Numerical and analytical investigation of the synchronization of dipolarly coupled vortex spin-torque nano-oscillators

Belanovsky, A. D.; Locatelli, Nicolas; Skirdkov, P. N.; Araujo, Flavio Abreu; Zvezdin, K. A.; Grollier, Julie; Cros, Vincent; Zvezdin, A. K.

doi:10.1063/1.4821073

Cited by 50 publications

(62 citation statements)

References 32 publications

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“…(8 and 9) can be done for the case of the thin disk ( ≪ ) when the magnetization is assumed to be independent of z to obtain a factor of 2 in Eq. (8). In this case the reduced components, ℎ , of the magnetostatic field are…”

Section: Magnetostatic Energymentioning

confidence: 99%

“…(10a,b) the MS energy is calculated as a four-dimensional numerical integral over the ellipse area using the normalized magnetization of the previous section as well as the above reduced magnetic field in Eq. (8). For the special case of the circular disk, the higher symmetry reduces the integration to one or more dimensions depending on the approximations …”

Section: Magnetostatic Energymentioning

confidence: 99%

“…For the special case of the circular disk the form of the MS energy [7,8] and gyrotropic frequency [1] are well known to depend only on the disk radius and thickness, but noncircular elliptical oscillators are also widely used [5,[9][10][11]. In particular, experimental results from Refs.…”

Section: Introductionmentioning

confidence: 99%

“…In these systems the vortex core can be forced off-center by an in-plane magnetic field pulse and gyrotropic precession is imaged as spiral motion of the core as it returns to the disk center as a result of dissipation. Outside of advancing the theoretical understanding of nanoscale magnetization dynamics, recent applied applications include vortex-based nanoscale oscillators driven by spin-torque [5,6] as well as synchronization [7,8] of coupled spin-torque oscillators.…”

Section: Introductionmentioning

confidence: 99%

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Vortex precession in thin elliptical ferromagnetic nanodisks

Zaspel

2017

Journal of Magnetism and Magnetic Materials

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The magnetostatic energy is calculated for a magnetic vortex in a noncircular elliptical nanodisk.It is well-known that the energy of a vortex in the circular disk is minimized though an ansatz that eliminates the magnetostatic charge at the disk edge. Beginning with this ansatz for the circular disk, a conformal mapping of a circle interior onto the interior of an ellipse results in the magnetization of the elliptical disk. This magnetization in the interior of an ellipse also has no magnetostatic charge at the disk edge also minimizing the magnetostatic energy. As expected the energy has a quadratic dependence on the displacement of the vortex core from the ellipse center, but reflecting the lower symmetry of the ellipse. Through numerical integration of the magnetostatic integral a general expression for the energy is obtained for ellipticity values from 1.0 to about 0.3. Finally a general expression for the gyrotropic frequency as described by the Thiele equation is obtained.

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Section: Magnetostatic Energymentioning

confidence: 99%

Section: Magnetostatic Energymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vortex precession in thin elliptical ferromagnetic nanodisks

Zaspel

2017

Journal of Magnetism and Magnetic Materials

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“…If several physical phenomena can be used to couple spin-torque oscillators, such as spin waves 5,6,18 or electric currents 7,19 , one of the most appealing towards the realization of dense arrays is the dipolar coupling. Indeed when oscillators are closely packed, with edge to edge distance below 500 nm, the dipolar coupling becomes intense and can synchronize their dynamics, as demonstrated theoretically [20][21][22] and experimentally 23 . Whereas it is possible to tune the coupling provided by spin waves 9 and electrical currents 24 , it remains a challenge to modify the interaction originating from the dipolar fields emitted by the oscillators.…”

mentioning

confidence: 99%

Controlling the synchronization properties of two dipolarly coupled vortex based spin-torque nano-oscillators by the intermediate of a third one

