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The synchronized magnetization dynamics in ferromagnets on a nonmagneticheavy metal caused by the spin Hall effect is investigated theoretically. Thedirect and inverse spin Hall effects near the ferromagnetic/nonmagneticinterface generate longitudinal and transverse electric currents. Thephenomenon is known as the spin Hall magnetoresistance effect, whose magnitudedepends on the magnetization direction in the ferromagnet due to the spintransfer effect. When another ferromagnet is placed onto the same nonmagnet,these currents are again converted to the spin current by the spin Hall effectand excite the spin torque to this additional ferromagnet, resulting in theexcitation of the coupled motions of the magnetizations. The in-phase orantiphase synchronization of the magnetization oscillations, depending on thevalue of the Gilbert damping constant and the field-like torque strength, isfound in the transverse geometry by solving the Landau-Lifshitz-Gilbertequation numerically. On the other hand, in addition to these synchronizations,the synchronization having a phase difference of a quarter of a period is alsofound in the longitudinal geometry. The analytical theory clarifying therelation among the current, frequency, and phase difference is also developed,where it is shown that the phase differences observed in the numericalsimulations correspond to that giving the fixed points of the energy suppliedby the coupling torque.

Dynamic coupling of ferromagnets via spin Hall magnetoresistance