Mutual synchronization of spin-torque oscillators within a ring array

An array of spin torque nano-oscillators (STNOs), coupled by dipolar interaction and arranged on a ring, has been studied numerically and analytically. The phase patterns and locking ranges are extracted as a function of the number N, their separation, and the current density mismatch between selected subgroups of STNOs. If [Formula: see text] for identical current densities through all STNOs, two degenerated modes are identified an in-phase mode (all STNOs have the same phase) and a splay mode (the phase makes a 2[Formula: see text] turn along the ring). When inducing a current density mismatch between two subgroups, additional phase shifts occur. The locking range (maximum current density mismatch) of the in-phase mode is larger than the one for the splay mode and depends on the number N of STNOs on the ring as well as on the separation. These results can be used for the development of magnetic devices that are based on STNO arrays.