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Magnetic Field and Ferromagnetic Proximity Effects

  • Vladimir Litvinov
Chapter

Abstract

The chapter examines various magnetic gaps in the Dirac spectrum and proximity-induced surface Hall conductivity. Topological phase transitions in a parallel magnetic field, the current-induced torque, and possible device applications are discussed.

Keywords

Topological insulator in perpendicular magnetic field Topological insulator in parallel magnetic field Magnetic gaps Proximity ferromagnetism in topological insulators Anomalous quantum Hall effect Topological phase transition Spin-transfer torque Spin–orbit torque 

References

  1. 1.
    Yu, R., Zhang, W., Zhang, H.J., Zhang, S.C., Dai, X., Fang, Z.: Science. 329, 61 (2010)CrossRefGoogle Scholar
  2. 2.
    Essin, A.M., Moore, J.E., Vanderbilt, D.: Phys. Rev. Lett. 102, 146805 (2009)CrossRefGoogle Scholar
  3. 3.
    Garate, I., Franz, M.: Phys. Rev. Lett. 104, 146802 (2010)CrossRefGoogle Scholar
  4. 4.
    Zhang, Y., He, K., Chang, C.Z., Song, C.L., Wang, L.L., Chen, X., Jia, J.F., Fang, Z., Dai, X., Shan, W.Y., Shen, S.Q., Niu, Q., Qi, X.L., Zhang, S.C., Ma, X.C., Xue, Q.K.: Nat. Phys. 6, 584 (2010)CrossRefGoogle Scholar
  5. 5.
    Chen, Y.L., Chu, J.H., Analitis, J.G., Liu, Z.K., Igarashi, K., Kuo, H.H., Qi, X.L., Mo, S.K.: Science. 329, 659 (2010)CrossRefGoogle Scholar
  6. 6.
    Chang, C.Z., Zhang, J., Feng, X., Shen, J., Zhang, Z., Guo, M., Li, K., Ou, Y., Wei, P., Wang, L.L., Ji, Z.Q., Feng, Y., Ji, S., Chen, X., Jia, J., Dai, X., Fang, Z., Zhang, S.C., He, K., Wang, Y., Lu, L., Ma, X.C., Xue, Q.K.: Science. 340, 167 (2013)CrossRefGoogle Scholar
  7. 7.
    Checkelsky, J.G., Yoshimi, R., Tsukazaki, A., Takahashi, K.S., Kozuka, Y., Falson, J., Kawasaki, M., Tokura, Y.: Nat. Phys. 10, 731 (2014)CrossRefGoogle Scholar
  8. 8.
    Kou, X., Guo, S., Fan, Y., Pan, L., Lang, M., Jiang, Y., Shao, Q., Nie, T., Murata, K., Tang, J., Wang, Y., He, L., Lee, T., Lee, W., Wang, K.L.: Phys. Rev. Lett. 113, 137201 (2014)CrossRefGoogle Scholar
  9. 9.
    Chang, C.-Z., Zhao, W., Kim, D.Y., Zhang, H.J., Assaf, B.A., Heiman, D., Zhang, S.C., Liu, C.X., Chan, M.H.W., Moodera, J.S.: Nat. Mater. 14, 473 (2015)CrossRefGoogle Scholar
  10. 10.
    Wei, P., Katmis, F., Assaf, B.A., Steinberg, H., Jarillo-Herrero, P., Heiman, D., Moodera, J.S.: Phys. Rev. Lett. 110, 186807 (2013)CrossRefGoogle Scholar
  11. 11.
    Jiang, Z., Chang, C.Z., Tang, C., Zheng, J.G., Moodera, J.S., Shi, J.: AIP Adv. 6, 055809 (2016)CrossRefGoogle Scholar
  12. 12.
    Katmis, F., Lauter, V., Nogueira, F.S., Assaf, B.A., Jamer, M.E., Wei, P., Satpati, B., Freeland, J.W., Eremin, I., Heiman, D., Jarillo-Herrero, P., Moodera, J.S.: Nature. 533, 513 (2016)CrossRefGoogle Scholar
  13. 13.
