Optimizing magnetodipolar interactions for synchronizing vortex based spin-torque nano-oscillators

Physical Review B - Condensed Matter and Materials Physics

Volumn 92, Issue 4, 2015, Pages

  Abreu Araujo, F ^a   Belanovsky, A D ^b,c   Skirdkov, P N ^b,c   Zvezdin, K A ^b,c   Zvezdin, A K ^b,c   Locatelli, N ^d,e   Lebrun, R ^d,e   Grollier, J ^d,e   Cros, V ^d,e   De Loubens, G ^f   Klein, O ^f  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b PROKHOROV GENERAL PHYSICS INSTITUTE   (Russian Federation)

^c MOSCOW INSTITUTE OF PHYSICS AND TECHNOLOGY   (Russian Federation)

^d CNRS   (France)

^e UNIVERSITÉ PARIS SACLAY   (France)

^f SERVICE DE PHYSIQUE DE L ETAT CONDENSÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84939206503     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.92.045419     Document Type: Article

References (52)

1. A. N. Slavin and V. S. Tiberkevich, Nonlinear self-phase-locking effect in an array of current-driven magnetic nanocontacts, Phys. Rev. B 72, 092407 (2005). PRBMDO 1098-0121 10.1103/PhysRevB.72.092407
2. A. N. Slavin and V. S. Tiberkevich, Theory of mutual phase locking of spin-torque nanosized oscillators, Phys. Rev. B 74, 104401 (2006). PRBMDO 1098-0121 10.1103/PhysRevB.74.104401
3. J. Grollier, V. Cros, and A. Fert, Synchronization of spin-transfer oscillators driven by stimulated microwave currents, Phys. Rev. B 73, 060409 (2006). PRBMDO 1098-0121 10.1103/PhysRevB.73.060409
4. S. M. Rezende, F. M. de Aguiar, R. L. Rodríguez-Suárez, and A. Azevedo, Mode locking of spin waves excited by direct currents in microwave nano-oscillators, Phys. Rev. Lett. 98, 087202 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.087202
5. B. Georges, J. Grollier, V. Cros, and A. Fert, Impact of the electrical connection of spin transfer nano-oscillators on their synchronization: An analytical study, Appl. Phys. Lett. 92, 232504 (2008). APPLAB 0003-6951 10.1063/1.2945636
6. A. Ruotolo, V. Cros, B. Georges, A. Dussaux, J. Grollier, C. Deranlot, R. Guillemet, K. Bouzehouane, S. Fusil, and A. Fert, Phase-locking of magnetic vortices mediated by antivortices, Nat. Nano 4, 528 (2009). 1748-3387 10.1038/nnano.2009.143
7. R. Bonin, G. Bertotti, C. Serpico, I. D. Mayergoyz, and M. d'Aquino, Analytical treatment of synchronization of spin-torque oscillators by microwave magnetic fields, Eur. Phys. J. B 68, 221 (2009). EPJBFY 1434-6028 10.1140/epjb/e2009-00091-9
8. X. Chen and R. H. Victora, Phase locking of spin-torque oscillators by spin-wave interactions, Phys. Rev. B 79, 180402 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.79.180402
9. A. Slavin, Microwave sources: Spin-torque oscillators get in phase, Nat. Nano 4, 479 (2009). 1748-3387 10.1038/nnano.2009.213
10. V. S. Tiberkevich, A. N. Slavin, E. Bankowski, and G. Gerhart, Phase-locking and frustration in an array of nonlinear spin-torque nano-oscillators, Appl. Phys. Lett. 95, 262505 (2009). APPLAB 0003-6951 10.1063/1.3278602
11. Y. Zhou and J. Åkerman, Perpendicular spin torque promotes synchronization of magnetic tunnel junction based spin torque oscillators, Appl. Phys. Lett. 94, 112503 (2009). APPLAB 0003-6951 10.1063/1.3100299
12. P. Tabor, V. S. Tiberkevich, A. N. Slavin, and S. Urazhdin, Hysteretic synchronization of nonlinear spin-torque oscillators, Phys. Rev. B 82, 020407 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.020407
