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Spin Currents and Nonlinear Dynamics of Vortex Spin Torque Nano-Oscillators

  • ELECTRICAL AND MAGNETIC PROPERTIES
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Abstract

Vortex spin torque nano-oscillators (STNOs) are multilayer spin-valve magnetic nanopillars, in which the magnetic layers (one or both) contain a magnetic vortex, the dynamics of which provides microwave radiation. In vortex STNOs, it was possible to achieve a high microwave signal power (on the order of 1 μW) and a relatively narrow linewidth (several hundreds of kHz). To further increase the power and improve the spectral characteristics of vortex STNOs, the collective dynamics and synchronization conditions in the ensembles of such nanostructures are studied. The subject of this review is the latest achievements in the field of physics and technology of vortex STNOs.

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REFERENCES

  1. J. Slonczewski, “Current-driven excitation of magnetic multilayers,” J. Magn. Magn. Mater. 159, L1 (1996).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  3. M. Tsoi, A. G. M. Jansen, J. Bass, W, Chiang, M. Seck, V. Tsoi, and P. Wyder, “Excitation of a magnetic multilayer by an electric current,” Phys. Rev. Lett. 80, 4281 (1998).

    Article  CAS  Google Scholar 

  4. E. B. Myers, D, Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, “Current-induced switching of domains in magnetic multilayer devices,” Science 285, 867 (1999).

    Article  CAS  Google Scholar 

  5. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D, Ralph, “Current-driven magnetization reversal and spin-wave excitations in Co/Cu/Co pillars,” Phys. Rev. Lett. 84, 3149 (2000).

    Article  CAS  Google Scholar 

  6. A. K. Zvezdin, A. V. Khval’kovskii, and K. A. Zvezdin, “The generalized Landau-Lifshitz equation and spin transfer processes in magnetic nanostructures,” Phys. Usp. 51, 412–417 (2008).

    Article  CAS  Google Scholar 

  7. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: A spin-based electronics vision for the future,” Science 294, 1488 (2001).

    Article  CAS  Google Scholar 

  8. A. V. Khvalkovskiy, D. Apalkov, S. Watts, R. Chepulskii, R. S. Beach, A. Ong, X. Tang, A. Driskill-Smith, W. H. Butler, P. B. Visscher, D. Lottis, E. Chen, V. Nikitin, and M. Krounbi, “Basic principles of STT-MRAM cell operation in memory arrays,” J. Phys. D: Appl. Phys. 46, 074001 (2013).

    Article  Google Scholar 

  9. D. A. Allwood, G. Xiong, C, Faulkner, D. Atkinson, D. Petit, and R. P. Cowburn, “Magnetic domain-wall logic,” Science 309, 1688 (2005).

    Article  CAS  Google Scholar 

  10. A. Chanthbouala, R. Matsumoto, J. Grollier, V. Cros, A. Anane, A. Fert, A. V. Khvalkovskiy, K. Zvezdin, K. A. 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, 626–630 (2011).

    Article  CAS  Google Scholar 

  11. S. I. Kiselev, J, Sankey, I. N. Krivorotov, N, Emley, R. J. Schoelkopf, R. A. Buhrman, and D, Ralph, “Microwave oscillations of a nanomagnet driven by a spin-polarized current,” Nature 425, 380–383 (2003).

    Article  CAS  Google Scholar 

  12. A. Dussaux, B. Georges, J. Grollier, V. Cros, A. V. 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).

    Article  CAS  Google Scholar 

  13. W. H. Rippard, M. R. Pufall, S. Kaka, S. E. Russek, and T. J. Silva, “Direct-current induced dynamics in Co90Fe10/Ni80Fe20 point contacts,” Phys. Rev. Lett. 92, 027201 (2004).

    Article  CAS  Google Scholar 

  14. I. N. Krivorotov, N, Emley, J, Sankey, S. I. Kiselev, D. Ralph, and R. A. Buhrman, “Time-domain measurements of nanomagnet dynamics driven by spin-transfer torques,” Science 307, 228 (2005).

    Article  CAS  Google Scholar 

  15. A. Jenkins, R. Lebrun, E. Grimaldi, S. Tsunegi, P. Bortolotti, H. Kubota, K. Yakushiji, A. Fukushima, G. De Loubens, O. Klein, S. Yuasa, and V. Cros, “Spin-torque resonant expulsion of the vortex core for an efficient radiofrequency detection scheme,” Nat. Nanotechnol. 11, 360 (2016).

