Modeling Multi-Magnet Networks Interacting via Spin Currents

  • Srikant SrinivasanEmail author
  • Vinh Diep
  • Behtash Behin-Aein
  • Angik Sarkar
  • Supriyo Datta
Reference work entry


The significant experimental advances of the last few decades in dealing with the interaction of spin currents and nanomagnets, at the device level, have allowed envisioning a broad class of devices that propose to implement information processing using spin currents and nanomagnets. To analyze such spin-magnet logic circuits, in general, we have developed a coupled spin-transport/magnetization-dynamics simulation framework that could be broadly applicable to various classes of spin-valve/spin-torque devices. Indeed, the primary purpose of this chapter is to describe in detail the overall approach we have developed to include a description of spin transport coupled with magnetization dynamics and to show how it was benchmarked against available data on experiments.

We address noncollinear spin transport in section “Circuit Representation of Spin Transport” using a lumped “four-component spin-circuit formalism” that describes the interaction of noncollinear magnets (required for modeling spin torque), by computing four-component currents and voltages at every node of a “circuit.” For modeling the magnetization dynamics, we use the standard Landau-Lifshitz-Gilbert (LLG) equation with the Slonczewski and the field-like terms included for spin torque. Section “A Coupled Spin-Transport/Magnetization-Dynamics Simulator” describes how this LLG model is coupled with the spin-transport model to analyze spin-torque experiments and spin-magnet circuits in general.

We include MATLAB codes in the Additional Information to facilitate a “hands-on” understanding of our model and hope it will enable interested readers to conveniently analyze their own experiments, develop a deeper insight into spin-magnet circuits, or come up with their own creative designs.

List of Abbreviations


All-spin logic


Complementary Metal Oxide Semiconductor


Complementary pair






Z-component of magnetization


Nonlocal spin-transfer torque


Non-magnetic region




Nonlocal resistance







Srikant Srinivasan was supported by the Institute for Nanoelectronics Discovery and Exploration (INDEX), while Angik Sarkar and Vinh Diep were supported by the Center for Science of Information (CSoI), an NSF Science and Technology Center.