13. S. Urazhdin, P. Tabor, V. S. Tiberkevich, and A. Slavin, Fractional synchronization of spin-torque nano-oscillators, Phys. Rev. Lett. 105, 104101 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.104101
14. H. Chen, J. Chang, and C. Chang, Synchronization of spin-torque nano-oscillators from an induced corrugated attractor, SPIN 01, 1 (2011). 2010-3247 10.1142/S2010324711000021
15. D. Li, Y. Zhou, B. Hu, and C. Zhou, Coupled perturbed heteroclinic cycles: Synchronization and dynamical behaviors of spin-torque oscillators, Phys. Rev. B 84, 104414 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.104414
16. M. d'Aquino, C. Serpico, R. Bonin, G. Bertotti, and I. D. Mayergoyz, Thermally induced synchronization and stochastic resonance between magnetization regimes in spin-transfer nano-oscillators, J. Appl. Phys. 111, 07C915 (2012). 10.1063/1.3679008
17. G. Finocchio, M. Carpentieri, A. Giordano, and B. Azzerboni, Non-adlerian phase slip and nonstationary synchronization of spin-torque oscillators to a microwave source, Phys. Rev. B 86, 014438 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.014438
18. D. Li, Y. Zhou, B. Hu, J. Åkerman, and C. Zhou, Multiple synchronization attractors of serially connected spin-torque nanooscillators, Phys. Rev. B 86, 014418 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.014418
19. K. Nakada, S. Yakata, and T. Kimura, Noise-induced synchronization in spin torque nano oscillators, J. Appl. Phys. 111, 07C920 (2012). JAPIAU 0021-8979 10.1063/1.3680537
20. S. Jain, V. Novosad, F. Y. Fradin, J. E. Pearson, V. Tiberkevich, A. N. Slavin, and S. D. Bader, From chaos to selective ordering of vortex cores in interacting mesomagnets, Nat. Commun. 3, 1330 (2012). 2041-1723 10.1038/ncomms2331
21. A. D. Belanovsky, N. Locatelli, P. N. Skirdkov, F. Abreu Araujo, J. Grollier, K. A. Zvezdin, V. Cros, and A. K. Zvezdin, Phase locking dynamics of dipolarly coupled vortex-based spin transfer oscillators, Phys. Rev. B 85, 100409 (R) (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.100409
22. A. D. Belanovsky, N. Locatelli, P. N. Skirdkov, F. Abreu Araujo, K. A. Zvezdin, J. Grollier, V. Cros, and A. K. Zvezdin, Numerical and analytical investigation of the synchronization of dipolarly coupled vortex spin-torque nano-oscillators, Appl. Phys. Lett. 103, 122405 (2013). APPLAB 0003-6951 10.1063/1.4821073
23. S. Jain, V. Novosad, F. Y. Fradin, J. E. Pearson, and S. D. Bader, Dynamics of coupled vortices in perpendicular field, Appl. Phys. Lett. 104, 082409 (2014). APPLAB 0003-6951 10.1063/1.4866900
24. S. I. Kiselev, J. C. Sankey, I. N. Krivorotov, N. C. Emley, R. J. Schoelkopf, R. A. Buhrman, and D. C. Ralph, Microwave oscillations of a nanomagnet driven by a spin-polarized current, Nature 425, 380 (2003). NATUAS 0028-0836 10.1038/nature01967
25. S. Kaka, M. R. Pufall, W. H. Rippard, T. J. Silva, S. E. Russek, and J. A. Katine, Mutual phase-locking of microwave spin torque nano-oscillators, Nature 437, 389 (2005). NATUAS 0028-0836 10.1038/nature04035
26. S. E. Russek, W. H. Rippard, T. Cecil, and R. Heindl, Spin-Transfer Nano-Oscillators, in Handbook of Nanophysics: Functional Nanomaterials, edited by K. D. Sattler (CRC Press, Boca Raton, FL, 2010), pp. 1-23.
