Interplay of Linear and Nonlinear Localization Mechanisms in Spin-Torque Oscillators with a Field Well
DOI:
https://doi.org/10.15407/ujpe64.10.947Keywords:
spin-torque oscillator, spin-wave bullet, localized mode, magnetization dynamicsAbstract
The magnetization dynamics in a spin-torque oscillator with nonuniform profile of a static magnetic field creating a field well is studied by analytic calculations and numerical simulations. It is demonstrated that, in the case of sufficiently deep and narrow field well, the linear localization in the field well dominates the nonlinear self-localization, despite a negative nonlinear frequency shift. A change of the localization mechanism results in a qualitatively different dependence of the generation power on the driving current. For the dominant linear localization, the soft generation mode is realized, while, for the nonlinear self-localization, we observe a hard mode of auto-oscillator excitation. Simultaneously, a difference in the profiles of the excited spin-wave mode can become evident and distinguishable in experiments only in the case of a nonsymmetric field well.
References
J.A. Katine, F.J. Albert, R.A. Buhrman, E.B. Myers, D.C. Ralph. Current-driven magnetization reversal and spin-wave excitations in Co/Cu/Co pillars, Phys. Rev. Lett. 84, 3149 (2000). https://doi.org/10.1103/PhysRevLett.84.3149
R. Ramaswamy, J.M. Lee, K. Cai, H. Yang. Recent advances in spin-orbit torques: Moving towards device applications. Appl. Phys. Rev. 5, 031107 (2018). https://doi.org/10.1063/1.5041793
K. Ando, S. Takahashi, K. Harii, K. Sasage, J. Ieda, S. Maekawa, E. Saitoh. Electric manipulation of spin relaxation using the spin Hall effect. Phys. Rev. Lett. 101, 036601 (2008). https://doi.org/10.1103/PhysRevLett.101.036601
A. Hamadeh, O. d'Allivy Kelly, C. Hahn, H. Meley, R. Bernard, A.H. Molpeceres, V.V. Naletov, M. Viret, A. Anane, V. Cros, S.O. Demokritov, J.L. Prieto, M. Mu?noz, G. de Loubens, O. Klein. Full control of the spin-wave damping in a magnetic insulator using spin-orbit torque. Phys. Rev. Lett. 113, 197203 (2014). https://doi.org/10.1103/PhysRevLett.113.197203
S.I. Kiselev, J.C. Sankey, I.N. Krivorotov, N.C. Emley, R.J. Schoelkopf, R.A. Buhrman, D.C. Ralph. Microwave oscillations of a nanomagnet driven by a spin-polarized current. Nature 425, 380 (2003). https://doi.org/10.1038/nature01967
W.H. Rippard, M.R. Pufall, S. Kaka, S.E. Russek, T.J. Silva. Direct-current induced dynamics in Co90Fe10/Ni80Fe20 point contacts. Phys. Rev. Lett. 92, 027201 (2004). https://doi.org/10.1103/PhysRevLett.92.027201
O. Prokopenko, E. Bankowski, T. Meitzler, V. Tiberkevich, A. Slavin. Spin-torque nano-oscillator as a microwave signal source. IEEE Magn. Lett. 2, 3000104 (2011). https://doi.org/10.1109/LMAG.2010.2102007
S. Tsunegi, H. Kubota, K. Yakushiji, M. Konoto, S. Tamaru, A. Fukushima, H. Arai, H. Imamura, E. Grimaldi, R. Lebrun, J. Grollier, V. Cros, S. Yuasa. High emission power and Q factor in spin torque vortex oscillator consisting of FeB free layer. Appl. Phys. Express 7, 063009 (2014). https://doi.org/10.7567/APEX.7.063009
