Physical Principles of Spin Torque

  • Jonathan Z. SunEmail author


Spin torque refers to the exchange of spin angular momentum between a transport spin current carried by electrons and a ferromagnet. The macroscopic manifestation of this angular momentum exchange is a torque exerted on the ferromagnet by the presence of the spin current. The spin current is often accompanied by a net charge-current transport, although this is not always necessary. There are two types of torque commonly associated with such interactions, one is exchange-like and the other energy nonconserving. These two types of torques have different vectorial relationship with the electron spin polarization and the magnet’s moment. The exchange-like torque is in the direction perpendicular to the plane formed by the magnet moment and the spin polarization and is therefore often called the “perpendicular torque.” The energy-nonconserving torque lies in the plane, hence the name the “in-plane torque.” The perpendicular torque has been known for many decades, as it gives rise to exchange-like coupling between ferromagnetic thin films across a spacer layer of either a nonmagnetic metal or a tunnel barrier. A detailed understanding of the in-plane spin torque has emerged more recently. The in-plane spin torque is associated mainly with nonequilibrium and noncollinear transport of spin current across interfaces between nonmagnetic and ferromagnetic materials. It originates from the dephasing of an electron’s spin precession as it enters or leaves a ferromagnet–nonmagnetic interface. The in-plane spin torque gives rise to new dynamic behaviors of the ferromagnet that is the subject of many interesting investigations and with potential for applications. Its physical origin and implications are the main subjects of this review.


Tunnel Junction Spin Current Tunnel Barrier Uniaxial Anisotropy Spin Valve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Abbreviations




Antiparallel to parallel


Current Perpendicular to plane


Free layer




Giant magnetoresistance


Insulator or tunnel barrier


Injection layer


In-plane magnetic anisotropy


Metal oxide semiconductor field-effect transistor


Magnetic tunnel junction


Nonmagnetic metal


Parallel to antiparallel


Perpendicular magnetic anisotropy


Reference layer


Synthetic antiferromagnet


Scanning electron microscopy


Spin-transfer torque


Spin valve


Transmission electron microscopy


Tunnel magnetoresistance



The author acknowledges valuable and consistent support from IBM Research for his research on this topic.