    Article  CAS  Google Scholar 

  16. P. Skirdkov, A. Popkov, and K. Zvezdin, “Vortex spin-torque diode: The impact of DC bias,” Appl. Phys. Lett. 113, 242403 (2018).

    Article  CAS  Google Scholar 

  17. S. Bohlens, B. Kruger, A. Drews, M. Bolte, et al., “Current controlled random-access memory based on magnetic vortex handedness,” Appl. Phys. Lett. 93, 142508 (2008).

    Article  CAS  Google Scholar 

  18. K. Nakano, D. Chiba, N. Ohshima, S. Kasai, T. Sato, et al., “All-electrical operation of magnetic vortex core memory cell,” Appl. Phys. Lett. 99, 262505 (2011).

    Article  CAS  Google Scholar 

  19. J. Grollier, D. Querlioz, K. Y. Camsari, K. Everschor-Sitte, S. Fukami, and M. D. Stiles, “Neuromorphic spintronics,” Nat. Electron. 3, 360–370 (2020).

    Article  Google Scholar 

  20. L. Shen, J. Xia, G. Zhao, X. Zhang, M. Ezawa, O. A. Tretiakov, X. Liu, and Y. Zho, “Spin torque nano-oscillators based on antiferromagnetic skyrmions,” Appl. Phys. Lett. 114, 042402 (2019).

    Article  CAS  Google Scholar 

  21. K. Everschor-Sitte, J. Masell, R. M. Reeve, and M. Klaui, “Perspective: Magnetic skyrmions-Overview of recent progress in an active research field,” J. Appl. Phys. 124, 240901 (2018).

    Article  CAS  Google Scholar 

  22. S. Wang, A. Qaiumzadeh, and A. Brataas, “Current-driven dynamics of magnetic hopfions,” Phys. Rev. Lett. 123, 147203 (2019).

    Article  CAS  Google Scholar 

  23. F. Zheng, F. N. Rybakov, A. B. Borisov, D. Song, et al., “Experimental observation of chiral magnetic bobbers in B20-type FeGe,” Nat. Nanotechnol. 13, 451–455 (2018).

    Article  CAS  Google Scholar 

  24. Y. Wen, Z. Feng, B. F. Miao, R. X. Cao, L. Sun, B. You, D. Wu, W. Zhang, Z. S. Jiang, R. Cheng, and H. F. Ding, “Fast and controllable switching the circulation and polarity of magnetic vortices,” J. Met., Mater. Miner. 370, 68–75 (2014).

    CAS  Google Scholar 

  25. R.-C. Peng, J.-M. Hub, T. Yang, X. Cheng, J.-J. Wang, H.-B. Huang, L.-Q. Chen, and C.-W. Nan, “Switching the chirality of a magnetic vortex deterministically with an electric field,” Mater. Res. Lett. 6, No. 12, 669–675 (2018).

    Article  CAS  Google Scholar 

  26. V. A. Orlov, R. Yu. Rudenko, A. V. Kobyakov, A. V. Luk’yanenko, P. D. Kim, V. S. Prokopenko, and I. N. Orlova, “Magnetization dynamics in two-dimensional arrays of square microelements,” J. Exp. Theor. Phys. 126, No. 4, 523–534 (2018).

    Article  CAS  Google Scholar 

  27. T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, No. 5481, 930–932 (2000).

    Article  CAS  Google Scholar 

  28. J. Wu, D. Carlton, J. Park, Y. Meng, et al., “Direct observation of imprinted antiferromagnetic vortex states in CoO/Fe/Ag(001) discs,” Nat. Phys. 7, 303–306 (2011).

    Article  CAS  Google Scholar 

  29. V. L. Mironov, B. A. Gribkov, A. A. Fraerman, S. A. Gusev, S. N. Vdovichev, I. R. Karetnikova, I. M. Nefedov, and I. A. Shereshevsky, “MFM probe control of magnetic vortex chirality in elliptical Co nanoparticles,” J. Magn. Magn. Mater. 312, 153 (2007).

    Article  CAS  Google Scholar 

  30. K. Yu. 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 (2006).

    Article  CAS  Google Scholar 

  31. S. V. Vonsovskii, Magnetism (Nauka, Moscow, 1032) [in Russian].

  32. L. G. Korzunin and I. M. Izmozherov, “Numerical simulation of the influence of inhomogeneities on the properties of magnetization nanostructures,” Phys. Met. Metallogr. 122, 183 (2021).

    Article  Google Scholar 

  33. N. A. Usov and S. E. Peschany, “Magnetization curling in a fine cylindrical particle,” J. Magn. Magn. Mater. 118, 290–294 (1993).