V.E. Demidov, S. Urazhdin, R. Liu, B. Divinskiy, A. Telegin, S.O. Demokritov. Excitation of coherent propagating spin waves by pure spin currents. Nature Commun 7, 10446 (2016). https://doi.org/10.1038/ncomms10446
A. Giordano, R. Verba, R. Zivieri, A. Laudani, V. Puliafito, G. Gubbiotti, R. Tomasello, G. Siracusano, B. Azzerboni, M. Carpentieri, A. Slavin, G. Finocchio. Spin-Hall nano-oscillator with oblique magnetization and Dzyaloshinskii-Moriya interaction as generator of skyrmions and nonreciprocal spin-waves. Sci. Rep. 6, 36020 (2016). https://doi.org/10.1038/srep36020
J. Torrejon, M. Riou, F.A. Araujo, S. Tsunegi, G. Khalsa, D. Querlioz, P. Bortolotti, V. Cros, K. Yakushiji, A. Fukushima, H. Kubota, S. Yuasa, M.D. Stiles, J. Grollier. Neuromorphic computing with nanoscale spintronic oscillators. Nature 547, 428 (2017). https://doi.org/10.1038/nature23011
V.E. Demidov, S. Urazhdin, H. Ulrichs, V. Tiberkevich, A. Slavin, D. Baither, G. Schmitz, S.O. Demokritov. Magnetic nano-oscillator driven by pure spin current,. Nat. Mater. 11, 1028 (2012). https://doi.org/10.1038/nmat3459
V.E. Demidov, S. Urazhdin, A. Zholud, A.V. Sadovnikov, A.N. Slavin, S.O. Demokritov. Spin-current nano-oscillator based on nonlocal spin injection. Sci. Rep. 5, 8578 (2015). https://doi.org/10.1038/srep08578
A. Slavin, V. Tiberkevich. Nonlinear auto-oscillator theory of microwave generation by spin-polarized current. IEEE Trans. Magn. 45, 1875 (2009). https://doi.org/10.1109/TMAG.2008.2009935
V.S. Pribiag, I.N. Krivorotov, G.D. Fuchs, P.M. Braganca, O. Ozatay, J.C. Sankey, D.C. Ralph, R.A. Buhrman. Magnetic vortex oscillator driven by d.c. spin-polarized current. Nature Phys. 3, 498 (2007). https://doi.org/10.1038/nphys619
V.E. Demidov, S. Urazhdin, E.R.J. Edwards, M.D. Stiles, R.D. McMichael, S.O. Demokritov. Control of magnetic fluctuations by spin current. Phys. Rev. Lett. 107, 107204 (2011). https://doi.org/10.1103/PhysRevLett.107.107204
J. Slonczewski. Excitation of spin waves by an electric current. J. Magn. Magn. Mater. 195, L261 (1999). https://doi.org/10.1016/S0304-8853(99)00043-8
M.A. Hoefer, M.J. Ablowitz, B. Ilan, M.R. Pufall, T.J. Silva. Theory of magnetodynamics induced by spin torque in perpendicularly magnetized thin films. Phys. Rev. Lett. 95, 267206 (2005). https://doi.org/10.1103/PhysRevLett.95.267206
G. Consolo, L. Lopez-Diaz, B. Azzerboni, I. Krivorotov, V. Tiberkevich, A. Slavin. Excitation of spin waves by a current-driven magnetic nanocontact in a perpendicularly magnetized waveguide. Phys. Rev. B 88, 014417 (2013). https://doi.org/10.1103/PhysRevB.88.014417
A. Slavin, V. Tiberkevich. Spin wave mode excited by spin-polarized current in a magnetic nanocontact is a standing self-localized wave bullet. Phys. Rev. Lett. 95, 237201 (2005). https://doi.org/10.1103/PhysRevLett.95.237201
G. Consolo, B. Azzerboni, G. Gerhart, G.A. Melkov, V. Tiberkevich, A.N. Slavin. Excitation of self-localized spin-wave bullets by spin-polarized current in in-plane magnetized magnetic nanocontacts: A micromagnetic study. Phys. Rev. B 76, 144410 (2007). https://doi.org/10.1103/PhysRevB.76.144410