  1. 1.
    Mott NF (1964) Adv Phys 13:325ADSCrossRefGoogle Scholar
  2. 2.
    Fert A, Campbell IA (1976) J Phys F 6:849ADSCrossRefGoogle Scholar
  3. 3.
    Valet T, Fert A (1993) Phys Rev B 48:7099ADSCrossRefGoogle Scholar
  4. 4.
    Son PCV, Kempen HV, Wyder P (1987) Phys Rev Lett 58:2271ADSCrossRefGoogle Scholar
  5. 5.
    Johnson M, Silsbee RH (1985) Phys Rev Lett 55:1790ADSCrossRefGoogle Scholar
  6. 6.
    Julliere M (1975) Phys Lett A 54:225ADSCrossRefGoogle Scholar
  7. 7.
    Maekawa S, Gäfvert U (1982) IEEE Trans Magn MAG-18:707ADSCrossRefGoogle Scholar
  8. 8.
    Slonczewski JC (1989) Phys Rev B 39:6995ADSCrossRefGoogle Scholar
  9. 9.
    Meservey R, Tedrow PM (1993) Phys Rep 238:173ADSCrossRefGoogle Scholar
  10. 10.
    Spin-flip scattering is included phenomenologically and only in the limit of spin-flip scattering life-time≫momentum-scattering life-time, so as to preserve the electron spin as a “good” quantum-number for sub-band structuresGoogle Scholar
  11. 11.
    Slonczewski JC (2002) J Magn Magn Mater 247:324ADSCrossRefGoogle Scholar
  12. 12.
    Slonczewski J (2007) In: Kronmuller H, Parkin S (ed) Handbook of magnetism and advanced magnetic materials, vol 5. p 2648Google Scholar
  13. 13.
    Slonczewski JC (2005) Phys Rev B 71:024411ADSCrossRefGoogle Scholar
  14. 14.
    Slonczewski JC (1996) J Magn Magn Mat 159:L1ADSCrossRefGoogle Scholar
  15. 15.
    Stiles MD, Zangwill A (2002) Phys Rev B 66:014407ADSCrossRefGoogle Scholar
  16. 16.
    Berger L (1978) J Appl Phys 49:2156ADSCrossRefGoogle Scholar
  17. 17.
    Berger L (1984) J Appl Phys 55:1954ADSCrossRefGoogle Scholar
  18. 18.
    Bazaliy YB, Jones BA, Zhang SC (1998) Phys Rev B 57:R3213ADSCrossRefGoogle Scholar
  19. 19.
    Berger L (1996) Phys Rev B 54:9353ADSCrossRefGoogle Scholar
  20. 20.
    Sun JZ (1999) J Magn Magn Mater 202:157ADSCrossRefGoogle Scholar
  21. 21.
    Sun JZ (2000) Phys Rev B 62:570ADSCrossRefGoogle Scholar
  22. 22.
    Tsoi M, Jansen AGM, Bass J, Chiang WC, Seck M, Tsoi V, Wyder P (1998) Phys Rev Lett 80:4281ADSCrossRefGoogle Scholar
  23. 23.
    Myers EB, Ralph DC, Katine JA, Louie RN, Buhrman RA (1999) Science 285:867CrossRefGoogle Scholar
  24. 24.
    Sun JZ (2001) Physica C 350:215ADSCrossRefGoogle Scholar
  25. 25.
    Katine JA, Albert FJ, Buhrman RA, Myers EB, Ralph DC (2000) Phys Rev Lett 84:3149ADSCrossRefGoogle Scholar
  26. 26.
    Slonczewski JC (1974) Unpublished IBM internal memoGoogle Scholar
  27. 27.
    Moodera JS, Kinder LR, Wong TM, Meservey R (1995) Phys Rev Lett 74:3273ADSCrossRefGoogle Scholar
  28. 28.
    Miyazaki T, Tezuka N (1995) J Magn Magn Mater 139:L231ADSCrossRefGoogle Scholar
  29. 29.
    Kwo J, Wertheim GK, Gurvitch M, Buchanan DNE (1983) IEEE Trans Magn MAG-19:795ADSCrossRefGoogle Scholar
  30. 30.
    Shoji A, Aoyagi M, Kosaka S, Shinoki F, Hayakawa H (1985) Appl Phys Lett 46:1098ADSCrossRefGoogle Scholar
  31. 31.
    Wulfhekel W, Klaua M, Ullmann D, Zavaliche F, Kirschner J, Urban R, Monchesky T, Heinrich B (2001) Appl Phys Lett 78:509ADSCrossRefGoogle Scholar
  32. 32.
    Butler WH, Zhang XG, Schulthess TC, MacLaren JM (2001) Phys Rev B 63:054416ADSCrossRefGoogle Scholar
  33. 33.
    Mathon J, Umerski A (2001) Phys Rev B 63:220403ADSCrossRefGoogle Scholar
