Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators

Locatelli, Nicolas; Hamadeh, A.; Araujo, Flavio Abreu; Belanovsky, A. D.; Skirdkov, P. N.; Lebrun, Romain; Naletov, V. V.; Zvezdin, K. A.; Muñoz, Manuel; Grollier, Julie; Klein, O.; Cros, Vincent; Loubens, G. de

doi:10.1038/srep17039

Cited by 120 publications

(95 citation statements)

References 59 publications

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“…The same approach has been used and shown to be accurate in many dynamical regimes to date [37][38][39][40][41][42][43]. In this formalism, the Landau-Lifshitz equation of motion describing conservative magnetization dynamics is cast as a function of a complex amplitude a, using a Holstein-Primakoff transformation.…”

Section: Analytical Formalismmentioning

confidence: 99%

Reconfigurable wave band structure of an artificial square ice

et al. 2016

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Artificial square ices are structures composed of magnetic nanoelements arranged on the sites of a twodimensional square lattice, such that there are four interacting magnetic elements at each vertex, leading to geometrical frustration. Using a semianalytical approach, we show that square ices exhibit a rich spin-wave band structure that is tunable both by external magnetic fields and the magnetization configuration of individual elements. Internal degrees of freedom can give rise to equilibrium states with bent magnetization at the element edges leading to characteristic excitations; in the presence of magnetostatic interactions these form separate bands analogous to impurity bands in semiconductors. Full-scale micromagnetic simulations corroborate our semianalytical approach. Our results show that artificial square ices can be viewed as reconfigurable and tunable magnonic crystals that can be used as metamaterials for spin-wave-based applications at the nanoscale.

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Section: Analytical Formalismmentioning

confidence: 99%

Reconfigurable wave band structure of an artificial square ice

et al. 2016

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“…Above all, the exciting topic in this research field is the synchronization of spin-torque oscillators by the magnetic [7][8][9][10] and/or electrical [11][12][13][14][15] couplings. The synchronization of spin-torque oscillators results in an enhancement of the emission power and an increase of the quality factor of the practical devices.…”

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confidence: 99%

Mutual synchronization of spin-torque oscillators consisting of perpendicularly magnetized free layers and in-plane magnetized pinned layers

Taniguchi

Tsunegi

2017

Appl. Phys. Express

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A mutual synchronization of spin-torque oscillators coupled through current injection is studied theoretically. Models of electrical coupling in parallel and series circuits are proposed. Solving the Landau-Lifshitz-Gilbert equation, excitation of in-phase or antiphase synchronization, depending on the ways the oscillators are connected, is found. It is also found from both analytical and numerical calculations that the current-frequency relations for both parallel and series circuits are the same as that for a single spin-torque oscillator.Spin-torque oscillators have been a fascinating research target in the field of spintronics from the viewpoints of both nonlinear science and practical applications such as microwave generator and communication devices [1][2][3][4][5][6]. Above all, the exciting topic in this research field is the synchronization of spin-torque oscillators by the magnetic [7][8][9][10] and/or electrical [11][12][13][14][15] couplings. The synchronization of spin-torque oscillators results in an enhancement of the emission power and an increase of the quality factor of the practical devices. In addition, new applications such as brain-inspired computing based on the synchronized spin-torque oscillators are proposed very recently [16][17][18][19].An attractive structure of spin-torque oscillator for practical applications is that consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer [20][21][22] because this type of spin-torque oscillator results in high emission power, narrow linewidth, and wide frequency tunability simultaneously. The oscillation properties of this type of spin-torque oscillator, such as the relation between the injected current and the oscillation frequency, as a single oscillator have been investigated both experimentally [22] and theoretically [23]. A possibility to excite a mutual synchronization in this type of spin-torque oscillators, however, has not been investigated yet.In this letter, a theoretical study on the mutual synchronization of spin-torque oscillators consisting of perpendicularly magnetized free layers and in-plane magnetized pinned layers is presented. We focus on the coupling of spin-torque oscillators through the current injection, and develop models of the coupling in the parallel and series circuits. Solving the Landau-Lifshitz-Gilbert (LLG) equation numerically, we show that two spin-torque oscillators indicate in-phase or antiphase synchronization depending on the way the oscillators are connected. An analytical theory clarifying the relation between the current, oscillation frequency, and phase difference is also developed. Both the numerical and analytical calculations indicate that the dependence of oscillation frequency on the current for both the parallel and series circuits are identical to that of a single spin-torque oscillator.The system under consideration is schematically shown in Fig. 1. There are two spin-torque oscillators, and each oscillator consists of a free layer F k (k = 1, 2) and a pinned ...