    Ralph, D.C., Stiles, M.D.: J. Magn. Magn. Mater. 320, 1190 (2008)CrossRefGoogle Scholar
  14. 14.
    Mellnik, R., Lee, J.S., Richardella, A., Grab, J.L., Mintun, P.J., Fischer, M.H., Vaezi, A., Manchon, A., Kim, E.-A., Samarth, N., Ralph, D.C.: Nature. 511, 449 (2014)CrossRefGoogle Scholar
  15. 15.
    Fanchiang, Y.T., Chen, K.H.M., Tseng, C.C., Chen, C.C., Cheng, C.K., Yang, S.R., Wu, C.N., Lee, S.F., Hong, M., Kwo, J.: Nat. Commun. 9, 223 (2018)CrossRefGoogle Scholar
  16. 16.
    Hirahara, T., Eremeev, S.V., Shirasawa, T., Okuyama, Y., Kubo, T., Nakanishi, R., Akiyama, R., Takayama, A., Hajiri, T., Ideta, S., Matsunami, M., Sumida, K., Miyamoto, K., Takagi, Y., Tanaka, K., Okuda, T., Yokoyama, T., Hasegawa, S., Chulkov, E.V.: Nano Lett. 17(6), 3493 (2017)CrossRefGoogle Scholar
  17. 17.
    Yoshimi, R., Yasuda, K., Tsukazaki, A., Takahashi, K.S., Nagaosa, N., Kawasaki, M., Tokura, Y.: Nat. Commun. 6, 8530 (2015)CrossRefGoogle Scholar
  18. 18.
    Lu, H.-Z., Zhao, A., Shen, S.-Q.: Phys. Rev. Lett. 111, 146802 (2013)CrossRefGoogle Scholar
  19. 19.
    Qi, X.-L., Wu, Y.-S., Zhang, S.-C.: Phys. Rev. B74, 085308 (2006)CrossRefGoogle Scholar
  20. 20.
    Romming, N., Kubetzka, A., Hanneken, C., von Bergmann, K., Wiesendanger, R.: Phys. Rev. Lett. 114, 177203 (2015)CrossRefGoogle Scholar
  21. 21.
    Kanazawa, N., Seki, S., Tokura, Y.: Adv. Mater. 29, 1603227 (2017)CrossRefGoogle Scholar
  22. 22.
    Yu, G., Jenkins, A., Ma, X., Razavi, S.A., He, C., Yin, G., Shao, Q., He, Q.l., Wu, H., Li, W., Jiang, W., Han, X., Li, X., Bleszynski-Jayich, A.C., Amiri, P.K., Wang, K.L.: Nano Lett. 18, 980 (2017)CrossRefGoogle Scholar
  23. 23.
    Zhang, S., Kronast, F., van der Laan, G., Hesjedal, T.: Nano Lett. 18, 1057 (2018)CrossRefGoogle Scholar
  24. 24.
    Romming, N., Hanneken, C., Menzel, M., Bickel, J.E., Wolter, B., von Bergmann, K., Kubetzka, A., Wiesendanger, R.: Science. 341, (2013)Google Scholar
  25. 25.
    Zyuzin, A.A., Hook, M.D., Burkov, A.A.: Phys. Rev. B83, 245428 (2011)CrossRefGoogle Scholar
  26. 26.
    Zyuzin, A.A., Burkov, A.A.: Phys. Rev. B83, 195413 (2011)CrossRefGoogle Scholar
  27. 27.
    Jackiw, R.: Phys. Rev. D29, 2375 (1984)MathSciNetGoogle Scholar
  28. 28.
    Haldane, F.D.M.: Phys. Rev. Lett. 61, 2015 (1988)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Yoshimi, R., Tsukazaki, A., Kozuka, Y., Falson, J., Takahashi, K.S., Checkelsky, J.G., Nagaosa, N., Kawasaki, M., Tokura, Y.: Nat. Commun. 6, 6627 (2015)CrossRefGoogle Scholar
  30. 30.
    Honma, K., Sato, T., Souma, S., Sugawara, K., Tanaka, Y., Takahashi, T.: Phys. Rev. Lett. 115, 266401 (2015)CrossRefGoogle Scholar
  31. 31.
    Kobayashi, Y., Sato, K., Yasui, Y., Moyoshi, T., Sato, M., Kakurai, K.: J. Physical Soc. Japan. 78, 084720 (2009)CrossRefGoogle Scholar
  32. 32.
    Tokura, Y., Seki, S.: Adv. Mater. 22, 1554 (2010)CrossRefGoogle Scholar
