Angular dependence of ferromagnetic resonance as indicator of the nature of magnetoelectric coupling in ferromagnetic-ferroelectric heterostructures

Abstract

We investigate theoretically how ferromagnetic resonance (FMR) in a multiferroic heterostructure provides quantitative information on multiferroic coupling. In particular, we analyze the asymmetry of the angular dependence of FMR on the direction of resonance magnetic fields as experimentally reported for ${\mathrm{Co}/\mathrm{BaTiO}}_{3}$ [Jedrecy et al., Phys. Rev. B 88, 121409(R) (2013)] and for ${\mathrm{permalloy}/\mathrm{Pb}(\mathrm{MgNb})\mathrm{O}}_{3}\ensuremath{-}{\mathrm{PbTiO}}_{3}$ [Nan et al., Sci. Rep. 4, 3688 (2014)]. Based on both analytical expressions for the dependence of FMR on the magnetic-field orientation and full numerical simulations which account for mutually coupled polarization $\mathbf{P}$ and magnetization $\mathbf{M}$ dynamics, we conclude that it is the linear magnetoelectric coupling in $\mathbf{P}$ and $\mathbf{M}$ originating from spin-dependent screening that leads to the experimentally observed asymmetry in FMR angular behavior. This suggests that angular resolved FMR is well suited to quantify the type and the strength of magnetoelectric coupling. In addition, we predict a pronounced thickness dependence of the resonance asymmetries and show how the FMR angular asymmetry can be tuned by an external static electric field. The possibility to observe electric-field-assisted FMR in the absence of an external static magnetic field is also discussed.