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The collective dynamics in populations of magnetic spin torque oscillators(STO) is an intensely studied topic in modern magnetism. Here, we show thatarrays of STO coupled via dipolar fields can be modeled using a variant of theKuramoto model, a well-known mathematical model in non-linear dynamics. Byinvestigating the collective dynamics in arrays of STO we find that thesynchronization in such systems is a finite size effect and show that thecritical coupling-for a complete synchronized state-scales with the number ofoscillators. Using realistic values of the dipolar coupling strength betweenSTO we show that this imposes an upper limit for the maximum number ofoscillators that can be synchronized. Further, we show that the lack of longrange order is associated with the formation of topological defects in thephase field similar to the two-dimensional XY model of ferromagnetism. Ourresults shed new light on the synchronization of STO, where controlling themutual synchronization of several oscillators is considered crucial forapplications.

Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model