  In this paper, using micromagnetic simulations, we investigate the
stress-induced frequency tunability of double-vortex nano-oscillators
comprising magnetostrictive and non-magnetostrictive ferromagnetic layers
separated vertically by a non-magnetic spacer. We show that the the relative
orientations of the vortex core polarities $p_{1}$ and $p_{2}$ have a strong
impact on the eigen-frequencies of the dynamic modes. When the two vortices
with antiparallel polarities have different eigen-frequencies and the
magnetostatic coupling between them is sufficiently strong, the stress-induced
magnetoelastic anisotropy can lead to the single-frequency gyration mode of the
two vortex cores. Additionally, for the case of parallel polarities, we
demonstrate that for sufficiently strong magnetostatic coupling, the
magnetoelastic anisotropy leads to the coupled vortex gyration in the
stochastic regime and to the lateral separation of the vortex core
trajectories. These findings offer a fine control over gyration frequencies and
trajectories in vortex-based oscillators via adjustable elastic stress, which
can be easily generated and tuned electrically, mechanically or optically.
