  We demonstrate piezostrain-induced frequency pulling in stacked double-vortex
structures, magnetostatically coupled through the nonmagnetic spacer. We study
the effect of the Cu spacer thickness on the strain-induced gyrotropic
frequency shift in double-vortex structures comprising of magnetostrictive
CoFeB and nonmagnetostricitve Py layers. For the two stacked vortices with
different eigen-frequencies, the strain-induced magnetoelastic anisotropy leads
to the downshift of the gyration frequency of the magnetostricitve vortex. We
show that for increased dipolar coupling between the layers (i.e. decreased
spacer thickness), a strain-induced frequency pulling regime is obtained, where
the resonance frequency of the nonmagnetostrictive Py vortex is upshifted
towards the gyration resonance of the magnetostrictive CoFeB vortex. This
result offers an additional degree of freedom for the manipulation of the
dynamical regimes and synchronization conditions in spintronic oscillators,
controlled by voltage and tunable by strain