    Article  Google Scholar 

  34. R. P. Cowburn and M. E. Welland, “Phase transitions in planar magnetic nanostructures,” Appl. Phys. Lett. 72, 2041 (1998).

    Article  CAS  Google Scholar 

  35. K. Y. Guslienko, “Magnetic vortex state stability, reversal and dynamics in restricted geometries,” J. Nanosci. Nanotechnol. 8, 2745–2760 (2008).

    Article  CAS  Google Scholar 

  36. K. Metlov and K. Guslienko, “Stability of magnetic vortex in soft magnetic nano-sized circular cylinder,” J. Magn. Magn. Mater. 242245, No. 2, 1015–1017 (2002).

    Article  Google Scholar 

  37. K. Guslienko and K. L. Metlov, “Evolution and stability of a magnetic vortex in a small cylindrical ferromagnetic particle under applied field,” Phys. Rev. B 63, 100403 (2001).

    Article  CAS  Google Scholar 

  38. K. Yu. Guslienko, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, “Field evolution of magnetic vortex state in ferromagnetic disks,” Appl. Phys. Lett. 78, 3848–3850 (2001).

    Article  CAS  Google Scholar 

  39. C. Chappert, A. Fert A., and A. F. Van Dau, “The emergence of spin electronics in data storage,” Nat. Mater. 6, 813–823 (2007).

    Article  CAS  Google Scholar 

  40. A. A. Thiele, “Applications of the gyrocoupling vector and dissipation dyadic in the dynamics of magnetic domains,” J. Appl. Phys. 45, No. 1, 377–393 (1974).

    Article  Google Scholar 

  41. D. L. Huber, “Dynamics of spin vortices in two dimensional planar magnets,” Phys. Rev. B 26, No. 7, 3758–3765 (1982).

    Article  CAS  Google Scholar 

  42. D. L. Huber, “Equation of motion of a spin vortex in a two-dimensional planar magnet,” J. Appl. Phys. 53, No. 3, 1899–1900 (1982).

    Article  Google Scholar 

  43. F. G. Mertens and A. R. Bishop, Dynamics of Vortices in Two-Dimensional Magnets, Nonlinear Science at the Dawn of the 21th Century, Ed. by P. L. Christiansen, M. P. Soerensen, and A, Scott (Springer, Berlin, 2000), pp. 137–170.

  44. D. D. Sheka, “Field momentum and gyroscopic dynamics of classical systems with topological defects,” J. Phys. A: Math. Gen. 39, No. 50, 15477–15489 (2006).

    Article  Google Scholar 

  45. 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).

    Article  CAS  Google Scholar 

  46. Y. Gaididei, V. Kravchuk, and D. Sheka, “Magnetic vortex dynamics induced by an electrical current,” Int. J. Quantum Chem. 110, 8397 (2010).

    Google Scholar 

  47. B. A. Ivanov and E. Zaspel, “Excitation of spin dynamics by spin-polarized current in vortex state magnetic disks,” Phys. Rev. Lett. 99, 247208 (2007).

    Article  CAS  Google Scholar 

  48. N. A. Usov and S. E. Peschanyi, “Vortex distribution of magnetization in a thin ferromagnetic cylinder,” Phys. Met. Metallogr. 78, No. 6, 13–24 (1994).

    CAS  Google Scholar 

  49. http://math.nist.gov/oommf/.

  50. http://mumax.github.io/.

  51. http://nmag.soton.ac.uk/nmag/.

  52. http://www.micromagus.de/home.html.

  53. https://deparkes.co.uk/2014/05/30/list-micromagnetic- simulation-software/.

  54. D. V. Berkov and J. Miltat, “Spin-torque driven magnetization dynamics: Micromagnetic modeling,” J. Magn. Magn. Mater. 320, 1238–1259 (2008).

    Article  CAS  Google Scholar 

  55. J. Leliaert and J. Mulkers, “Tomorrow’s micromagnetic simulations,” J. Appl. Phys. 125, 180901 (2019).

    Article  CAS  Google Scholar 

  56. B. A. Ivanov, G. G. Avanesyan, A. V. Khvalkovskiy, N. E. Kulagin, C. E. Zaspel, and K. A. Zvezdin, “Non-newtonian dynamics of the fast motion of a magnetic vortex,” J. Exp. Theor. Phys. Lett. 91, No. 4, 178 (2010).

    Article  CAS  Google Scholar 

  57. S. S. Cherepov, B, Koop, V. Korenivski, D, Worledge, A. Yu. Galkin, S. R. Khymyn, and B. A. Ivanov, “Core-core dynamics in spin vortex pairs,” Phys. Rev. Lett. 109, 097204 (2012).

