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...
