Anisotropic surface-state-mediated RKKY interaction between adatoms

Physical Review B - Condensed Matter and Materials Physics

Volumn 85, Issue 4, 2012, Pages

  Patrone, Paul N ^a,b,c   Einstein, T L ^a  

^a Bldg 142   (United States)

^b The Institute for Research in Electronics and Applied Physics   (United States)

^c NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84856471416     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.85.045429     Document Type: Article

References (95)

1. J. Frenkel and T. Kontorova, J. Phys. (USSR) 1, 137 (1939).
2. P. Bak, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/45/6/001 45, 587 (1982).
3. S. Narasimhan and D. Vanderbilt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.1564 69, 1564 (1992).
4. J. C. Hamilton, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88. 126101 88, 126101 (2002).
5. J. C. Hamilton and S. M. Foiles, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.882 75, 882 (1995).
6. R. Pushpa, J. Rodriguez-Laguna, and S. N. Santalla, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.085409 79, 085409 (2009).
7. V. S. Stepanyuk, A. N. Baranov, D. V. Tsivlin, W. Hergert, P. Bruno, N. Knorr, M. A. Schneider, and K. Kern, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.205410 68, 205410 (2003).
8. V. S. Stepanyuk, L. Niebergall, R. C. Longo, W. Hergert, and P. Bruno, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70.075414 70, 075414 (2004).
9. J. D. Howe, P. Bhopale, Y. Tiwary, and K. A. Fichthorn, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.121410 81, 121410 (R) (2010).
10. W. Luo and K. A. Fichthorn, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.115433 72, 115433 (2005). (Pubitemid 43033171)
11. H. Brune, H. Roder, C. Boragno, and K. Kern, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.49.2997 49, 2997 (1994).
12. S. G. Davison and M. Stȩlicka, Basic Theory of Surface States (Oxford University Press, Oxford, 1996).
13. P. Han and P. S. Weiss, Surf. Sci. Rep. 0167-5729 10.1016/j.surfrep.2011. 11.001 67, 19 (2012).
14. M. A. Ruderman and C. Kittel, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.96.99 96, 99 (1954).
15. K. Yosida, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.106.893 106, 893 (1959).
16. T. Kasuya, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.16.45 16, 45 (1956).
17. C. Kittel, Solid State Phys. PTPKAV 0081-1947 10.1016/S0081-1947(08) 60030-2 22, 1 (1968).
18. K. H. Lau and W. Kohn, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(78) 90053-5 75, 69 (1978).
19. B. Fischer and M. W. Klein, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.11.2025 11, 2025 (1975);
20. M. T. Béal-Monod, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.36.8835 36, 8835 (1987).
21. P. Hyldgaard and M. Persson, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/12/1/103 12, L13 (2000).
22. G. D. Mahan, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/ S0217979295000562 9, 1327 (1995);
23. See also T. L. Einstein, Surf. Sci. SUSCAS 0039-6028 10.1016/0039- 6028(78)90062-6 75, L161 (1978).
24. In studying the oscillatory exchange coupling of magnetic multilayers, F. Herman and R. Schrieffer [Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.46. 5806 46, 5806 (1992)] showed that long-period superoscillations in the RKKY coupling could be explained by generalizing plane-wave wave functions to Bloch functions as well as incorporating boundary scattering at the film edges. The latter effect is irrelevant here, and we do not complicate our analysis with the former, given that there is no evidence for analogous superoscillations in adatom-adatom interactions.
25. B. G. Briner, P. Hofmann, M. Doering, H.-P. Rust, E. W. Plummer, and A. M. Bradshaw, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.58.13931 58, 13931 (1998).
26. T. L. Einstein, in Physical Structure of Solid Surfaces, edited by, W.N. Unertl, (Elsevier, Amsterdam, 1996), Chap 11.
27. L. M. Roth, H. J. Zeiger, and T. A. Kaplan, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.149.519 149, 519 (1966).
28. S. Lounis, P. Zahn, A. Weismann, M. Wenderoth, R. G. Ulbrich, I. Mertig, P. H. Dederichs, and S. Blügel [Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.035427 83, 035427 (2011)] very recently revisited with greater detail and novel applications the RKKY for anisotropic Fermi surfaces in 3D.
29. At Γ ̄ there is also a deeper, filled SS as well as a higher, empty image-potential SS. For example, for Cu(111) photoemission finds the minimum of the former at - 5.25 eV [S. G. Louie, P. Thiry, R. Pinchaux, Y. Pétroff, D. Chandesris, and J. Lecante, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.44.549 44, 549 (1980);
