Commensurability and chaos in magnetic vortex oscillations

Petit-Watelot, Sébastien; Kim, Joo-Von; Ruotolo, A.; Otxoa, R. M.; Bouzéhouane, K.; Grollier, Julie; Vansteenkiste, Arne; Wiele, Ben Van de; Cros, Vincent; Devolder, T.

doi:10.1038/nphys2362

Cited by 105 publications

(120 citation statements)

References 38 publications

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“…The nanocontact STOs presented in this study can also sustain gyrotropic vortex motion 47,48 , generating frequencies primarily below 1 GHz and showing operation in zero applied magnetic field 49 . Whereas we have not investigated the gyrotropic motion in detail, we here present an example of such operation.…”

Section: Resultsmentioning

confidence: 99%

Mutually synchronized bottom-up multi-nanocontact spin–torque oscillators

et al. 2013

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Spin-torque oscillators offer a unique combination of nanosize, ultrafast modulation rates and ultrawide band signal generation from 100 MHz to close to 100 GHz. However, their low output power and large phase noise still limit their applicability to fundamental studies of spin-transfer torque and magnetodynamic phenomena. A possible solution to both problems is the spin-wave-mediated mutual synchronization of multiple spin-torque oscillators through a shared excited ferromagnetic layer. To date, synchronization of high-frequency spin-torque oscillators has only been achieved for two nanocontacts. As fabrication using expensive top-down lithography processes is not readily available to many groups, attempts to synchronize a large number of nanocontacts have been all but abandoned. Here we present an alternative, simple and cost-effective bottom-up method to realize large ensembles of synchronized nanocontact spin-torque oscillators. We demonstrate mutual synchronization of three high-frequency nanocontact spin-torque oscillators and pairwise synchronization in devices with four and five nanocontacts.

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Section: Resultsmentioning

confidence: 99%

Mutually synchronized bottom-up multi-nanocontact spin–torque oscillators

et al. 2013

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“…In a system with magnetic vortex oscillations, the sense of gyration of the magnetic vortex depends on the vortex core polarity, and can undergo sudden reversals as a critical velocity is reached. Driving currents can tune the self-sustained vortex oscillations and the frequency of the core reversals, resulting in phase-locked or chaotic states, within a devil's staircase structure [34]. In two capacitively coupled Josephson junctions, the phase-locked structure of the oscillations forms a devil's staircase, and chaotic dynamics develops between the main resonances as this coupling capacitance passes a critical value [35].…”

Section: Introductionmentioning

confidence: 99%

Structured chaos in a devil's staircase of the Josephson junction

Shukrinov

Botha

Medvedeva

et al. 2014

Chaos

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The phase dynamics of Josephson junctions under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally the influence of the radiation and Josephson junction parameters on the structured chaos is investigated and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

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“…STT describes the momentum transfer from spin-polarized electrons to a local magnetization and therefore provides a direct coupling between dc charge currents and magnetization dynamics. Depending on external conditions, a rich variety of physical phenomena with technologically interesting outcomes are possible, including different modes of spin wave generation [3][4][5][6][7][8], vortex gyration [9][10][11][12], and the nucleation and manipulation of magnetic droplet solitons [13][14][15][16]. Regardless of the particular magnetization dynamics, devices where a stable oscillatory state can be achieved are generally referred to as spin torque oscillators [17,18] (STOs), and are typically composed of two ferromagnetic layers decoupled by a non-magnetic spacer (although recent studies also report on STOs based on single ferromagnet layers [19]).…”

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confidence: 99%

Generation linewidth of mode-hopping spin torque oscillators

et al. 2014

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Experiments on spin torque oscillators commonly observe multi-mode signals. Recent theoretical works have ascribed the multi-mode signal generation to coupling between energy-separated spin wave modes. Here, we analyze in detail the dynamics generated by such mode coupling. We show analytically that the mode-hopping dynamics broaden the generation linewidth and makes it generally well described by a Voigt lineshape. Furthermore, we show that the mode-hopping contribution to the linewidth can dominate in which case it provides a direct measure of the mode-hopping rate. Due to the thermal drive of mode-hopping events, the mode-hopping rate also provides information on the energy barrier separating modes and temperature-dependent linewidth broadening. Our results are in good agreement with experiments, revealing the physical mechanism behind the linewidth broadening in multi-mode spin torque oscillators.Nanoscopic excitation of high-amplitude magnetization dynamics has recently emerged due to the discovery of the spin-transfer torque (STT) effect and advances in nano-fabrication [1,2]. STT describes the momentum transfer from spin-polarized electrons to a local magnetization and therefore provides a direct coupling between dc charge currents and magnetization dynamics. Depending on external conditions, a rich variety of physical phenomena with technologically interesting outcomes are possible, including different modes of spin wave generation [3][4][5][6][7][8], vortex gyration [9][10][11][12], and the nucleation and manipulation of magnetic droplet solitons [13][14][15][16]. Regardless of the particular magnetization dynamics, devices where a stable oscillatory state can be achieved are generally referred to as spin torque oscillators [17,18] (STOs), and are typically composed of two ferromagnetic layers decoupled by a non-magnetic spacer (although recent studies also report on STOs based on single ferromagnet layers [19]). STOs are engineered to enforce magnetization dynamics in one of the ferromagnetic layers (the "free" layer) whereas the second layer (the "fixed" layer) acts both as a polarizer and a reference to probe the dynamics via magnetoresistive effects [20][21][22][23][24][25].STOs have been traditionally regarded as single mode oscillators [26,27] based on the mode selection imposed by the balance of STT and magnetic damping as well as the survival of the mode with the lowest threshold. However, recent experiments have shown multi-mode generation in a large variety of geometries [28][29][30], revealing evidence of mode-hopping [31][32][33], periodic mode transitions [5,7], and even coexistence [8]. Furthermore, such a multi-mode generation leads to broader linewidths ascribed to the reduction of the magnetization dynamics coherence. In order to understand the underlying physics of these observations, a multi-modal theoretical description is required.A first step towards this goal was recently proposed [32][33][34] by extending the Slavin -Tiberkevich autooscillator theory [27] for two coupled modes. T...

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Commensurability and chaos in magnetic vortex oscillations

Cited by 105 publications

References 38 publications

Mutually synchronized bottom-up multi-nanocontact spin–torque oscillators

Mutually synchronized bottom-up multi-nanocontact spin–torque oscillators

Structured chaos in a devil's staircase of the Josephson junction

Generation linewidth of mode-hopping spin torque oscillators

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