  34. 34.
    Zhang XG, Butler WH (2004) Phys Rev B 70:172407ADSCrossRefGoogle Scholar
  35. 35.
    Parkin SSP, Kaiser C, Panchula A, Hughes PM, Samant M, Yang SH (2004) Nat Mater 3:862ADSCrossRefGoogle Scholar
  36. 36.
    Yuasa S, Nagahama T, Fukushima A, Ando YSK (2004) Nat Mater 3:868ADSCrossRefGoogle Scholar
  37. 37.
    Ikeda S, Hayakawa J, Ashizawa Y, Lee YM, Miura K, Hasegawa H, Tsunoda M, Matsukura F, Ohno H (2008) Appl Phys Lett 93:082508ADSCrossRefGoogle Scholar
  38. 38.
    Huai Y, Albert F, Nguyen P, Pakala M, Valet T (2004) Appl Phys Lett 84:3118ADSCrossRefGoogle Scholar
  39. 39.
    Sun JZ, Ralph DC (2008) J Magn Magn Mater 320:1227ADSCrossRefGoogle Scholar
  40. 40.
    Slonczewski JC, Sun JZ (2007) J Magn Magn Mater 310:169ADSCrossRefGoogle Scholar
  41. 41.
    Vaz CAF, Bland JAC, Lauhoff G (2008) Rep Prog Phys 71:056501ADSCrossRefGoogle Scholar
  42. 42.
    Dennis CL, Borges RP, Buda LD, Ebels U, Gregg JF, Hehn M, Jouguelet E, Ounadjela K, Petej I, Prejbeanu IL, Thornton MJ (2002) J Phys Condens Matter 14:R1175ADSCrossRefGoogle Scholar
  43. 43.
    Herring C, Kittel C (1951) Phys Rev 81:869ADSCrossRefzbMATHGoogle Scholar
  44. 44.
    Shanker R (1980) Principles of quantum mechanics. Plenum, New York, p 391Google Scholar
  45. 45.
    Brataas A, Nazarov YV, Bauer GEW (2000) Phys Rev Lett 84:2481ADSCrossRefGoogle Scholar
  46. 46.
    Tserkovnyak Y, Brataas A, Bauer GEW, Halperin BI (2005) Rev Mod Phys 77:1375ADSCrossRefGoogle Scholar
  47. 47.
    Sankey JC, Cui YT, Sun JZ, Buhrman JCS, Ralph DC (2008) Nat Phys 4:67CrossRefGoogle Scholar
  48. 48.
    Sharvin YV (1965) Zh Eksp Teor Fiz 48:984 (Sov Phys JETP 21:655 (1965))Google Scholar
  49. 49.
    Slonczewski JC (1999) J Magn Magn Mater 195:L261ADSCrossRefGoogle Scholar
  50. 50.
    Bazaliy YB (2007) arXiv:0710.2564v1Google Scholar
  51. 51.
    Tsoi M, Sun JZ, Parkin SSP (2004) Phys Rev Lett 93:036602ADSCrossRefGoogle Scholar
  52. 52.
    Kim W, Lee TD, Lee KJ (2008) Appl Phys Lett 93:232506ADSCrossRefGoogle Scholar
  53. 53.
    Waintal X, Myers EB, Brouwer PW, Ralph DC (2000) Phys Rev B 62:12317ADSCrossRefGoogle Scholar
  54. 54.
    Hernández S, Victora RH (2010) Appl Phys Lett 97:062506ADSCrossRefGoogle Scholar
  55. 55.
    Bauer GEW, Tserkovnyak Y, Huertas-Hernando D, Brataas A (2003) Phys Rev B 67:094421ADSCrossRefGoogle Scholar
  56. 56.
    Landauer R (1988) IBM J Res Develop 32:307MathSciNetCrossRefGoogle Scholar
  57. 57.
    Büttiker M (1988) IBM J Res Devlop 32:317CrossRefGoogle Scholar
  58. 58.
    Jedema FJ, Nijboer MS, Filip AT, van Wees BJ (2003) Phys Rev B 67:085319ADSCrossRefGoogle Scholar
  59. 59.
    Kimura T, Otani Y, Hamrle J (2006) Phys Rev Lett 96:037201ADSCrossRefGoogle Scholar
  60. 60.
    Yang T, Kimura T, Otani Y (2008) Nat Phys 4:851CrossRefGoogle Scholar
  61. 61.
    Lifshitz EM, Pitaevskii LP (1981) Statistical physics part 2, Chapter 7, Magnetism. Wheaton, Exeter, p 285Google Scholar
  62. 62.
    Kittel C (1986) Chapter 15, Ferromagnetism and antiferromagnetism. In: Introduction to Solid State Physics, 6th edn. Wiley, New York, p 434Google Scholar
  63. 63.
    Tserkovnyak Y, Brataas A, Bauer GEW (2002) Phys Rev B 66:224403ADSCrossRefGoogle Scholar
