Magnetism in Topological Insulators pp 117-142 | Cite as
Indirect Exchange Interaction Mediated by Dirac Fermions
Chapter
First Online:
- 518 Downloads
Abstract
Based on the model of s-d interaction discussed in Chap. 6, the indirect exchange interaction between a pair of magnetic impurities is calculated. The interaction carries the signature of the topological surface states. The chapter discusses possible magnetic textures induced by the indirect exchange.
Keywords
Indirect exchange interaction Spin–spin interaction via Dirac fermions Magnetic exchange in topological insulators RKKY oscillations Non-RKKY oscillations Bloembergen-Rowland magnetic interaction RKKY-type interaction in an electron gas with inverted bandsReferences
- 1.Zhu, J.-J., Yao, D.X., Zhang, S.-C., Chang, K.: Phys. Rev. Lett. 106, 097201 (2011)CrossRefGoogle Scholar
- 2.Bloembergen, N., Rowland, T.J.: Phys. Rev. 97, 1679 (1955)CrossRefGoogle Scholar
- 3.Abrikosov, A.A., Gorkov, L.P., Dzyaloshinski, I.E.: Quantum Field Theoretical Methods in Statistical Mechanics. Pergamon, New York (1965)zbMATHGoogle Scholar
- 4.Ruderman, M.A., Kittel, C.: Phys. Rev. 96, 99 (1954)CrossRefGoogle Scholar
- 5.Kasuya, T.: Prog. Theor. Phys. 16, 45 (1956)CrossRefGoogle Scholar
- 6.Yosida, K.: Phys. Rev. 106, 893 (1957)CrossRefGoogle Scholar
- 7.De Gennes, P.G.: J. Phys. Radium. 23, 630 (1962)CrossRefGoogle Scholar
- 8.Mattis, D.C.: The Theory of Magnetism Made Simple. World Scientific, Singapore (2006)CrossRefGoogle Scholar
- 9.Bloembergen, N., Rowland, T.J.: Phys. Rev. 97(6), 1680 (1955)CrossRefGoogle Scholar
- 10.Litvinov, V.I.: Sov. Phys. Semicond. 19, 345 (1985)Google Scholar
- 11.Abrikosov, A.A.: J. Low Temp. Phys. 39(1/2), 217 (1980)CrossRefGoogle Scholar
- 12.Liu, L., Bastard, G.: Phys. Rev. B25(1), 487 (1982)CrossRefGoogle Scholar
- 13.Abanin, D.A., Pesin, D.A.: Phys. Rev. Lett. 106, 136802 (2011)CrossRefGoogle Scholar
- 14.Fischer, B., Klein, M.W.: Phys. Rev. B11, 2025–2029 (1975)CrossRefGoogle Scholar
- 15.Litvinov, V.I., Dugaev, V.K.: Phys. Rev. B58(7), 3584 (1996)CrossRefGoogle Scholar
- 16.Lu, H.-Z., Shan, W.-Y., Wang, Y., Niu, Q., Shen, S.-Q.: Phys. Rev. 115407, B81 (2010)Google Scholar
- 17.Shan, W.-Y., Lu, H.-Z., Shen, S.-Q.: New J. Phys. 12, 043048 (2010)CrossRefGoogle Scholar
- 18.Shen, S.-Q., Shan, W.-Y., Lu, H.-Z.: arXiv:1009.5502v3 [cond-mat.mes-hall]Google Scholar
- 19.Litvinov, V.I., Dugaev, V.K.: Phys. Rev. Lett. 86(24), 5593 (2001)CrossRefGoogle Scholar
- 20.Dugaev, V.K., Litvinov, V.I.: Superlattices Microstruct. 16, 413 (1994)CrossRefGoogle Scholar
- 21.Litvinov, V.I., Dugaev, V.K.: Phys. Rev. B. 58, 3584 (1998)CrossRefGoogle Scholar
- 22.Dugaev, V.K., Litvinov, V.I., Barnas, J.: Phys. Rev. B. 74, 224438 (2006)CrossRefGoogle Scholar
- 23.Litvinov, V.: Wide Bandgap Semiconductor Spintronics. Pan Stanford, Singapore (2016)CrossRefGoogle Scholar
- 24.Liu, Q., Liu, C.-X., Xu, C., Qi, X.-L., Zhang, S.-C.: Phys. Rev. Lett. 102, 156603 (2009)CrossRefGoogle Scholar
- 25.Efimkin, D.K., Galitski, V.: Phys. Rev. B. 89, 115431 (2014)CrossRefGoogle Scholar
- 26.Hsieh, T.H., Lin, H., Liu, J., Duan, W., Bansil, A., Fu, L.: Nat. Commun. 3, 982 (2012)CrossRefGoogle Scholar
- 27.Tanaka, Y., Ren, Z., Sato, T., Nakayama, K., Souma, S., Takahashi, T., Segawa, K., Ando, Y.: Nat. Phys. 8, 800 (2012)CrossRefGoogle Scholar
- 28.Dugaev, V.K., Litvinov, V.I., Barnas, J.: Phys. Rev. B74, 224438 (2006)CrossRefGoogle Scholar
- 29.Litvinov, V.I.: Sov. Phys. Solid State. 27(4), 740 (1985)Google Scholar
- 30.Abramovitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions. National Bureau of Standards, Gaithersburg (1964)Google Scholar
- 31.Litvinov, V.I.: Phys. Rev. B89, 235316 (2014)CrossRefGoogle Scholar
Copyright information
© Springer Nature Switzerland AG 2020