S. Bonetti, V. Tiberkevich, G. Consolo, G. Finocchio, P. Muduli, F. Mancoff, A. Slavin, J. ? Akerman. Experimental evidence of self-localized and propagating spin wave modes in obliquely magnetized current-driven nanocontacts. Phys. Rev. Lett. 105, 217204 (2010). https://doi.org/10.1103/PhysRevLett.105.217204
L. Yang, R. Verba, V. Tiberkevich, T. Schneider, A. Smith, Z. Duan, B. Youngblood, K. Lenz, J. Lindner, A.N. Slavin, I.N. Krivorotov. Reduction of phase noise in nanowire spin orbit torque oscillators. Sci. Rep. 5, 16942 (2015). https://doi.org/10.1038/srep16942
K. Wagner, A. Smith, T. Hache, J.-R. Chen, L. Yang, E. Montoya, K. Schultheiss, J. Lindner, J. Fassbender, I. Krivorotov, H. Schultheiss. Injection locking of multiple auto-oscillation modes in a tapered nanowire spin Hall oscillator. Sci. Rep. 8, 16040 (2018). https://doi.org/10.1038/s41598-018-34271-4
Z. Duan, A. Smith, L. Yang, B. Youngblood, J. Lindner, V.E. Demidov, S.O. Demokritov, I.N. Krivorotov. Nanowire spin torque oscillator driven by spin-orbit torques. Nature Commun. 5, 5616 (2014). https://doi.org/10.1038/ncomms6616
M. Dvornik, A.A. Awad, J. ? Akerman. Origin of magnetization auto-oscillations in constriction-based spin Hall nano-oscillators. Phys. Rev. Applied 9, 014017 (2018). https://doi.org/10.1103/PhysRevApplied.9.014017
H. Mazraati, S.R. Etesami, S.A.H. Banuazizi, S. Chung, A. Houshang, A.A. Awad, M. Dvornik, J. ? Akerman. Auto-oscillating spin-wave modes of constriction-based spin Hall nano-oscillators in weak in-plane fields. Phys. Rev. Applied 10, 054017 (2018). https://doi.org/10.1103/PhysRevApplied.10.054017
M. Dvornik, J. ? Akerman. Anomalous nonlinearity of the magnonic edge mode. arXiv:1804.01585 [cond-mat.mes-hall].
B. Divinskiy, V.E. Demidov, S. Urazhdin, R. Freeman, A.B. Rinkevich, S.O. Demokritov. Controllable excitation of quasi-linear and bullet modes in a spin-Hall nano-oscillator. Appl. Phys. Lett. 114, 042403 (2019). https://doi.org/10.1063/1.5064841
A. Houshang, R. Khymyn, H. Fulara, A. Gangwar, M. Haidar, S.R. Etesami, R. Ferreira, P.P. Freitas, M. Dvornik, R.K. Dumas, J. ? Akerman. Spin transfer torque driven higher-order propagating spin waves in nanocontact magnetic tunnel junctions. Nature Commun. 9, 4374 (2018). https://doi.org/10.1038/s41467-018-06589-0
H. Ulrichs, V.E. Demidov, S.O. Demokritov. Micromagnetic study of auto-oscillation modes in spin-Hall nano-oscillators. Appl. Phys. Lett. 104, 042407 (2014). https://doi.org/10.1063/1.4863660
G. Consolo, G. Finocchio, G. Siracusano, S. Bonetti, A. Eklund, J. ? Akerman, B. Azzerboni. Non-stationary excitation of two localized spin-wave modes in a nanocontact spin torque oscillator. J. Appl. Phys. 114, 153906 (2013). https://doi.org/10.1063/1.4825065
S. Bonetti, R. Kukreja, Z. Chen, F. Maci'a, J.M. Hern'andez, A. Eklund, D. Backes, J. Frisch, J. Katine, G. Malm, S. Urazhdin, A. D. Kent, J. St?ohr, H. Ohldag, H.A. D?urr. Direct observation and imaging of a spin-wave soliton with p-like symmetry. Nature Commun. 6, 8889 (2015). https://doi.org/10.1038/ncomms9889
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