    Article  CAS  Google Scholar 

  58. P. D. Kim, V. A. Orlov, V. S. Prokopenko, S. S. Zamai, V. Ya. Prints, R. Yu. Rudenko, and T. V. Rudenko, “On the low-frequency resonance of magnetic vortices in micro- and nanodots,” Phys. Solid State 57, 29–36 (2015).

    Article  CAS  Google Scholar 

  59. K. Y. Guslienko, G. N. Kakazei, J. Ding, X. M. Liu, and A. O. Adeyeye, “Giant moving vortex mass in thick magnetic nanodots,” Sci. Rep. 5,13881 (2015).

    Article  CAS  Google Scholar 

  60. M. Goiriena-Goikoetxea, K. Y. Guslienko, I. Rouco, M. Orue, E. Berganza, M. Jaafar, A. Asenjo, M. L. Fernández-Gubieda, L. Fernández Barquín, and A. García-Arriba, “Magnetization reversal in circular vortex dots of small radius,” Nanoscale 9, 11269–11278 (2017).

    Article  CAS  Google Scholar 

  61. A. M. Kosevich, V. P. Voronov, and I. V. Manzhos, “Nonlinear collective excitations in an easy-plane magnet,” Zh. Eksp. Teor. Fiz. 84, No. 1, 148–160 (1983).

    CAS  Google Scholar 

  62. A. M. Kosevich, B. A. Ivanov, and A. S. Kovalev, Nonlinear Waves of Magnetization. Dynamic and Topological Solitons (Naukova dumka, Kiev, 1983), p. 192 [in Russian].

    Google Scholar 

  63. B. A. Ivanov and D. D. Sheka, “Vortices in the cone phase of a classical quasi-two-dimensional ferromagnet,” Fiz. Nizk. Temp. 21, No. 10, 1148–1156 (1995).

    CAS  Google Scholar 

  64. B. A. Ivanov and G. M. Wysin, “Magnon modes for a circular two–dimensional easy–plane ferromagnet in the cone state,” Phys. Rev. B 65, No. 13, 134434 (2002).

    Article  CAS  Google Scholar 

  65. V. P. Kravchuk and D. D. Sheka, “Thin ferromagnetic nanodisk in transverse magnetic field,” Phys. Solid State 49, No. 10, 1923–1931 (2007).

    Article  CAS  Google Scholar 

  66. A. Dussaux, A. V. Khvalkovskiy, P. Bortolotti, J. R. Grollie, V. Cros, and A. Fert, “Field dependence of spin-transfer-induced vortex dynamics in the nonlinear regime,” Phys. Rev. B 86, 014402 (2012).

    Article  CAS  Google Scholar 

  67. G. de Loubens, B. Pigeau, F. Lochner, F. Boust, K. Y. Guslienko, H. Hurdequint, L. W. Molenkamp, G. Schmidt, A. N. Slavin, V. S. Tiberkevich, N. Vukadinovic, and O. Klein, “Bistability of vortex core dynamics in a single perpendicularly magnetized nanodisk,” Phys. Rev. Lett. 102, 177602 (2009).

    Article  CAS  Google Scholar 

  68. K. Yu. Guslienko, X. F. Han, D. J. Keavney, R. Divan, and S. D. Bader, “Magnetic vortex core dynamics in a ferromagnetic dot,” Phys. Rev. Lett. 96, 067205 (2006).

    Article  CAS  Google Scholar 

  69. P. N. Skirdkov, A. F. Popkov, and K. A. Zvezdin, “Vortex spin-torque diode: The impact of DC bias,” Appl. Phys. Lett. 113, 242403 (2018).

    Article  CAS  Google Scholar 

  70. P. N. Skirdkov and K. A. Zvezdin, “Spin-torque diodes: From fundamental research to applications,” Ann. Phys. 532, 12 (2020).

    Article  CAS  Google Scholar 

  71. P. N. Skirdkov, A. D. Belanovsky, K. A. Zvezdin, A. K. Zvezdin, N. Locatelli, J. Grollier, and V. Cros, “Influence of shape imperfection on dynamics of vortex spin-torque nano-oscillator,” SPIN 02, 01, 1250005 (2012).

    Article  Google Scholar 

  72. V. A. Orlov, G. S. Patrin, and I. N. Orlova, “Interaction of a magnetic vortex with magnetic anisotropy nonuniformity,” J. Exp. Theor. Phys. 131, 589–599 (2020).