30. S. D. Kevan, N. G. Stoffel, and N. V. Smith, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.31.3348 31, 3348 (1985)]
31. F [W. Jacob, V. Dose, U. Kolac, Th. Fauster, and A. Goldmann, Z. Phys. B ZPCMDN 0722-3277 10.1007/BF01726194 63, 459 (1986)].
32. S. D. Kevan and R. H. Gaylord, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.36.5809 36, 5809 (1987).
33. L. Bürgi, L. Peterson, H. Brune, and K. Kern, Surf. Sci. Lett. SUSCAS 0039-6028 10.1016/S0039-6028(99)01102-4 447, L157 (2000). (Pubitemid 30557930)
34. K. Berland, T. L. Einstein, and P. Hyldgaard, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.035427 85, 035427 (2012).
35. For justification, see, for example, C. M. Bender and S. Orszag, Advanced Mathematical Methods for Scientists and Engineers (Springer, New York, 1999), pp. 276-279.
36. Similarly, there is evidence of a more fragile metallic surface state on noble-metal surfaces at the Y ̄ point [W. W. Pai, J. S. Ozcomert, N. C. Bartelt, T. L. Einstein, and J. E. Reutt-Robey, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(94)91487-7 307-309, 747 (1994);
37. S. H. Liu, C. Hinnen, C. N. van Huong, N. R. de Tacconi, and K.-M. Ho, J. Electroanal. Chem. JECHES 0022-0728 10.1016/S0022-0728(84)80327-7 176, 325 (1984);
38. R. Courths, H. Wern, U. Hau, B. Cord, V. Bachelier, and S. Hüfner, J. Phys. F JPFMAT 0305-4608 10.1088/0305-4608/14/6/023 14, 1559 (1984)].
39. Note also the 2D RKKY-like behavior found in calculations of interactions between Co atoms on the (110) faces of noble metals [E. Simon, B. Lazarovits, L. Szunyogh, and B. jfalussy, Philos. Mag. JPFMAT 1478-6435 10.1080/ 14786430802322206 88, 2667 (2008)].
40. L. Petersen, B. Schaefer, E. Lægsgaard, I. Stensgaard, and F. Besenbacher, Surf. Sci. SUSCAS 0039-6028 10.1016/S0039-6028(00)00379-4 457, 319 (2000).
41. E. Simon, B. jfalussy, B. Lazarovits, A. Szilva, L. Szunyogh, and G. M. Stocks, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.224416 83, 224416 (2011).
42. E. W. Plummer and J. B. Hannon, Prog. Surf. Sci. PSSFBP 0079-6816 10.1016/0079-6816(94)90075-2 46, 149 (1994).
43. P. T. Sprunger, L. Petersen, E. W. Plummer, E. Læsgaard, and F. Besenbacher, Science SCIEAS 0036-8075 10.1126/science.275.5307.1764 275, 1764 (1997). (Pubitemid 27136707)
44. Ph. Hofmann, B. G. Briner, M. Doering, H.-P. Rust, E. W. Plummer, and A. M. Bradshaw, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.265 79, 265 (1997).
45. T. Balasubramanian, L. I. Johansson, P.-A. Glans, C. Virojanadara, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.64.205401 64, 205401 (2001).
46. P. Hyldgaard and M. Persson, Chalmers/G o teborg University, Appl. Phys. Rep. No. 1999-36, 1999 (unpublished).
47. J. Harris, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.31.1770 31, 1770 (1985).
48. Yu. A. Bychkov and E. I. Rashba, JETP Lett. 39, 78 (1984).
49. S. LaShell, B. A. McDougall, and E. Jensen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3419 77, 3419 (1996).
50. G. Nicolay, F. Reinert, S. Hüfner, and P. Blaha, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.033407 65, 033407 (2001).
51. L. Petersen and P. Hedegård, Surf. Sci. SUSCAS 0039-6028 10.1016/S0039-6028(00)00441-6 459, 49 (2000).
52. F to the imprecise treatment of the surface potential in their calculational scheme.
53. T. Hirahara, T. Nagao, I. Matsuda, G. Bihlmayer, E. V. Chulkov, Yu.M. Koroteev, P. M. Echenique, M. Saito, and S. Hasegawa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.146803 97, 146803 (2006). (Pubitemid 44498533)
54. Yu. M. Koroteev, G. Bihlmayer, J. E. Gayone, E. V. Chulkov, S. Blügel, P. M. Echenique, and Ph. Hofmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.046403 93, 046403 (2004).
55. C. R. Ast and H. Höchst, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.177602 87, 177602 (2001).
56. S. Agergaard, Ch. Søndergaard, H. Li, M. B. Nielsen, S. V. Hoffmann, Z. Li, and Ph. Hofmann, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/3/1/315 3, 15 (2001).
57. T. Hirahara, K. Miyamoto, I. Matsuda, T. Kadono, A. Kimura, T. Nagao, G. Bihlmayer, E. V. Chulkov, S. Qiao, K. Shimada, H. Namatame, M. Taniguchi, and S. Hasegawa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.153305 76, 153305 (2007).
58. M. Bode, M. Heide, K. von Bergmann, P. Ferriani, S. Heinze, G. Bihlmayer, A. Kubetzka, O. Pietzsch, S. Blügel, and R. Wiesendanger, Nature (London) NATUAS 0028-0836 10.1038/nature05802 447, 190 (2007). (Pubitemid 46763084)
59. L. Zhou, J. Wiebe, S. Lounis, E. Vedmedenko, F. Meier, S. Blügel, P. H. Dederichs, and R. Wiesendanger, Nat. Phys. NATUAS 1745-2473 10.1038/nphys1514 6, 187 (2010).
