Merging droplets in double nanocontact spin torque oscillators

We demonstrate how magnetic droplet soliton pairs, nucleated by two separated nanocontact (NC) spin torque oscillators, can merge into a single droplet soliton. A detailed description of the magnetization dynamics of this merger process is obtained by micromagnetic simulations: A droplet pair with a steady-state in-phase spin precession is generated through the spin-transfer torque effect underneath two separate NCs, followed by a gradual expansion of the droplets’ volume and the out-phase of magnetization on the inner side of the two droplets, resulting in the droplets merging into a larger droplet. This merger occurs only when the NC separation is smaller than a critical value. A transient breathing mode is observed before the merged droplet stabilizes into a steady precession state. The precession frequency of the merged droplet is lower than that of the droplet pair, consistent with its larger size. Merged droplets can again break up into droplet pairs at high enough magnetic field with a strong hysteretic response.

Figure 1

Current- and magnetic-field-induced merging of a droplet pair. (a) Schematic of the NC-STO. A magnetic field is applied in the out-of-plane direction with a strength of 0.5 T. The current through each NC is fixed at $I=-15\mathrm{mA}$. (b) Time evolution of the $z$ component of average magnetization. (c)–(h) Transient snapshots of magnetization for a small region around the NCs. The colored cones display the $x$ component of the magnetization.

Figure 2

(a) Time trace of the magnetization averaged over the simulation area; the magnetization changes from a droplet pair precession orbital (red) to a merged droplet precession orbital (blue). (b)–(e) Magnetization $x$-component evolution for four typical procession states during the merger process.

Figure 3

(a) Frequency spectra of the droplet pair and the merged droplet calculated by FFT from the in-plane magnetization $m_x$. (b) Frequency diagram of final precession state for two NCs as a function of separation distance d.

Figure 4

(a) Critical separation distance $d_c$ as a function of current for merging a droplet pair into a merged droplet at three different magnetic fields. (b) Operational range as a function of magnetic field for a given current.

Figure 5

Separation process of a merged droplet into a droplet pair. The blue and red curves show the $z$-component magnetization as a function of magnetic field sweeping loop. The applied current in each NC is fixed to be $-10\mathrm{mA}$. The typical magnetization configurations are shown by a series of snapshots taken during the recovery process.