    Article  CAS  Google Scholar 

  73. M. Kuepferling, S. Zullino, A. Sola, B. Van de Wiele, G. Durin, M. Pasquale, K. Rott, G. Reiss, and G. Bertotti, “Vortex dynamics in Co–Fe–B magnetic tunnel junctions in presence of defects,” J. Appl. Phys. 117, 17E107 (2015).

  74. T. Okuno, K. Shigeto, T. Ono, K. Mibu, and T. Shinjo, “MFM study of magnetic vortex cores in circular permalloy dots: behavior in external field,” J. Magn. Magn. Mater. 240, 1–6 (2002).

    Article  CAS  Google Scholar 

  75. A. Thiaville, J. M. Garcia, R. Dittrich, J. Miltat, and T. Schrefl, “Micromagnetic study of Bloch-point-mediated vortex core reversal,” Phys. Rev. B 67, 094410 (2003).

    Article  CAS  Google Scholar 

  76. R. Wang and X. Dong, “Sub-nanosecond switching of vortex cores using a resonant perpendicular magnetic field,” Appl. Phys. Lett. 100, 082402 (2012)

    Article  CAS  Google Scholar 

  77. M. -W. Yoo, J. Lee, and S-K. Kim, “Radial-spin-wave-mode-assisted vortex-core magnetization reversals,” Appl. Phys. Lett. 100, 172413 (2012).

    Article  CAS  Google Scholar 

  78. D. J. Keavney, X. M. Cheng, and K. S. Buchanan, “Polarity reversal of a magnetic vortex core by a unipolar, nonresonant in-plane pulsed magnetic field,” Appl. Phys. Lett. 94, 172506 (2009).

    Article  CAS  Google Scholar 

  79. R. Hertel, S. Gliga, M. Fahnle, and C. M. Schneider, “Ultrafast nanomagnetic toggle switching of vortex cores,” Phys Rev Lett. 98, 117201 (2007).

    Article  CAS  Google Scholar 

  80. J.-G. Caputo, Y. Gaididei, F. G. Mertens, and D. D. Sheka, “Vortex polarity switching by a spin-polarized current,” Phys. Rev. Lett. 98, 056604 (2007).

    Article  CAS  Google Scholar 

  81. K. Yamada, S. Kasai, Y. Nakatani, K. Kobayashi, et al., “Electrical switching of the vortex core in a magnetic disk,” Nat. Mater. 6, 270–273 (2007).

    Article  CAS  Google Scholar 

  82. D. D. Sheka, Y. Gaididei, and F. G. Mertens, “Current induced switching of vortex polarity in magnetic nanodisks,” Appl. Phys. Lett. 91, 082509 (2007).

    Article  CAS  Google Scholar 

  83. W. Jin, H. He, Y. Chen, and Y. Liu, “Controllable vortex polarity switching by spin polarized current,” J. Appl. Phys. 105, 013906 (2009).

    Article  CAS  Google Scholar 

  84. A. V. Khvalkovskiy, A. N. Slavin, J. Grollier, K. A. Zvezdin, and K. Y. Guslienko, “Critical velocity for the vortex core reversal in perpendicular bias magnetic field,” Appl. Phys. Lett. 96, 022504 (2010).

    Article  CAS  Google Scholar 

  85. Y. Liu, S. Gliga, R. Hertel, and C. M. Schneider, “Current-induced magnetic vortex core switching in a Permalloy nanodisk,” Appl. Phys. Lett. 91, 112501 (2007).

    Article  CAS  Google Scholar 

  86. V. Uhlíř, M. Urbánek, L. Hladík, J. Spousta, et al., “Dynamic switching of the spin circulation in tapered magnetic nanodisks,” Nat. Nanotechnol. 8, 341–346 (2013).

    Article  CAS  Google Scholar 

  87. N. Locatelli, A. E. Ekomasov, A. V. Khvalkovskiy, Sh. A. Azamatov, K. A. Zvezdin, J. Grollier, E. G. Ekomasov, and V. Cros, “Reversal process of a magnetic vortex core under the combined action of a perpendicular field and spin transfer torque,” Appl. Phys. Lett. 102, 062401 (2013).

    Article  CAS  Google Scholar 

  88. K. Yamada, S. Kasai, Y. Nakatani, K. Kobayashi, and T. Ono, “Current-induced switching of magnetic vortex core in ferromagnetic elliptical disks,” Appl. Phys. Lett. 96, 192508 (2010).

    Article  CAS  Google Scholar 

  89. S.-K. Kim, Y.-S. Choi, K.-S. Lee, K. Y. Guslienko, and D.-E. Jeong, “Electric-current-driven vortex-core reversal in soft magnetic nanodots,” Appl. Phys. Lett. 91, 082506 (2007).