  33. 33.
    Stagraczynski, S., Chotorlishvili, L., Dugaev, V.K., Jia, C.-L., Ernst, A., Komnik, A., Berakdar, J.: Phys. Rev. B94, 174436 (2016)CrossRefGoogle Scholar
  34. 34.
    Wray, L.A., Xu, S.Y., Xia, Y., Hsieh, D., Fedorov, A.V., Hor, Y.S., Cava, R.J., Bansil, A., Lin, H., Hasan, M.Z.: Nat. Phys. 7, 33 (2011)CrossRefGoogle Scholar
  35. 35.
    Yokoyama, T., Tanaka, Y., Nagaosa, N.: Phys. Rev. B81, 121401 (2010)CrossRefGoogle Scholar
  36. 36.
    Wu, Z., Peeters, F.M., Chang, K.: Phys. Rev. B82, 115211 (2010)CrossRefGoogle Scholar
  37. 37.
    Büttiker, M., Imry, Y., Landauer, R., Pinhas, S.: Phys. Rev. B31, 6207 (1985)CrossRefGoogle Scholar
  38. 38.
    Yokoyama, T.: Phys. Rev. B84, 113407 (2011)CrossRefGoogle Scholar
  39. 39.
    Wakatsuki, R., Ezawa, M., Nagaosa, N.: Sci. Rep. 5, 13638 (2015)CrossRefGoogle Scholar
  40. 40.
    Slonczewski, J.C.: J. Magn. Magn. Mater. 159, L1 (1996)CrossRefGoogle Scholar
  41. 41.
    Berger, L.: Phys. Rev. B54, 9353 (1996)CrossRefGoogle Scholar
  42. 42.
    Chernyshov, M.O., Liu, X., Furdyna, J.K., Lyanda-Geller, Y., Rokhinson, L.P.: Nat. Phys. 5, 656 (2009)CrossRefGoogle Scholar
  43. 43.
    Miron, M., Gaudin, G., Auffret, S., Rodmacq, B., Schuhl, A., Pizzini, S., Vogel, J., Gambardella, P.: Nat. Mater. 9, 230 (2010)CrossRefGoogle Scholar
  44. 44.
    Ramaswamy, R., Lee, J.M., Cai, K., Yang, H.: Appl. Phys. Lett. 5, 031107 (2018)Google Scholar
  45. 45.
    Manchon, I. Miron, M., Jungwirth, T., Sinova, J., Zelezny, J., Thiaville, A., Garello, K., Gambardella, P.: Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems, arXiv:1801.09636v1 [cond-mat.mes-hall]. Rev. Mod. Phys. (2018)Google Scholar
  46. 46.
    Yokoyama, T., Zang, J., Nagaosa, N.: Phys. Rev. B81, 241410(R) (2010)CrossRefGoogle Scholar
  47. 47.
    Fischer, M.H., Vaezi, A., Manchon, A., Kim, E.A.: Phys. Rev. B93, 125303 (2016)CrossRefGoogle Scholar
  48. 48.
    Ghosh, S., Manchon, A.: Phys. Rev. B97, 134402 (2018)CrossRefGoogle Scholar
  49. 49.
    Fan, Y., Upadhyaya, P., Kou, X., Lang, M., Takei, S., Wang, Z., Tang, J., He, L., Chang, L.-T., Montazeri, M., Yu, G., Jiang, W., Nie, T., Schwartz, R.N., Tserkovnyak, Y., Wang, K.L.: Nat. Mater. 13, 699 (2014)CrossRefGoogle Scholar
  50. 50.
    Ndiaye, P.B., Akosa, C.A., Fischer, M.H., Vaezi, A., Kim, E.-A., Manchon, A.: Phys. Rev. B96, 014408 (2017)CrossRefGoogle Scholar
  51. 51.
    Kiselev, S.I., Sankey, J.C., Krivorotov, I.N., Emley, N.C., Schoelkopf, R.J., Buhrman, R.A., Ralph, D.C.: Nature. 425, 380 (2003)CrossRefGoogle Scholar
  52. 52.
    Semenov, Y.G., Duan, X., Kim, K.W.: Phys. Rev. B89, 201405(R) (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vladimir Litvinov
    • 1
  1. 1.Sierra Nevada CorporationIrvineUSA

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