Synchronization of spin-torque-driven nano-oscillators for point contacts on a quasi-one-dimensional nanowire: Micromagnetic simulations

D. V. Berkov

Phys. Rev. B 87, 014406 – Published 4 January 2013

Abstract

In this paper we present numerical simulation studies of the synchronization of two coupled spin-torque nano-oscillators (STNO) in the quasi-one-dimensional (1D) geometry: magnetization oscillations are induced in a thin NiFe nanostripe by a spin-polarized current injected via square-shaped CoFe nanomagnets on the top of this stripe. In a sufficiently large out-of-plane field, a propagating oscillation mode appears in such a system. Due to the absence of the geometrically caused wave decay in 1D systems, this mode is expected to enable a long-distance synchronization between STNOs. Indeed, our simulations predict that synchronization of two STNOs on a nanowire is possible up to the intercontact distance $Δ L = 3 μ m$ (for the nanowire width $w = 50 nm$ ). However, we have also found several qualitatively important features of the synchronization behavior for this system, which make the achievement of a stable synchronization in this geometry a highly nontrivial task. In particular, there exists a minimal distance between the nanocontacts, below which a synchronization of STNOs cannot be achieved. Further, when the current value in the first contact is kept constant, the synchronized oscillation power depends nonmonotonously on the current value in the second contact. Finally, for one and the same current values through the contacts, there might exist several synchronized states (with different frequencies), depending on the initial conditions.

Received 25 May 2012

DOI:https://doi.org/10.1103/PhysRevB.87.014406

Authors & Affiliations

D. V. Berkov^*

Innovent Technology Development, Pruessingstr. 27B, D-07745, Jena, Germany

^*db@innovent-jena.de

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Vol. 87, Iss. 1 — 1 January 2013

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Images

Figure 1
(a) Oscillation frequency $f$ and (b) oscillation power of the $m_{x}$ component $P_{x}$ (b) as functions of the current strength through the point contact for a system with a single point contact only. For $I = 7.25$ mA, the snapshot of the $m_{x}$ component is shown in (c) and the spatial distribution of the oscillation power in a stationary wave-emitting regime in (d). The length of the nanostripe region shown in (c) and (d) is approximately 630 nm.Reuse & Permissions
Figure 2
Upper scheme: system geometry with currents. 2D plots: oscillation power $P_{x} (I_{1}, f)$ as function of $f$ and current strength in the first contact $I_{1}$ for various intercontact distances $Δ L$ as shown in the legend (in all cases $I_{2} = Const = 6.7 mA$ ). Note very broad spectral lines (meaning quasichaotic magnetization dynamics and absence of any synchronization) for the smallest intercontact distances $Δ L = 500$ nm. Synchronization can be observed starting from $Δ L = 1000$ nm. Color map used for all images here and on all subsequent figures is shown in the upper right inset on the figure.Reuse & Permissions
Figure 3
Examples of spectral power maps $P_{x} (I_{1}, f)$ for two intercontact distances $Δ L$ . In all cases, the final value of the second current is $I_{2} = 6.7$ mA. Left column: $I_{2}$ was increased from zero to its final value instantly. Right column: $I_{2}$ was increased linearly in time within $Δ t = 10$ ns. Ellipses accentuate the areas of spectral maps where different synchronization behavior for these two simulation protocols is clearly seen.Reuse & Permissions
Figure 4
Snapshots of the $m_{x}$ component for two synchronized states, for which the phase difference $Δ ϕ$ between oscillations under the point contacts is $Δ ϕ < π / 2$ [in-phase oscillations in (a)] and $Δ ϕ > π / 2$ [out-of-phase oscillations in (b)]. The intercontact distance is $Δ L = 1500$ nm; currents are $I_{1} \approx 6.8$ mA and $I_{2} = 6.7$ mA. Time interval between two subsequent snapshots is $Δ t = 0.002$ ns; both snapshot series (a) and (b) cover the half period of the magnetization oscillations. Spatial distribution of the oscillation power for the case (b) is shown in (c).Reuse & Permissions
Figure 5
Dependencies of the oscillation power $P_{x}$ on the current strength in the first contact $I_{1}$ for various intercontact distances $Δ L$ indicated on the subplots (again, in all cases the final value of the second current is $I_{2} = 6.7$ mA). Solid lines: $P (I_{1})$ for the case in which $I_{2}$ was increased instantly. Dashed lines: $P (I_{1})$ for $I_{2}$ increased to its final value linearly in time within $Δ t = 10$ ns. For $Δ L < 700$ nm, only quasichaotic oscillations without synchronization are observed, and for $Δ L > 2200$ nm, the same results are obtained for both simulation protocols.Reuse & Permissions

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