Title: Dynamic coupling of ferromagnets via spin Hall magnetoresistance,
Abstract: The synchronized magnetization dynamics in ferromagnets on a nonmagnetic
heavy metal caused by the spin Hall effect is investigated theoretically. The
direct and inverse spin Hall effects near the ferromagnetic/nonmagnetic
interface generate longitudinal and transverse electric currents. The
phenomenon is known as the spin Hall magnetoresistance effect, whose magnitude
depends on the magnetization direction in the ferromagnet due to the spin
transfer effect. When another ferromagnet is placed onto the same nonmagnet,
these currents are again converted to the spin current by the spin Hall effect
and excite the spin torque to this additional ferromagnet, resulting in the
excitation of the coupled motions of the magnetizations. The in-phase or
antiphase synchronization of the magnetization oscillations, depending on the
value of the Gilbert damping constant and the field-like torque strength, is
found in the transverse geometry by solving the Landau-Lifshitz-Gilbert
equation numerically. On the other hand, in addition to these synchronizations,
the synchronization having a phase difference of a quarter of a period is also
found in the longitudinal geometry. The analytical theory clarifying the
relation among the current, frequency, and phase difference is also developed,
where it is shown that the phase differences observed in the numerical
simulations correspond to that giving the fixed points of the energy supplied
by the coupling torque.