60. In earlier work members of this group [J. Wiebe, F. Meier, K. Hashimoto, G. Bihlmayer, S. Blügel, P. Ferriani, S. Heinze, and R. Wiesendanger, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.193406 72, 193406 (2005)] (Pubitemid 43029505)
61. found that on clean Pt(111) the Shockley state is unoccupied (nonmetallic) but that some bulk bands contribute strongly to the local density of states at the surface. Zhou find strong directional dependence in the RKKY interaction and can fit to the generic 2D expression in the close-packed [1 1 ̄ 0] direction.
62. V. Chis and B. Hellsing, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.226103 93, 226103 (2004). (Pubitemid 40072799)
63. Y.-P. Xie, Y. Luo, and S.-J. Liu, Chin. Phys. PRLTAO 1009-1963 10.1088/1009-1963/16/5/043 16, 1429 (2007). (Pubitemid 46838982)
64. S.-J. Tang, H.-T. Jeng, C.-S. Hsue, Ismail, P. T. Sprunger, and E. W. Plummer, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.045405 77, 045405 (2008).
65. R. Sathiyanarayanan, T. J. Stasevich, and T. L. Einstein, Surf. Sci. SUSCAS 0039-6028 10.1016/j.susc.2008.01.022 602, 1243 (2008);
66. R. Sathiyanarayanan and T. L. Einstein, Surf. Sci. SUSCAS 0039-6028 10.1016/j.susc.2009.05.012 603, 2387 (2009).
67. V. V. Cheianov and V. I. Fal'ko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.226801 97, 226801 (2006); (Pubitemid 44826903)
68. V. V. Cheianov, Eur. Phys. J. Spec. Top. PRLTAO 1951-6355 10.1140/epjst/e2007-00225-5 148, 55 (2007);
69. V. V. Cheianov, V. Fal'ko, O. Syljuåsen, and B. L. Altshuler, Solid State Commun. SSCOA4 0038-1098 10.1016/j.ssc.2009.07.008 149, 1499 (2009);
70. V. V. Cheianov, O. Syljuåsen, B. L. Altshuler, and V. Fal'ko, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.233409 80, 233409 (2009);
71. V. V. Cheianov, O. Syljuåsen, B. L. Altshuler, and V. Fal'ko, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/89/56003 89, 56003 (2010).
72. L. Brey, H. A. Fertig, and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.116802 99, 116802 (2007); (Pubitemid 47429443)
73. E. H. Hwang and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.156802 101, 156802 (2008).
74. S. Saremi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.184430 76, 184430 (2007).
75. C. Bena and S. A. Kivelson, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.125432 72, 125432 (2005); (Pubitemid 43028947)
76. C. Bena, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.076601 100, 076601 (2008). (Pubitemid 351393576)
77. L. Simon, C. Bena, F. Vonau, D. Aubel, H. Nasrallah, M. Habar, and J. C. Peruchetti, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2009-00142-3 69, 351 (2009).
78. J. E. Bunder and H.-H. Lin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.153414 80, 153414 (2009).
79. A. V. Shytov, D. A. Abanin, and L. S. Levitov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.016806 103, 016806 (2009);
80. D. A. Abanin, A. V. Shytov, and L. S. Levitov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.086802 105, 086802 (2010).
81. A. M. Black-Schaffer, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82. 073409 82, 073409 (2010).
82. M. Sherafati and S. Satpathy, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.165425 83, 165425 (2011);
83. M. Sherafati and S. Satpathy, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.125416 84, 125416 (2011).
84. B. Uchoa, T. G. Rappoport, and A. H. Castro Neto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.016801 106, 016801 (2011);
85. B. Uchoa, T. G. Rappoport, and A. H. Castro Neto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.159901 106, 159901 (E) (2011).
86. E. Kogan, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.115119 84, 115119 (2011).
87. Section IV G of A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim [Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys. 81.109 81, 109 (2009)] has a short review of RKKY in graphene.
88. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.82.3045 82, 3045 (2010).
89. Q. Liu, C.-X. Liu, C. Xu, X.-L. Qi, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.156603 102, 156603 (2009).
90. D. A. Abanin and D. A. Pesin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.136802 106, 136802 (2011).
91. J.-J. Zhu, D.-X. Yao, S.-C. Zhang, and K. Chang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.097201 106, 097201 (2011).
92. T. L. Einstein, Langmuir LANGD5 0743-7463 10.1021/la00059a021 7, 2520 (1991).
93. P. Hyldgaard and T. L. Einstein, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2002-00236-0 59, 265 (2002);
94. P. Hyldgaard and T. L. Einstein, J. Cryst. Growth JCRGAE 0022-0248 10.1016/j.jcrysgro.2004.11.216 275, e1637 (2005). (Pubitemid 40429070)
95. T. L. Einstein, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.16.3411 16, 3411 (1977).