    Article  CAS  Google Scholar 

  90. K. Nakano, D. Chiba, N. Ohshima, S. Kasai, T. Sato, Y. Nakatani, K. Sekiguchi, K. Kobayashi, and T. Ono, “All-electrical operation of magnetic vortex core memory cell,” Appl. Phys. Lett. 99, 262505 (2011).

    Article  CAS  Google Scholar 

  91. K. Yu. Guslienko, K. S. Buchanan, S. D. Bader, and V. Novosad, “Dynamics of coupled vortices in layered magnetic nanodots,” Appl. Phys. Lett. 86, 223112 (2005).

    Article  CAS  Google Scholar 

  92. N. Locatelli, V. V. Naletov, J. Grollier, G. de Loubens, V. Cros, C. Deranlot, C. Ulysse, G. Faini, O. Klein, and A. Fert, “Dynamics of two coupled vortices in a spin valve nanopillar excited by spin transfer torque,” Appl. Phys. Lett. 98, No. 6, 062501 (2011).

    Article  CAS  Google Scholar 

  93. S. S. Cherepov, B. C. Koop, A. Yu. Galkin, R. S. Khymyn, B. A. Ivanov, D. C. Worledge, and V. Korenivski, “Core-core dynamics in spin vortex pairs,” Phys. Rev. Lett. 109, 097204 (2012).

    Article  CAS  Google Scholar 

  94. V. Sluka, A. Kakay, A. M. Deac, D. E. Burgler, C. M. Schneider, and R. Hertel, “Spin-torque induced dynamics at fine-split frequencies in nano-oscillators with two stacked vortices,” Nat. Commun. 6, 6409 (2015).

    Article  CAS  Google Scholar 

  95. N. Locatelli, R. Lebrun, V. Naletov, A. Hamadeh, G. De Loubens, O. Klein, J. Grollier, and V. Cros, “Improved spectral stability in spin-transfer nano oscillators: single vortex versus coupled vortices dynamics,” IEEE Trans. Magn. 51, 4300206 (2015).

    Article  Google Scholar 

  96. A. Hamadeh, N. Locatelli, V. Naletov, R. Lebrun, G. Loubens, J. Grollier, O. Klein, and V. Cros, “Origin of spectral purity and tuning sensitivity in a spin transfer vortex nano-oscillator,” Phys. Rev. Lett. 11, No. 25, 257201 (2014).

    Article  CAS  Google Scholar 

  97. A. Ekomasov, S. Stepanov, K. Zvezdin, and E. Ekomasov, “Influence of perpendicular magnetic field and polarized current on the dynamics of coupled magnetic vortices in a thin nanocolumnar trilayer conducting structure,” Phys. Met. Metallogr. 118, No. 4, 328–333 (2017).

    Article  CAS  Google Scholar 

  98. E. G. Ekomasov, S. V. Stepanov, M. I. Fakhretdinov, G. I. Antonov, A. E. Ekomasov, and K. A. Zvezdin, “Coupled dynamics of magnetic vortices in a three-layer thin conducting permalloy nanodisk,” Chelyab. Fiz.-Matem. Zhurn. 5, No. 2, 161–17 (2020).

    Google Scholar 

  99. S. Stepanov, A. Ekomasov, K. Zvezdin, and E. Ekomasov, “Dynamics of coupled magnetic vortices in trilayer conducting nanocylinder,” Phys. Solid State 60, No. 6, 1055–1060 (2018).

    Article  CAS  Google Scholar 

  100. A. Ekomasov, S. Stepanov, K. Zvezdin, and E. Ekomasov, “Spin current induced dynamics and polarity switching of coupled magnetic vertices in three-layer nanopillars,” J. Magn. Magn. Mater. 471, 513–520 (2019).

    Article  CAS  Google Scholar 

  101. E. G. Ekomasov, S. V. Stepanov, K. A. Zvezdin, N. G. Pugach, and G. I. Antonov, “The effect of the spin-polarized current on the dynamics and structural changes of magnetic vortices in a large-diameter three-layer conducting nanocylinder,” Phys. Met. Metallogr. 122, No. 3, 197–204 (2021).

    Article  CAS  Google Scholar 

  102. F. A. Araujo, H. Kubota, K. Yakushiji, A. Fukushima, and S. Yuasa, “Nonlinear behavior and mode coupling in spin-transfer nano-oscillators,” Phys. Rev. Appl. 2, 061001 (2014).

