A detailed analytical and numerical study of the spin wave modes of two nanopillar spin torque nano-oscillators coupled by magnetostatic interactions is presented under the macrospin approximation. Results show that the normal modes of the system oscillate with the magnetizations in-phase or anti-phase in both disks. The frequencies and critical current densities necessary to induce auto-oscillations of the spin wave modes of the coupled system depend on the relative position of the nanopillars and the applied magnetic field. If the oscillators are identical, these modes are degenerate at a certain relative position of the nanopillars, while if the oscillators are non-identical, such degeneracy is removed. Then, we can conclude that the magnetostatic coupling between two spin transfer torque nano-oscillators is a powerful mechanism to control the spin wave modes of these systems.

The stability of the magnetization auto-oscillations of the ferromagnetic free layer of a cylindrical nanopillar structure is studied theoretically using a classical Hamiltonian formalism for weakly interacting nonlinear waves, in a weakly dissipative system. The free layer corresponds to a very thin circular disk, made of a soft ferromagnetic material like Permalloy, and it is magnetized in plane by an externally applied magnetic field. There is a dc electric current that traverses the structure, becomes spin polarized by a fixed layer, and excites the modes of the free layer through the transfer of spin angular momentum. If this current exceeds a critical value, it is possible to generate a large amplitude periodic auto-oscillation of a dynamic mode of the magnetization. We separate our theoretical study into two parts. First, we consider an approximate expression for the demagnetizing field in the disk, i.e., (H) over bar (D) = -4 pi M-z(z) over cap or a very thin film approximation, and secondly we consider the effect of the full demagnetizing field, where one sees important effects due to the edges of the disk. In both cases, as the applied current density is increased, we determine the modes that will first auto-oscillate and when these become unstable to the growth of other modes, i.e., their ranges of "isolated" auto-oscillation.Project Fondecyt, Financiamiento Basal para Centros Cientificos y Tecnologicos de Excelencia, Project CEDENNA (Chile), CONICY

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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 $$N\ge 6$$ N ≥ 6 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$$\pi$$ π 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.