Synchronization of Spin Hall Oscillators With Magnetodipolar Coupling

Abstract

We have found that the stacked spin Hall oscillator (SHO) based on the spin Hall effect and anisotropy magnetoresistance is synchronized via magnetodipolar interaction calculated with consideration of the shape of the SHO. Employing a macrospin simulation approach, we have obtained the boundary separating the synchronized and nonsynchronized states as a function of the difference in the natural frequency between two SHOs. We have also found that the emitted microwave power is enhanced by synchronization of a larger number of SHOs. It is anticipated that the results will be tested with existing experimental techniques.