    Article  CAS  Google Scholar 

  103. L. Shen, J. Xia, G. Zhao, X. Zhang, M. Ezawa, O. A. Tretiakov, X. Liu, and Y. Zhou, “Spin torque nano-oscillators based on antiferromagnetic skyrmions,” Appl. Phys. Lett. 114, 042402 (2019).

    Article  CAS  Google Scholar 

  104. M. E. Stebliy, A. V. Ognev, A. S. Samardak, A. G. Kolesnikov, L. A. Chebotkevich, and X. Han, “High-frequency switching of magnetic bistability in an asymmetric double disk nanostructure,” Appl. Phys. Lett. 104, 112405 (2014).

    Article  CAS  Google Scholar 

  105. A. V. Bondarenko, E. Holmgren, B. C. Koop, T. Descamps, B. A. Ivanov, and V. Korenivski, “Stochastic dynamics of strongly-bound magnetic vortex pairs,” AIP Adv. 7, 056007 (2017).

    Article  CAS  Google Scholar 

  106. E. Holmgren, A. Bondarenko, B. A. Ivanov, and V. Korenivski, “Resonant pinning spectroscopy with spin-vortex pairs,” Phys. Rev. B 97, 094406 (2018).

    Article  CAS  Google Scholar 

  107. E. Holmgren, A. Bondarenko, M. Persson, B. A. Ivanov, and V. Korenivski, “Transient dynamics of strongly coupled spin vortex pairs: Effects of anharmonicity and resonant excitation on inertial switching,” Appl. Phys. Lett. 112, 192405 (2018).

    Article  CAS  Google Scholar 

  108. W. Jin, H. He, Y. Chen, and Y. Liu, “Controllable vortex polarity switching by spin polarized current,” J. Appl. Phys. 105, 013906 (2009).

    Article  CAS  Google Scholar 

  109. K.-S. Lee, M.-W. Yoo, Y.-S. Choi, and S.-K. Kim, “Edge-soliton-mediated vortex-core reversal dynamics,” Phys. Rev. Lett. 106, 147201 (2011).

    Article  CAS  Google Scholar 

  110. A. S. Jenkins, R. Lebrun, E. Grimaldi, S. Tsunegi, P. Bortolotti, H. Kubota, K. Yakushiji, A. Fukushima, G. de Loubens, O. Klein, S. Yuasa, and V. Cros, “Spin-torque resonant expulsion of the vortex core for an efficient radiofrequency detection scheme,” Nat. Nanotechnol. 11, 360–364 (2016).

    Article  CAS  Google Scholar 

  111. A. Ekomasov, A. Khval’kovskii, K. Zvezdin, and E. Ekomasov, “Simulation of static and dynamic scenarios of polarization switching of magnetic vortices in a nanocolumnar conducting three-layer structure,” Izv. RAN Cer. Fiz. 77, No. 10, 1490–1492 (2013).

    Google Scholar 

  112. A. Ekomasov, C. Stepanov, and E. Ekomasov, “Simulation of vortex core switching in a nanocolumnar conductive three-layer structure,” Pis’ma o Mater. 6, 46 (2016).

  113. A. D. Belanovsky, N. Locatelli, P. N. Skirdkov, A. F. Abreu, 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).

  114. N. Locatelli, A. Hamadeh, AraujoF. Abreu, A. D. Belanovsky, P. N. Skirdkov, R. Lebrun, V. V. Naletov, K. A. Zvezdin, M. Munoz, J. Grollier, O. Klein, V. Cros, and G. de Loubens, “Efficient synchronization of dipolarly coupled vortex-based spin transfer nano-oscillators,” Sci. Rep. 5, 17039 (2015).

    Article  CAS  Google Scholar 

  115. A. D. Belanovsky, N. Locatelli, P. N. Skirdkov, A. F. Abreu, J. Grollier, K. A. Zvezdin, 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).

    Article  CAS  Google Scholar 

  116. A. F. Abreu, A. D. Belanovsky, P. N. Skirdkov, K. A. Zvezdin, A. K. Zvezdin, N. Locatelli, R. Lebrun, J. Grollier, V. Cros, G. de Loubens, and O. Klein, “Optimizing magnetodipolar interactions for synchronizing vortex-based spin-torque nano-oscillators,” Phys. Rev. B 92, 045419 (2015).

    Article  CAS  Google Scholar 

  117. J. Grollier, V. Cros, and A. Fert, “Synchronization of spin-transfer oscillators driven by stimulated microwave currents,” Phys. Rev. B 73, 060409 (2006).

    Article  CAS  Google Scholar 

  118. 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).

