Analytical solution of the strain-controlled magnetic domain wall motion in bilayer piezoelectric/magnetostrictive nanostructures

The one-dimensional propagation of magnetic domain walls in an isotropic, linearly elastic, magnetostrictive material is investigated in the framework of the extended Landau-Lifshitz-Gilbert equation where the effects of a spin-polarized current and a rate-independent dry-friction dissipation are taken into account. In our analysis, it is assumed that the ferromagnet is subject to a spatially-uniform biaxial in-plain stress generated by a piezoelectric substrate combined with the former in a multiferroric heterostructure. Moreover, a possible connection between the dry-friction mechanism and the piezo-induced strains is conjectured. By adopting the traveling waves ansatz, the effect of such a stress on the domain wall dynamics is explored in both steady and precessional regimes. In particular, it is proved that the magnetoelastic contribution, while does not formally modify the classical solution, affects both the propagation threshold and the Walker Breakdown conditions involved in the steady regime, in agreement with recent experimental results. In the precessional regime, it is shown that the existence of a correlation between the piezo-induced strains and dry-friction leads to an upward shift of the domain wall velocity.