Araujo

Grollier

2016

Journal of Applied Physics

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In this paper, we propose to control the strength of phase-locking between two dipolarly coupled vortex based spin-torque nano-oscillators by placing an intermediate oscillator between them. We show through micromagnetic simulations that the strength of phase-locking can be largely tuned by a slight variation of current in the intermediate oscillator. We develop simplified numerical simulations based on analytical expressions of the vortex core trajectories that will be useful for investigating large arrays of densely packed spin-torque oscillators interacting through their stray fields.Spin-torque nano-oscillators are magnetic autooscillators of deep submicron dimensions. Made of spinvalves 1,2 or magnetic tunnel junctions, 3 they can be fabricated on top of a plane of CMOS transistors and they operate at room temperature. The torque on magnetization is generated by sending a spin-polarized current through the ferromagnetic layer. For high enough current densities, this spin-torque can induce sustained magnetization precessions that are then converted into voltage oscillations by magneto-resistive effects. The frequency of these microwave oscillators can be tuned over several GHz by changing the amplitude of the injected dc current or applied magnetic field. Because to this high non-linearity, spin-torque nano-oscillators are sensitive to small variations of magnetic field and electric current 4 . In particular, several spin-torque nano-oscillators can mutually synchronize even if their individual frequencies are initially different [5][6][7][8][9][10][11] . Thanks to these features they are excellent candidates for building computing systems inspired from neural synchronization in the brain [12][13][14][15] . Indeed bio-inspired computing with oscillators requires to be able to fabricate very large arrays of interacting oscillators, and to be able to control the degree of coupling between the oscillators 16,17 . If several physical phenomena can be used to couple spin-torque oscillators, such as spin waves 5,6,18 or electric currents 7,19 , one of the most appealing towards the realization of dense arrays is the dipolar coupling. Indeed when oscillators are closely packed, with edge to edge distance below 500 nm, the dipolar coupling becomes intense and can synchronize their dynamics, as demonstrated theoretically 20-22 and experimentally 23 . Whereas it is possible to tune the coupling provided by spin waves 9 and electrical currents 24 , it remains a challenge to modify the interaction originating from the dipolar fields emitted by the oscillators. In this letter, we propose to adjust the dipolar coupling between two close-by spin-torque oscillators by inserting a third oscillator between them. We study numerically how the amplitude of the current sent through the intermediate oscillator modifies the coupling between the other two. For this purpose, we perform full micromagnetic simulations of the three coupled oscillators in order to have an accurate estimate of the dipolar interactions. Then we develop muc...

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Frequency Tunability of Spin‐Torque Vortex Oscillator in Permalloy Nanodisks with Modified Material Properties

Bhattacharjee¹,

Barman²

2023

Physica Rapid Research Ltrs

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The manipulation of the vortex state in magnetic nanostructures has received a lot of interest in recent decades, with potential applications in nonvolatile magnetic random‐access memory and logic networks. For wireless communication advancements, nano‐sized, and low‐phase‐noise, adjustable transmitter‐receiver networks are critical. Herein, it is shown that by using micromagnetic simulations when the saturation magnetization is reduced in a particular region of a magnetic nanodisk, the frequency tunability in such disks can be achieved. The gyrotropic mode of the vortex core is excited with spin‐polarized current and an in‐plane static magnetic field and found that an isolated magnetic vortex shows different resonance frequencies at different saturation magnetization regions. The dynamics of the mutual synchronization between two such dipolarly coupled magnetic vortices are numerically investigated, and the essential distances at which synchronization occurs are also identified. These incredibly small vortex‐based oscillator devices have linewidths of the order of 40–60 MHz, making them prospective candidates for signal‐processing applications and a strong new tool for basic research on vortex dynamics in magnetic nanostructures.

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Numerical and analytical investigation of the synchronization of dipolarly coupled vortex spin-torque nano-oscillators

Cited by 50 publications

References 32 publications

Vortex precession in thin elliptical ferromagnetic nanodisks

Vortex precession in thin elliptical ferromagnetic nanodisks

Controlling the synchronization properties of two dipolarly coupled vortex based spin-torque nano-oscillators by the intermediate of a third one

Frequency Tunability of Spin‐Torque Vortex Oscillator in Permalloy Nanodisks with Modified Material Properties

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