We show how to utilize magnetostriction to synchronize two mechanical vibration modes in a cavity magnomechanical system. The dispersive magnetostrictive interaction provides necessary nonlinearity required for achieving synchronization. Strong phase correlation between two mechanical oscillators can be established, leading to the synchronization robust against thermal noise. We develop a theoretical framework to analyze the synchronization by solving the constraint conditions of steady-state limit cycles. We determine that the strong cavity-magnon linear coupling can enhance and regulate the synchronization, which offers a new path to modulate synchronization. The work reveals a new mechanism for achieving and modulating synchronization and indicates that cavity magnomechanical systems can be an ideal platform to explore rich synchronization phenomena.

Accepted to Phys. Rev. Research