107. Santos, E.J.G.; Ayuela, A.; Sánchez-Portal, D. Strain-tunable spin moment in Ni-doped graphene. J. Phys. Chem. C 2012, 116, 1174-1178.
108. Peng, F.; Hongbin, W. Strain enhanced exchange interaction between impurities in graphene. Physica B Condens. Matter 2012, 407, 3434-3436.
109. Power, S.R.; Gorman, P.D.; Duffy, J.M.; Ferreira, M.S. Strain-induced modulation of magnetic interactions in graphene. Phys. Rev. B 2012, 86, 195423:1-195423:6.
110. Ni, Z.H.; Yu, T.; Lu, Y.H.; Wang, Y.Y.; Feng, Y.P.; Shen, Z.X. Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2008, 2, 2301-2305.
111. Neek-Amal, M.; Covaci, L.; Peeters, F.M. Nanoengineered nonuniform strain in graphene using nanopillars. Phys. Rev. B 2012, 86, 041405:1-041405:5.
112. Xu, P.; Yang, Y.; Barber, S.D.; Ackerman, M.L.; Schoelz, J.K.; Qi, D.; Kornev, I.A.; Dong, L.; Bellaiche, L.; Barraza-Lopez, S.; Thibado, P.M. Atomic control of strain in freestanding graphene. Phys. Rev. B 2012, 85, 121406:1-121406:5.
113. Neek-Amal, M.; Peeters, F.M. Strain-engineered graphene through a nanostructured substrate. I. Deformations. Phys. Rev. B 2012, 85, 195445:1-195445:11.
114. Šimánek, E.; Heinrich, B. Gilbert damping in magnetic multilayers. Phys. Rev. B 2003, 67, 144418:1-144418:12.
115. Heinrich, B.; Tserkovnyak, Y.; Woltersdorf, G.; Brataas, A.; Urban, R.; Bauer, G.E.W. Dynamic exchange coupling in magnetic bilayers. Phys. Rev. Lett. 2003, 90, 187601:1-187601:4.
116. Guimarães, F.S.M.; Costa, A.T.; Muniz, R.B.; Mills, D.L. Spin currents in metallic nanostructures: Explicit calculations. Phys. Rev. B 2011, 84, 054403:1-054403:9.
117. Guimarães, F.S.M.; Kirwan, D.F.; Costa, A.T.; Muniz, R.B.; Mills, D.L.; Ferreira, M.S. Carbon nanotube: A low-loss spin-current waveguide. Phys. Rev. B 2010, 81, 153408:1-153408:4.
118. Guimarães, F.S.M.; Costa, A.T.; Muniz, R.B.; Ferreira, M.S. Graphene-based spin-pumping transistor. Phys. Rev. B 2010, 81, 233402:1-233402:4.
119. Guimarães, F.S.M.; Costa, A.T.; Muniz, R.B.; Ferreira, M.S. Graphene as a non-magnetic spin current lens. J. Phys. Condens. Matter 2011, 23, doi:10.1088/0953-8984/23/17/175302.
120. Abanin, D.A.; Morozov, S.V.; Ponomarenko, L.A.; Gorbachev, R.V.; Mayorov, A.S.; Katsnelson, M.I.; Watanabe, K.; Taniguchi, T.; Novoselov, K.S.; Levitov, L.S.; Geim, A.K. Giant nonlocality near the Dirac point in graphene. Science 2011, 332, 328-330.
121. Power, S.R.; Guimarães, F.S.M.; Costa, A.T.; Muniz, R.B.; Ferreira, M.S. Dynamic RKKY interaction in graphene. Phys. Rev. B 2012, 85, 195411:1-195411:6.
122. Heinrich, A.J.; Gupta, J.A.; Lutz, C.P.; Eigler, D.M. Single-atom spin-flip spectroscopy. Science 2004, 306, 466-469.
123. Loth, S.; von Bergmann, K.; Ternes, M.; Otte, A.F.; Lutz, C.P.; Heinrich, A.J. Controlling the state of quantum spins with electric currents. Nat. Phys. 2010, 6, 340-344.
124. Khajetoorians, A.A.; Chilian, B.; Wiebe, J.; Schuwalow, S.; Lechermann, F.; Wiesendanger, R. Detecting excitation and magnetization of individual dopants in a semiconductor. Nature 2010, 467, 1084-1087.
125. Khajetoorians, A.A.; Lounis, S.; Chilian, B.; Costa, A.T.; Zhou, L.; Mills, D.L.; Wiebe, J.; Wiesendanger, R. Itinerant nature of atom-magnetization excitation by tunneling electrons. Phys. Rev. Lett. 2011, 106, 037205:1-037205:4.
126. Sielemann, R.; Kobayashi, Y.; Yoshida, Y.; Gunnlaugsson, H.P.; Weyer, G. Magnetism at single isolated iron atoms implanted in graphite. Phys. Rev. Lett. 2008, 101, 137206:1-137206:4.
127. Meier, F.; Zhou, L.; Wiebe, J.; Wiesendanger, R. Revealing magnetic interactions from single-atom magnetization curves. Science 2008, 320, 82-86.
128. Zhou, L.; Wiebe, J.; Lounis, S.; Vedmedenko, E.; Meier, F.; Blügel, S.; Dederichs, P.; Wiesendanger, R. Strength and directionality of surface Ruderman-Kittel-Kasuya-Yosida interaction mapped on the atomic scale. Nat. Phys. 2010, 6, 187-191.
129. Krstic, V.; Ewels, C.P.; Wågberg, T.; Ferreira, M.S.; Janssens, A.M.; Stephan, O.; Glerup, M. Indirect magnetic coupling in light-element-doped single-walled carbon nanotubes. ACS Nano 2010, 4, 5081-5086.