Supplementary material


  1. 1.
    Welser JJ et al (2008) The quest for the next information processing technology. J Nanoparticle Res 10(1):1–10CrossRefGoogle Scholar
  2. 2.
    Theis TN, Solomon PM (2010) It’s time to reinvent the transistor! Science 327(5973):1600–1601CrossRefADSGoogle Scholar
  3. 3.
    Behin-Aein B et al (2010) Proposal for an all-spin logic device with built-in memory. Nat Nanotechnol 5(4):266–270CrossRefADSGoogle Scholar
  4. 4.
    Dery H et al (2007) Spin-based logic in semiconductors for reconfigurable large-scale circuits. Nature 447(7144):573–576CrossRefADSGoogle Scholar
  5. 5.
    Wang JG, Meng H, Wang JP (2005) Programmable spintronics logic device based on a magnetic tunnel junction element. J Appl Phys 97(10):10D509Google Scholar
  6. 6.
    Huang BQ, Monsma DJ, Appelbaum I (2007) Experimental realization of a silicon spin field-effect transistor. Appl Phys Lett 91(7):72501CrossRefADSGoogle Scholar
  7. 7.
    Johnson M, Silsbee RH (1985) Interfacial charge-spin coupling – injection and detection of spin magnetization in metals. Phys Rev Lett 55(17):1790–1793CrossRefADSGoogle Scholar
  8. 8.
    Jedema FJ, Filip AT, van Wees BJ (2001) Electrical spin injection and accumulation at room temperature in an all-metal mesoscopic spin valve. Nature 410(6826):345–348CrossRefADSGoogle Scholar
  9. 9.
    Huang B, Monsma DJ, Appelbaum I (2007) Coherent spin transport through a 350 micron thick silicon wafer. Phys Rev Lett 99(17):177209CrossRefADSGoogle Scholar
  10. 10.
    Tsoi M et al (1998) Excitation of a magnetic multilayer by an electric current. Phys Rev Lett 80(19):4281–4284CrossRefADSGoogle Scholar
  11. 11.
    Katine JA et al (2000) Current-driven magnetization reversal and spin-wave excitations in Co/Cu/Co pillars. Phys Rev Lett 84(14):3149–3152CrossRefADSGoogle Scholar
  12. 12.
    Grollier J et al (2001) Spin-polarized current induced switching in Co/Cu/Co pillars. Appl Phys Lett 78(23):3663–3665CrossRefADSGoogle Scholar
  13. 13.
    Srinivasan S et al (2011) All-spin logic device with inbuilt nonreciprocity. IEEE Trans Magn 47(10):4026–4032CrossRefADSGoogle Scholar
  14. 14.
    Behin-Aein B et al (2011) Switching energy-delay of all spin logic devices. Appl Phys Lett 98(12):123510CrossRefADSGoogle Scholar
  15. 15.
    Yang T, Kimura T, Otani Y (2008) Giant spin-accumulation signal and pure spin-current-induced reversible magnetization switching. Nat Phys 4(11):851–854CrossRefGoogle Scholar
  16. 16.
    Zou H, Ji Y (2011) Temperature evolution of spin-transfer switching in nonlocal spin valves with dipolar coupling. J Magn Magn Mater 323(20):2448–2452CrossRefADSGoogle Scholar
  17. 17.
    Datta S, Salahuddin S, Behin-Aein B (2012) Non-volatile spin switch for Boolean and non-Boolean logic. Appl Phys Lett 101(25):252411CrossRefADSGoogle Scholar
  18. 18.
    Srinivasan S et al (2011) Unidirectional information transfer with cascaded all spin logic devices: a ring oscillator. In: Device research conference (DRC), 2011 69th Annual, Santa Barbara, CAGoogle Scholar
  19. 19.
    Sarkar A et al (2011) Modeling all spin logic: multi-magnet networks interacting via spin currents. In: 2011 I.E. international electron devices meeting (IEDM), Washington DCGoogle Scholar
  20. 20.
    Sharad M et al (2012) Ultra low energy analog image processing using spin based neurons. In: Nanoscale Architectures (NANOARCH), 2012 IEEE/ACM international symposium on. 2012, Amsterdam, NetherlandsCrossRefGoogle Scholar
  21. 21.
    Brataas A, Bauer GEW, Kelly PJ (2006) Non-collinear magnetoelectronics. Phys Rep-Rev Section Phys Lett 427(4):157–255Google Scholar
  22. 22.
    Kovalev AA, Brataas A, Bauer GEW (2002) Spin transfer in diffusive ferromagnet-normal metal systems with spin-flip scattering. Phys Rev B 66(22):224424CrossRefADSGoogle Scholar
  23. 23.
    Xia K et al (2002) Spin torques in ferromagnetic/normal-metal structures. Phys Rev B 65(22):220401CrossRefADSGoogle Scholar
  24. 24.
    Zainuddin ANM et al (2010) Magnetoresistance of lateral semiconductor spin valves. J Appl Phys 108(12):123913CrossRefADSGoogle Scholar
  25. 25.
    Augustine C et al (2011) Numerical analysis of domain wall propagation for dense memory arrays. In: Electron devices meeting (IEDM), 2011 I.E. International, Washington DCGoogle Scholar
  26. 26.
    Takahashi S, Maekawa S (2003) Spin injection and detection in magnetic nanostructures. Physical Review B 67(5):052409CrossRefADSGoogle Scholar
  27. 27.
    Slonczewski JC (1996) Current-driven excitation of magnetic multilayers. J Magn Magn Mater 159(1–2):L1–L7CrossRefADSGoogle Scholar
  28. 28.
    Datta S (2005) Quantum transport: atom to transistor. Cambridge University Press, Cambridge, UK/New YorkCrossRefGoogle Scholar
