Mutual phase-locking of microwave spin torque nano-oscillators


The spin torque1,2 effect that occurs in nanometre-scale magnetic multilayer devices can be used to generate steady-state microwave signals in response to a d.c. electrical current3,4,5,6,7,8. This establishes a new functionality for magneto-electronic structures that are more commonly used as magnetic field sensors and magnetic memory elements9. The microwave power emitted from a single spin torque nano-oscillator (STNO) is at present typically less than 1 nW. To achieve a more useful power level (on the order of microwatts), a device could consist of an array of phase coherent STNOs, in a manner analogous to arrays of Josephson junctions and larger semiconductor oscillators10,11,12. Here we show that two STNOs in close proximity mutually phase-lock—that is, they synchronize, which is a general tendency of interacting nonlinear oscillator systems13,14,15. The phase-locked state is distinct, characterized by a sudden narrowing of signal linewidth and an increase in power due to the coherence of the individual oscillators. Arrays of phase-locked STNOs could be used as nanometre-scale reference oscillators. Furthermore, phase control of array elements (phased array) could lead to nanometre-scale directional transmitters and receivers for wireless communications.

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Figure 1: Structure and basic behaviour of a two-nano-contact device.
Figure 2: Locking behaviour.
Figure 3: Behaviour of individual oscillators.
Figure 4: Device power outputs.


  1. 1

    Slonczewski, J. C. Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mater. 159, L1–L7 (1996)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Berger, L. Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev. B 54, 9353–9358 (1996)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Katine, J. A., Albert, F. J., Buhrman, R. A., Myers, E. B. & Ralph, D. C. Current-driven magnetization reversal and spin wave excitations in Co/Cu/Co pillars. Phys. Rev. Lett. 84, 4212–4215 (2000)

    Article  Google Scholar 

  4. 4

    Tsoi, M. et al. Generation and detection of phase-coherent current-driven magnons in magnetic multilayers. Nature 406, 46–48 (2000)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Kiselev, S. I. et al. Microwave oscillations of a nanomagnet driven by a spin-polarized current. Nature 425, 380–383 (2003)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Rippard, W. H., Pufall, M. R., Kaka, S., Russek, S. E. & Silva, T. J. Direct-current induced dynamics in Co90Fe10/Ni80Fe20 point contacts. Phys. Rev. Lett. 92, 27201 (2004)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Covington, M., Al Haj Darwish, M., Ding, Y., Gokemeijer, N. J. & Seigler, M. Current-induced magnetization dynamics in current perpendicular to the plane spin valves. Phys. Rev. B 69, 184406 (2004)

    ADS  Article  Google Scholar 

  8. 8

    Krivorotov, I. N. et al. Time domain measurements of nanomagnet dynamics driven by spin-transfer torques. Science 307, 228–231 (2005)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Wolf, S. A. et al. Spintronics: a spin-based electronics vision for the future. Science 294, 1488–1495 (2001)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Benz, S. P. & Burroughs, C. J. Coherent emission from two dimensional Josephson junction arrays. Appl. Phys. Lett. 58, 2162–2164 (1991)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Wengler, M. J., Guan, B. & Track, E. K. 190-GHz radiation from a quasioptical Josephson junction array. IEEE Trans. Microwave Theory Tech. 43, 984–988 (1995)

    ADS  Article  Google Scholar 

  12. 12

    Popovic, Z. B., Weikle, R. M., Kim, M. & Rutledge, D. B. A 100-MESFET planar grid oscillator. IEEE Microwave Theory Tech. 39, 193–200 (1991)

    ADS  Article  Google Scholar 

  13. 13

    Strogatz, S. Sync: The Emerging Science of Spontaneous Order 51, 116 (Hyperion, New York, 2003)

    Google Scholar 

  14. 14

    York, R. A. Nonlinear analysis of phase relationships in quasi-optical oscillator arrays. IEEE Trans. Microwave Theory Tech. 41, 1799–1809 (1993)

    ADS  Article  Google Scholar 

  15. 15

    Rezavi, B. A study of injection locking and pulling in oscillators. IEEE J. Solid State Circuits 39, 1415–1424 (2004)

    ADS  Article  Google Scholar 

  16. 16

    Wiesenfeld, K., Colet, P. & Strogatz, S. H. Synchronization transitions in a disordered Josephson series array. Phys. Rev. Lett. 76, 404–407 (1996)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Finnegan, T. F. & Wahlsten, S. Observation of coherent microwave radiation emitted by coupled Josephson junctions. Appl. Phys. Lett. 21, 541–544 (1972)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Buck, J. & Buck, E. Mechanism of rhythmic synchronous flashing of fireflies. Science 159, 1319–1327 (1968)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Bennet, M., Schatz, M. F., Rockwood, H. & Wiesenfeld, K. Huygens's clocks. Proc. R. Soc. Lond. A 458, 563–579 (2002)

    MathSciNet  Article  Google Scholar 

  20. 20

    Suhl, H. The nonlinear behaviour of ferrites at high microwave signal levels. Proc. Inst. Radio Engrs. 44, 1270–1284 (1956)

    CAS  Google Scholar 

  21. 21

    Rippard, W. H., Pufall, M. R., Kaka, S., Silva, T. J. & Russek, S. E. Current-driven microwave dynamics in magnetic point contacts as a function of applied field angle. Phys. Rev. B 70, 100406 (2004)

    ADS  Article  Google Scholar 

  22. 22

    Baibich, M. N. et al. Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices. Phys. Rev. Lett. 61, 2472–2475 (1988)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Slonczewski, J. C. Excitation of spin waves by an electric current. J. Magn. Magn. Mater. 195, L261–L268 (1999)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Rippard, W. H., Pufall, M. R., Kaka, S., Silva, T. J. & Russek, S. E. Injection locking and phase control of spin transfer oscillators. Phys. Rev. Lett. 95, 067203 (2005)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Russek, S. E., McMichael, R. D., Donahue, M. J. & Kaka, S. in Spin Dynamics in Confined Magnetic Structures II (eds Hillebrands, B. & Ounadjela, K.) 93–156 (Springer, Berlin, 2003)

    Google Scholar 

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We thank P. Kabos and A. Kos for assistance with microwave apparatus, and A. Slavin, M. Stiles, T. Gerrits and R. Goldfarb for discussions. This work was partly supported by the US government.

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Correspondence to Shehzaad Kaka.

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Kaka, S., Pufall, M., Rippard, W. et al. Mutual phase-locking of microwave spin torque nano-oscillators. Nature 437, 389–392 (2005).

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