27. R. Lebrun, N. Locatelli, S. Tsunegi, J. Grollier, V. Cros, F. A. Araujo, H. Kubota, K. Yakushiji, A. Fukushima, and S. Yuasa, Nonlinear behavior and mode coupling in spin-transfer nano-oscillators, Phys. Rev. Applied 2, 061001 (2014). 10.1103/PhysRevApplied.2.061001
28. D. Li, Y. Zhou, C. Zhou, and B. Hu, Global attractors and the difficulty of synchronizing serial spin-torque oscillators, Phys. Rev. B 82, 140407 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.140407
29. G. Csaba, M. Pufall, W. Rippard, and W. Porod, Modeling of coupled spin torque oscillators for applications in associative memories, in Proceedings of the 12th IEEE Conference on Nanotechnology (IEEE-NANO) (IEEE, New York, 2012), pp. 1-4.
30. G. Csaba, M. Pufall, D. E. Nikonov, G. I. Bourianoff, A. Horvath, T. Roska, and W. Porod, Spin torque oscillator models for applications in associative memories, in Proceedings of the 13th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA) (IEEE, New York, 2012), pp. 1-2.
31. T. Roska, A. Horvath, A. Stubendek, F. Corinto, G. Csaba, W. Porod, T. Shibata, and G. Bourianoff, An associative memory with oscillatory cnn arrays using spin torque oscillator cells and spin-wave interactions architecture and end-to-end simulator, in Proceedings of the 13th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA) (IEEE, New York, 2012), pp. 1-3.
32. T. Shibata, R. Zhang, S. P. Levitan, D. E. Nikonov, and G. I. Bourianoff, Cmos supporting circuitries for nano-oscillator-based associative memories, in Proceedings of the 13th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA) (IEEE, New York, 2012), pp. 1-5.
33. F. B. Mancoff, N. D. Rizzo, B. N. Engel, and S. Tehrani, Phase-locking in double-point-contact spin-transfer devices, Nature 437, 393 (2005). NATUAS 0028-0836 10.1038/nature04036
34. B. Georges, J. Grollier, M. Darques, V. Cros, C. Deranlot, B. Marcilhac, G. Faini, and A. Fert, Coupling efficiency for phase locking of a spin transfer nano-oscillator to a microwave current, Phys. Rev. Lett. 101, 017201 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.017201
35. J. Shibata, K. Shigeto, and Y. Otani, Dynamics of magnetostatically coupled vortices in magnetic nanodisks, Phys. Rev. B 67, 224404 (2003). PRBMDO 0163-1829 10.1103/PhysRevB.67.224404
36. A. Vogel, A. Drews, T. Kamionka, M. Bolte, and G. Meier, Influence of dipolar interaction on vortex dynamics in arrays of ferromagnetic disks, Phys. Rev. Lett. 105, 037201 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.037201
37. A. Awad, G. Aranda, D. Dieleman, K. Y. Guslienko, G. N. Kakazei, B. A. Ivanov, and F. G. Aliev, Spin excitation frequencies in magnetostatically coupled arrays of vortex state circular permalloy dots, Appl. Phys. Lett. 97, 132501 (2010). APPLAB 0003-6951 10.1063/1.3495774
38. A. Barman, S. Barman, T. Kimura, Y. Fukuma, and Y. Otani, Gyration mode splitting in magnetostatically coupled magnetic vortices in an array, J. Phys. D: Appl. Phys. 43, 422001 (2010). JPAPBE 0022-3727 10.1088/0022-3727/43/42/422001
39. H. Jung, Y.-S. Yu, K.-S. Lee, M.-Y. Im, P. Fischer, L. Bocklage, A. Vogel, M. Bolte, G. Meier, and S.-K. Kim, Observation of coupled vortex gyrations by 70-ps-time- and 20-nm-space-resolved full-field magnetic transmission soft x-ray microscopy, Appl. Phys. Lett. 97, 222502 (2010). APPLAB 0003-6951 10.1063/1.3517496