  29. 29.
    Valet T, Fert A (1993) Theory of the perpendicular magnetoresistance in magnetic multilayers. Phys Rev B 48(10):7099–7113CrossRefADSGoogle Scholar
  30. 30.
    Johnson M, Silsbee RH (1987) Thermodynamic analysis of interfacial transport and of the thermomagnetoelectric system. Phys Rev B 35(10):4959–4972CrossRefADSGoogle Scholar
  31. 31.
    Fert A, Campbell IA (1968) 2-current conduction in nickel. Phys Rev Lett 21(16):1190CrossRefADSGoogle Scholar
  32. 32.
    Mott N (1936) The electrical conductivity of transition metals. Proc R Soc Lond Ser A Math Phys Sci 153(880):699–717CrossRefADSGoogle Scholar
  33. 33.
    Julliere M (1975) Tunneling between ferromagnetic-films. Phys Lett A 54(3):225–226CrossRefADSGoogle Scholar
  34. 34.
    Maekawa S, Gafvert U (1982) Electron-tunneling between ferromagnetic-films. IEEE Trans Magn 18(2):707–708CrossRefADSGoogle Scholar
  35. 35.
    Moodera JS et al (1995) Large magnetoresistance at room-temperature in ferromagnetic thin-film tunnel-junctions. Phys Rev Lett 74(16):3273–3276CrossRefADSGoogle Scholar
  36. 36.
    Mavropoulos P, Papanikolaou N, Dederichs PH (2000) Complex band structure and tunneling through ferromagnet/insulator/ferromagnet junctions. Phys Rev Lett 85(5):1088–1091CrossRefADSGoogle Scholar
  37. 37.
    Butler WH et al (2001) Spin-dependent tunneling conductance of Fe vertical bar MgO vertical bar Fe sandwiches. Phys Rev B 63(5):054416-1CrossRefADSGoogle Scholar
  38. 38.
    Schmidt G et al (2000) Fundamental obstacle for electrical spin injection from a ferromagnetic metal into a diffusive semiconductor. Phys Rev B 62(8):R4790–R4793CrossRefADSGoogle Scholar
  39. 39.
    Fert A, Jaffres H (2001) Conditions for efficient spin injection from a ferromagnetic metal into a semiconductor. Phys Rev B 64(18):184420CrossRefADSGoogle Scholar
  40. 40.
    Fert A et al (2007) Semiconductors between spin-polarized sources and drains. IEEE Trans Electron Devices 54(5):921–932CrossRefADSGoogle Scholar
  41. 41.
    Datta D et al (2012) Voltage asymmetry of spin-transfer torques. IEEE Trans Nanotechnol 11(2):261–272CrossRefADSGoogle Scholar
  42. 42.
    Kovalev AA, Bauer GEW, Brataas A (2006) Perpendicular spin valves with ultrathin ferromagnetic layers: magnetoelectronic circuit investigation of finite-size effects. Phys Rev B 73(5):054407CrossRefADSGoogle Scholar
  43. 43.
    Sun JZ (2000) Spin-current interaction with a monodomain magnetic body: a model study. Phys Rev B 62(1):570–578CrossRefADSGoogle Scholar
  44. 44.
    Augustine C, Panagopoulos G, Behin-Aein B, Srinivasan S, Sarkar A, Roy K (2011) Low-power functionality enhanced computation architecture using spin-based devices. In: Nanoscale architectures (NANOARCH), 2011 IEEE/ACM international symposium on, San Diego, 8–9 June 2011, pp 129–136Google Scholar
  45. 45.
    Manipatruni S, Nikonov, DE, Young IA (2012) Modeling and design of spintronic integrated circuits. Circuits Syst I Regul Papers, IEEE Trans 59(12):2801–2814MathSciNetCrossRefGoogle Scholar
  46. 46.
    Sharad M, Augustine C, Panagopoulos G, Roy K (2012) Spin-based neuron model with domain-wall magnets as synapse. Nanotechnol, IEEE Trans 11(4):843–853CrossRefADSGoogle Scholar
  47. 47.
    Bonhomme P, Manipatruni S, Iraei RM, Rakheja S, Sou-Chi Chang, Nikonov DE, Young IA, Naeemi A (2014) Circuit simulation of magnetization dynamics and spin transport. Electron Dev, IEEE Trans 61(5):1553–1560CrossRefADSGoogle Scholar
  48. 48.
    Sou-Chi Chang, Iraei RM, Manipatruni S, Nikonov DE, Young IA, Naeemi A (2014) Design and analysis of copper and aluminum interconnects for all-spin logic. Electron Dev, IEEE Trans 61(8):2905–2911CrossRefADSGoogle Scholar
  49. 49.
    Sou-Chi Chang, Manipatruni S, Nikonov, DE, Young IA, Naeemi A (2014) Design and analysis of si interconnects for all-spin logic. Magn, IEEE Trans 50(9):1–13CrossRefGoogle Scholar
  50. 50.
    Sun JZ et al (2009) A three-terminal spin-torque-driven magnetic switch. Appl Phys Lett 95(8):083506CrossRefADSGoogle Scholar
  51. 51.
    Behin-Aein, B, Sarkar A, Datta S (2012) Modeling circuits with spins and magnets for all-spin logic. In: Solid-state device research conference (ESSDERC), 2012 proceedings of the European, Bordeaux, FranceGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Srikant Srinivasan
    • 1
    • 2
    Email author
  • Vinh Diep
    • 1
  • Behtash Behin-Aein
    • 1
    • 3
  • Angik Sarkar
    • 1
  • Supriyo Datta
    • 1
  1. 1.School of Electrical and Computer EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Iowa State UniversityAmesUSA
  3. 3.Global FoundriesMilpitasUSA

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