  64. 64.
    Heinrich B, Tserkovnyak Y, Woltersdorf G, Brataas A, Urban R, Bauer GEW (2003) Phys Rev Lett 90:187601ADSCrossRefGoogle Scholar
  65. 65.
    Brataas A, Tserkovnyak Y, Bauer GEW, Kelly PJ (2012) arXiv:1108.0385v3Google Scholar
  66. 66.
    Thomas L, Parkin SSP (2007) In: Kronmüller H, Parkin S (eds) Handbook of magnetism and advanced magnetic materials, vol 2, Micromagnetism. Wiley, New YorkGoogle Scholar
  67. 67.
    Mancoff FB, Dave RW, Rizzo ND, Eschrich TC, Engel BN, Tehrani S (2003) Appl Phys Lett 83:1596ADSCrossRefGoogle Scholar
  68. 68.
    Brown WF (1963) Phys Rev 130:1677ADSCrossRefGoogle Scholar
  69. 69.
    He J, Sun JZ, Zhang S (2007) J Appl Phys 101:09A501Google Scholar
  70. 70.
    Apalkov DM, Visscher PB (2005) Phys Rev B 72:180405ADSCrossRefGoogle Scholar
  71. 71.
    Apalkov DM, Visscher PB (2005) J Magn Magn Mater 286:370ADSCrossRefGoogle Scholar
  72. 72.
    Visscher PB, Apalkov DM (2005) J Appl Phys 97:10C704CrossRefGoogle Scholar
  73. 73.
    Visscher PB, Apalkov DM (2006) J Appl Phys 99:08G513CrossRefGoogle Scholar
  74. 74.
    Visscher PB (2008) SPIE 7036:70360BADSCrossRefGoogle Scholar
  75. 75.
    Butler WH, Mewes T, Mewes CKA, Visscher PB, Rippard WH, Russek SE, Heindl R (2012) IEEE Trans Magn 48:4684ADSCrossRefGoogle Scholar
  76. 76.
    Liu H, Bedau D, Sun JZ, Mangin S, Fullerton EE, Katine JA, Kent AD (2014) J Magn Magn Mater 358–359:233CrossRefGoogle Scholar
  77. 77.
    Sun JZ (2006) IBM internal memoGoogle Scholar
  78. 78.
    Sun JZ, Robertazzi RP, Nowak J, Trouilloud PL, Hu G, Abraham DW, Gaidis MC, Brown SL, O’Sullivan EJ, Gallagher WJ, Worledge DC (2011) Phys Rev B 84:064413ADSCrossRefGoogle Scholar
  79. 79.
    Nowak JJ, Robertazzi RP, Sun JZ, Hu G, Abraham DW, Trouilloud PL, Brown S, Gaidis MC, O’Sullivan EJ, Gallagher WJ, Worledge DC (2011) IEEE Magn Lett 2:3000204CrossRefGoogle Scholar
  80. 80.
    Li Z, Zhang S (2004) Phys Rev B 69:134416ADSCrossRefGoogle Scholar
  81. 81.
    Li Z, He J, Zhang S (2005) Phys Rev B 72:212411ADSCrossRefGoogle Scholar
  82. 82.
    Zhu R, Visscher PB (2008) J Appl Phys 103:07A722Google Scholar
  83. 83.
    Pinna D, Kent AD, Stein DL (2013) Phys Rev B 88:104405ADSCrossRefGoogle Scholar
  84. 84.
    Bedau D, Liu H, Bouzaglou JJ, Kent AD, Sun JZ, Katine J, Fullerton EE, Mangin S (2010) Appl Phys Lett 96:022514ADSCrossRefGoogle Scholar
  85. 85.
    Bedau D, Liu H, Sun JZ, Katine JA, Fullerton EE, Mangin S, Kent AD (2010) Appl Phys Lett 97:262502ADSCrossRefGoogle Scholar
  86. 86.
    Berger L (1986) Phys Rev B 33:1572ADSCrossRefGoogle Scholar
  87. 87.
    Berger L (1988) J Appl Phys 63:1663ADSCrossRefGoogle Scholar
  88. 88.
    Hung CY, Berger L (1986) J Appl Phys 63:4276ADSCrossRefGoogle Scholar
  89. 89.
    Kiselev SI, Sankey JC, Krivorotov LN, Emley NC, Schoelkopf RJ, Buhrman RA, Ralph DC (2003) Nature 425:380ADSCrossRefGoogle Scholar
  90. 90.
    Slavin A, Tiberkevich V (2009) IEEE Trans Magn 45:1875ADSCrossRefGoogle Scholar
  91. 91.
    Slavin A, Tiberkevich V (2008) In: Demokritov SO (ed) Spin wave confinement. World Scientific, Hackensack, p 195CrossRefGoogle Scholar
  92. 92.
    Silva TJ, Rippard WH (2008) J Magn Magn Mater 320:1260ADSCrossRefGoogle Scholar
