We report a theoretical calculation of the strain-mediated magnetocapacitance of ferroelectric-ferromagnetic heterostructures. Our nonlinear theory predicts that this magnetocapacitance strongly depends on the strain state of a ferroelectric constituent. For multiferroic hybrids comprising a BaTiO${}_3$ or Pb(Zr${}_{0.5}$Ti${}_{0.5}$)O${}_3$ film and a FeBSiC, Terfenol-D, or FeGa substrate, the magnetocapacitive coefficient generally has a giant value $\sim$10${}^{-4}$ Oe${}^{-1}$. Remarkably, its magnitude further increases drastically near the strain-induced phase transition at which the out-of-plane polarization appears in the ferroelectric film. As a result, the magnetocapacitance of hybrids including Terfenol-D may exceed 100$\%$ already at the magnetic field of about 600 Oe. These theoretical results provide guidelines for the fabrication of multiferroic heterostructures exhibiting a strong magnetodielectric effect.

• Received 27 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.134111