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A mutual synchronization of spin-torque oscillators coupled through currentinjection is studied theoretically. Models of electrical coupling in paralleland series circuits are proposed. Solving the Landau-Lifshitz-Gilbert equation,excitation of in-phase or antiphase synchronization, depending on the ways theoscillators are connected, is found. It is also found from both analytical andnumerical calculations that the current-frequency relations for both paralleland series circuits are the same as that for a single spin-torque oscillator.

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