40. H. Jung, K.-S. Lee, D.-E. Jeong, Y.-S. Choi, Y.-S. Yu, D.-S. Han, A. Vogel, L. Bocklage, G. Meier, M.-Y. Im, P. Fischer, and S.-K. Kim, Tunable negligible-loss energy transfer between dipolar-coupled magnetic disks by stimulated vortex gyration, Sci. Rep. 1, 59 (2011). 2045-2322 10.1038/srep00059
41. D. V. Berkov, Synchronization of spin-torque-driven nano-oscillators for point contacts on a quasi-one-dimensional nanowire: Micromagnetic simulations, Phys. Rev. B 87, 014406 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.014406
42. A. Dussaux, B. Georges, J. Grollier, V. Cros, A. Khvalkovskiy, A. Fukushima, M. Konoto, H. Kubota, K. Yakushiji, S. Yuasa, K. A. Zvezdin, K. Ando, and A. Fert, Large microwave generation from current-driven magnetic vortex oscillators in magnetic tunnel junctions, Nat. Commun. 1, 8 (2010). 2041-1723 10.1038/ncomms1006
43. A. V. Khvalkovskiy, J. Grollier, A. Dussaux, K. A. Zvezdin, and V. Cros, Vortex oscillations induced by spin-polarized current in a magnetic nanopillar: Analytical versus micromagnetic calculations, Phys. Rev. B 80, 140401 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.80.140401
44. K. Guslienko, B. Ivanov, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, Eigenfrequencies of vortex state excitations in magnetic submicron-size disks, J. Appl. Phys. 91, 8037 (2002). JAPIAU 0021-8979 10.1063/1.1450816
45. A. A. Thiele, Steady-state motion of magnetic domains, Phys. Rev. Lett. 30, 230 (1973). PRLTAO 0031-9007 10.1103/PhysRevLett.30.230
46. Y. Gaididei, V. P. Kravchuk, and D. D. Sheka, Magnetic vortex dynamics induced by an electrical current, Int. J. Quantum Chem. 110, 83 (2010). IJQCB2 0020-7608 10.1002/qua.22253
47. K. Y. Guslienko, X. F. Han, D. J. Keavney, R. Divan, and S. D. Bader, Magnetic vortex core dynamics in cylindrical ferromagnetic dots, Phys. Rev. Lett. 96, 067205 (R) (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.067205
48. B. A. Ivanov and C. E. Zaspel, Excitation of spin dynamics by spin-polarized current in vortex state magnetic disks, Phys. Rev. Lett. 99, 247208 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.247208
49. A. Dussaux, A. V. Khvalkovskiy, P. Bortolotti, J. Grollier, V. Cros, and A. Fert, Field dependence of spin-transfer-induced vortex dynamics in the nonlinear regime, Phys. Rev. B 86, 014402 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.014402
50. A. Chanthbouala, R. Matsumoto, J. Grollier, V. Cros, A. Anane, A. Fert, A. V. Khvalkovskiy, K. A. Zvezdin, K. Nishimura, Y. Nagamine, H. Maehara, K. Tsunekawa, A. Fukushima, and S. Yuasa, Vertical-current-induced domain-wall motion in MgO-based magnetic tunnel junctions with low current densities, Nat. Phys. 7, 626 (2011). 1745-2473 10.1038/nphys1968
51. SpinPM is a micromagnetic code developed by the Istituto P.M. srl, Torino, Italy (www.istituto-pm.it) based on a fourth-order Runge-Kutta numerical scheme with an adaptative time-step control for the time integration.
52. K. Guslienko, Low-frequency vortex dynamic susceptibility and relaxation in mesoscopic ferromagnetic dots, Appl. Phys. Lett. 89, 022510 (2006). APPLAB 0003-6951 10.1063/1.2221904