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“…In the last few years, many efforts have been made to improve the spectral purity of spintorque oscillators, a crucial step towards most applications. From these studies, a promising approach consists in the synchronization of the oscillators to an external microwave source [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] (injection locking), or to other oscillators [21][22][23][24][25][26][27] (mutual synchronization). In both cases, a crucial parameter to optimize for applications is the locking range, which should be as large as possible.…”

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confidence: 99%

Enhancing the injection locking range of spin torque oscillators through mutual coupling

Romera

Talatchian

Lebrun

et al. 2016

Applied Physics Letters

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We investigate how the ability of the vortex oscillation mode of a spin-torque nanooscillator to lock to an external microwave signal is modified when it is coupled to another oscillator. We show experimentally that mutual electrical coupling can lead to locking range enhancements of a factor 1. 64. Furthermore, we analyze the evolution of the locking range as a function of the coupling strength through experiments and numerical simulations. By uncovering the mechanisms at stake in the locking range enhancement, our results will be useful for designing spin-torque nano-oscillators arrays with high sensitivities to external microwave stimuli.Spin-torque nano-oscillators (STNOs) are promising candidates for the next generation of multifunctional spintronic nano-devices [1] such as efficient integrated microwave generators [2] and detectors [3,4]. One of their characteristic features compared to other auto-oscillators is their high non-linearity [5]. On one hand, this high nonlinearity translates into one of their most attractive properties: their ability to easily adapt their frequencies to external stimuli. On the other hand, by increasing their sensitivity to noise, it has the undesirable effect of broadening the spectral linewidth. In the last few years, many efforts have been made to improve the spectral purity of spintorque oscillators, a crucial step towards most applications. From these studies, a promising approach consists in the synchronization of the oscillators to an external microwave source [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] (injection locking), or to other oscillators [21][22][23][24][25][26][27] (mutual synchronization). In both cases, a crucial parameter to optimize for applications is the locking range, which should be as large as possible. A first way to increase the locking range is to work in regimes where the oscillator's nonlinearity is the largest. However, as mentioned earlier, this comes at the detriment of spectral purity. In the case of injection locking, another possibility is to increase the power of the external signal, but this is limited by the breakdown voltage of the tunnel barrier of the device and results in an increase of power consumption. Therefore, finding alternative paths to enhance the locking range is an important step towards designing next generation's magnetic microwave devices.In this manuscript we combine experimental results with numerical simulations to show that the injection locking range of a spin-torque oscillator can be enhanced by coupling it to another spintorque oscillator. Furthermore, it is shown that the locking range can be tuned by changing the mutual coupling strength between oscillators. (7) is the free layer and numbers represent thickness in nanometers. Samples were grown by sputterdeposition and patterned down to the bottom electrode into circular nanopillars with a diameter of 200 nm. The nano-pillars exhibit a TMR of 64% and a resistance-area product of RA~1 Ω.μm 2 . With this combination of materials and geometry, th...

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Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators

Cited by 120 publications

References 59 publications

Reconfigurable wave band structure of an artificial square ice

Reconfigurable wave band structure of an artificial square ice

Mutual synchronization of spin-torque oscillators consisting of perpendicularly magnetized free layers and in-plane magnetized pinned layers

Enhancing the injection locking range of spin torque oscillators through mutual coupling

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