    Article  CAS  Google Scholar 

  119. B. Georges, J. Grollier, V. Cros, and A. Fert, Impact of the electrical connection of spin transfer nano-oscillators on their synchronization: analytical study, Appl. Phys. Lett. 92, 232504 (2008).

    Article  CAS  Google Scholar 

  120. 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,” Nature Nano. 4, 528 (2009).

    Article  CAS  Google Scholar 

  121. A. D. Belanovsky, N. Locatelli, P. N. Skirdkov, Araujo F. Abreu, 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 (2012).

    Article  CAS  Google Scholar 

  122. A. D. Belanovsky, N. Locatelli, P. N. Skirdkov, Araujo F. Abreu, 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).

    Article  CAS  Google Scholar 

  123. Y. Zhou and J. Akerman, “Perpendicular spin torque promotes synchronization of magnetic tunnel junction based spin torque oscillators,” Appl. Phys. Lett. 94, 112503 (2009).

    Article  CAS  Google Scholar 

  124. 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).

    Article  CAS  Google Scholar 

  125. A. N. Slavin and V. S. Tiberkevich, “Theory of mutual phase locking of spintorque nanosized oscillators,” Phys. Rev. B 74, 104401 (2006)

    Article  CAS  Google Scholar 

  126. S. Urazhdin, P. Tabor, V. S. Tiberkevich, and A. Slavin, “Fractional synchronization of spin-torque nano-oscillators,” Phys. Rev. Lett. 105, 104101 (2010).

    Article  CAS  Google Scholar 

  127. S. Kaka, M. Puffall, W. Rippard, T. Silva, S. Russek, and J. Katine, “Mutual phase-locking of microwave spin torque nano-oscillators,” Nature 437, 389–392 (2005).

    Article  CAS  Google Scholar 

  128. F. B. Mancoff, N. D. Rizzo, B. N. Engel, and S. Tehrani, “Phase-locking in double-point-contact spin-transfer devices,” Nature 437, 393–395 (2005).

    Article  CAS  Google Scholar 

  129. A. R. Safin, N. N. Udalov, and M. V. Kapranov, “Mutual phase locking of very nonidentical spin torque nanooscillators via spin wave interaction,” Eur. Phys. J. Appl. Phys. 67, No. 2, 20601 (2014).

    Article  Google Scholar 

  130. V. S. Tiberkevich, A. N. Slavin, E. Bankowski, and G. Gerhart, “Phase locking of vortex-based spin-torque nanocontact oscillators by antivortices,” Appl. Phys. Lett. 102, 052403 (2013).

    Article  CAS  Google Scholar 

  131. N. Locatelli, V. V. Naletov, J. Grollier, G. De Loubens, V. Cros, C. Deranlot, C. Ulysse, G. Faini, O. Klein, and A. Fert, “Dynamics of two coupled vortices in a spin valve nanopillar excited by spin transfer torque,” Appl. Phys. Lett. 98, 062501 (2011).

    Article  CAS  Google Scholar 

  132. J. Shibata, K. Shigeto, and Y. Otani, “Dynamics of magnetostatically coupled vortices in magnetic nanodisks,” Phys. Rev. B 67, 224404 (2003).

    Article  CAS  Google Scholar 

  133. 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).

    Article  CAS  Google Scholar 

  134. S. Sugimoto, Y. Fukuma, S. Kasai, T. Kimura, A. Barman, and Y. C. Otani, “Dynamics of coupled vortices in a pair of ferromagnetic disks,” Phys. Rev. Lett. 106, 197203 (2011).

    Article  CAS  Google Scholar 

  135. M. Romera, P. Talatchian, S. Tsunegi, F. Abreu, CrosV. Araujo, P. Bortolotti, J. Trastoy, K. Yakushiji, A. Fukushima, H. Kubota, S. Yuasa, M. Ernoult, D. Vodenicarevic, T. Hirtzlin, N. Locatelli, D. Querlioz, and J. Grollier, “Vowel recognition with four coupled spin-torque nano-oscillator,” Nature 563, 230 (2018).

    Article  CAS  Google Scholar 

  136. J. Grollier, D. Querlioz, K. Y. Camsari, K. Everschor-Sitte, et al., “Neuromorphic spintronics,” Nat. Electron. 3, 360–370 (2020).

    Article  Google Scholar 

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 20-12-50046.

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Zvezdin, K.A., Ekomasov, E.G. Spin Currents and Nonlinear Dynamics of Vortex Spin Torque Nano-Oscillators. Phys. Metals Metallogr. 123, 201–219 (2022). https://doi.org/10.1134/S0031918X22030140

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