Mutual synchronization of spin-torque oscillators within a ring array

Abstract

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.

Stray magnetic fields from elliptical-shaped and stadium-shaped ferromagnets

“…[13][14][15][16][17][18] Even after great development of numerical solvers, [19][20][21][22][23][24] deriving a solution of potential, or field, in terms of analytical functions or in forms of some integrals with simplified approximations, such as macrospin or rigid-vortex assumption, is highly demanded, particularly when many-body problems are of interest. [25][26][27][28][29] This is because it enables us to estimate various parameters, such as coercive and stray fields, with adequate calculation cost. The past works have mainly focused on the internal magnetic field and derived the solutions of the demagnetization coefficients for various shapes of ferromagnets such as ellipsoid, cylinder, and cuboid, [1][2][3][4][5][6][8][9][10] while the stray magnetic field, originated from magnetostatic interaction, for vortex, cylinder, and so on has also been investigated.…”