  93. 93.
    Ralph DC, Stiles MD (2008) J Magn Magn Mater 320:1190ADSCrossRefGoogle Scholar
  94. 94.
    Koch RH, Katine JA, Sun JZ (2004) Phys Rev Lett 92:088302ADSCrossRefGoogle Scholar
  95. 95.
    Sun JZ, Kuan TS, Katine JA, Koch RH (2004) Proc SPIE 5359:445ADSCrossRefGoogle Scholar
  96. 96.
    Nakayama M, Kai T, Shimomura N, Amando M, Kitagawa E, Nagase T, Yoshikawa M, Ikegawa T, Yoda H (2008) J Appl Phys 103:07A710Google Scholar
  97. 97.
    Kishi T, Yoda H, Kai T, Nagase T, Kitagawa E, Yoshikawa M, Nishiyama K, Daibou T, Nagamine M, Amano M, Takahasi S, Nakayama M, Shimomura N, Aikawa H, Ikegawa S, Yuasa S, Yakushiji K, Kubota H, Fukushima A, Oogane K, Miyazaki T, Ando K (2008) IEEE international electron devices meeting (IEDM), doi: 10.1109/IEDM.2008.4796680Google Scholar
  98. 98.
    Ikeda S, Miura K, Yamamoto H, Mizunuma K, Gan HD, Endo M, Kanai S, Hayakawa J, Matsukura F, Ohno H (2010) Nat Mater 9:721ADSCrossRefGoogle Scholar
  99. 99.
    Worledge DC, Hu G, Abraham DW, Sun JZ, Trouilloud PL, Nowak J, Brown S, Gaidis MC, O’Sullivan EJ, Robertazzi RP (2011) Appl Phys Lett 98:022501ADSCrossRefGoogle Scholar
  100. 100.
    Liu H, Bedau D, Sun JZ, Mangin S, Fullerton EE, Katine JA, Kent AD (2012) Phys Rev B 85:220405(R)ADSCrossRefGoogle Scholar
  101. 101.
    Gajek M, Nowak JJ, Sun JZ, Trouilloud PL, O’Sullivan EJ, Abraham DW, Gaidis MC, Hu G, Brown S, Zhu Y, Robertazzi RP, Gallagher WJ, Worledge DC (2012) Appl Phys Lett 100:132408ADSCrossRefGoogle Scholar
  102. 102.
    Sun JZ, Trouilloud PL, Gajek MJ, Nowak J, Robertazzi RP, Hu G, Abraham DW, Gaidis MC, Brown SL, O’Sullivan EJ, Gallagher WJ, Worledge DC (2012) J Appl Phys 111:07C711Google Scholar
  103. 103.
    Sun JZ, Brown SL, Chen W, Delenia EA, Gaidis MC, Harms J, Hu G, Jiang X, Kilaru R, Kula W, Lauer G, Liu LQ, Murthy S, Nowak J, O’Sullivan EJ, Parkin SSP, Robertazzi RP, Rice PM, Sandhu G, Topuria T, Worledge DC (2013) Phys Rev B 88:104426ADSCrossRefGoogle Scholar
  104. 104.
    Kubota H, Fukushima A, Ootani Y, Yuasa S, Ando K, Maehara H, Tsunekawa K, Djayaprawira DD, Watanabe N, Suzuki Y (2005) J Appl Phys 44:L1237ADSCrossRefGoogle Scholar
  105. 105.
    Hayakawa J, Ikeda S, Lee YM, Sasaki R, Matsukura T, Takahashi H, Ohno H (2005) J Appl Phys 44:1267CrossRefGoogle Scholar
  106. 106.
    Choi YS, Tsunekawa K, Nagamine Y, Djayaprawira D (2007) J Appl Phys 101:013907ADSCrossRefGoogle Scholar
  107. 107.
    Faure-Vincent J, Tiusan C, Bellouard C, Popova E, Hehn M, Montaigne F, Schuhl A (2002) Phys Rev Lett 89:107206ADSCrossRefGoogle Scholar
  108. 108.
    Tiusan C, Sicot M, Faure-Vincent J, Hehn M, Bellouard C, Montaigne F, Andrieu S, Schuhl A (2006) J Phys Condens Matter 18:941ADSCrossRefGoogle Scholar
  109. 109.
    Popova E, Keller N, Gendron F, Tiusan C, Schuhl A, Lesnik NA (2007) Appl Phys Lett 91:112504ADSCrossRefGoogle Scholar
  110. 110.
    Wang C, Cui YT, Katine JA, Buhrman RA, Ralph DC (2011) Nat Phys 7:496CrossRefGoogle Scholar
  111. 111.
    Endoh T, Ohsawa T, Koike H, Hanyu T, Ohno H (2012) Symposium on VLSI circuits, Honolulu, 13–15 June 2012, Session 10.3Google Scholar
  112. 112.
    Morris D, Bromberg D, Zhu JGJ, Pileggi L (2012) DAC 2012, San Francisco, 3–7 June 2012, 21.2Google Scholar
  113. 113.
    Devolder T (2011) Appl Phys Exp 4:093001ADSCrossRefGoogle Scholar
  114. 114.
    Meng H, Wang JP (2006) Appl Phys Lett 88:172506ADSCrossRefGoogle Scholar
  115. 115.
    Mangin S, Ravelosona D, Katine JA, Carey MJ, Terris BD, Fullerton EE (2006) Nat Mater 5:210ADSCrossRefGoogle Scholar
  116. 116.
    Worledge DC, Hu G, Trouilloud PL, Abraham DW, Brown SL, Gaidis MC, Nowak J, O’Sullivan EJ, Robertazzi RP, Sun JZ, Gallagher WJ (2010) International electron devices meetingGoogle Scholar
  117. 117.
    Hosomi M, Yamagishi H, Yamamoto T, Bessho K, Higo Y, Yamane K, Yamada H, Shoji M, Hachino H, Fukumoto C, Nagao H, Kano H (2005) IEEE IEDM 2005. IEEE 0-7803-9269-8/05Google Scholar
  118. 118.
    Kimura T, Hamrle J, Otani Y (2005) Phys Rev B 72:014461ADSCrossRefGoogle Scholar
  119. 119.
    Sun JZ, Gaidis MC, O’Sullivan EJ, Joseph EA, Hu G, Abraham DW, Nowak JJ, Trouilloud PL, Lu Y, Brown SL, Worledge DC, Gallagher WJ (2009) Appl Phys Lett 95:083506ADSCrossRefGoogle Scholar
  120. 120.
    Gaidis M, Sun J, O’Sullivan E, Hu G, DeBrosse J, Nowak J, Abraham D, Trouilloud P (2010) SSDM invited paper F7-1Google Scholar
  121. 121.
    Braganca PM, Katine J, Emley NC, Mauri D, Childress JR, Rice PM, Delenia E, Ralph DC, Buhrman RA (2009) IEEE Trans Nanotechnol 8:190ADSCrossRefGoogle Scholar
  122. 122.
    Liu L, Pai CF, Li Y, Tseng HW, Ralph DC, Buhrman RA (2012) Science 336:555ADSCrossRefGoogle Scholar
  123. 123.
    Wang Y, Sham LJ (2012) Phys Rev B 85:092403ADSCrossRefGoogle Scholar
  124. 124.
    Balashov T, Takacs AF, Dane M, Ernst A, Bruno P, Wulfhekel W (2008) Phys Rev B 78:174404ADSCrossRefGoogle Scholar
  125. 125.
    Manchon A, Zhang S (2009) Phys Rev B 79:094422ADSCrossRefGoogle Scholar
  126. 126.
    Miron IM, Gaudin G, Auffret S, Rodmacq B, Schuhl A, Pizzini S, Vogel J, Gambardella P (2010) Nat Mater 9:230ADSGoogle Scholar
  127. 127.
    Hirsch JE (1999) Phys Rev Lett 83:1834ADSCrossRefGoogle Scholar
  128. 128.
    Zhang S (2000) Phys Rev Lett 85:393ADSCrossRefGoogle Scholar
  129. 129.
    Ando K, Takahashi S, Harii K, Sasage K, Ieda J, Maekawa S, Saitoh E (2008) Phys Rev Lett 101:036601ADSCrossRefGoogle Scholar
  130. 130.
    Kajiwara Y, Harii K, Takahashi S, Ohe J, Uchida K, Uchida M, Mizuguchi M, Umezawa H, Kawai H, Ando K, Takanashi K, Maekawa S, Saitoh E (2010) Nature 464:262ADSCrossRefGoogle Scholar
  131. 131.
    Liu L, Moriyama T, Ralph DC, Buhrman RA (2011) Phys Rev Lett 106:036601ADSCrossRefGoogle Scholar
  132. 132.
    Hasan MZ, Kane CL (2010) Rev Mod Phys 82:3045ADSCrossRefGoogle Scholar
  133. 133.
    Qi XL, Zhang SC (2011) Rev Mod Phys 83:1057ADSCrossRefGoogle Scholar
  134. 134.
    Hatami M, Bauer GEW (2007) Phys Rev Lett 99:066603ADSCrossRefGoogle Scholar
  135. 135.
    Hatami M, Bauer GEW, Zhang Q, Kelly PJ (2009) Phys Rev B 79:174426ADSCrossRefGoogle Scholar
  136. 136.
    Huang SY, Wang WG, Lee SF, Kuo J, Chien CL (2011) Phys Rev Lett 107:216604ADSCrossRefGoogle Scholar
  137. 137.
    Slonczewski JC (2010) Phys Rev B 82:054403ADSCrossRefGoogle Scholar
  138. 138.
    Sun JZ (2010) Am Phys Soc. March Mtg. Paper J37.004Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.IBM ResearchYorktown HeightsUSA

Personalised recommendations