Mechanism of interfacial magnetoelectric coupling in composite multiferroics

We work out theoretically a mechanism for magnetoelectric (ME) coupling driven by a buildup of an interfacial spiral spin density in ferromagnet (FM)/ferroelectric (FE) composites. We infer an intrinsic linear ME coupling that is most pronounced in the vicinity of the FM/FE interface acting within the spin-diffusion length ${\lambda }_m$ of the order of nanometers. Our study delivers a strong coupling strength for $\mathrm{Co}\left(40 \mathrm{nm}\right)/{\mathrm{BaTiO}}_3$ that is in line with experiments. We identify a region of magnetic noncollinearity coupled to dielectric polarization that extends over ${\lambda }_m$ around the interface, functionalizing the interface for electric control of magnetotransport and surface magnetic anisotropy.

Figure 1

Exponential spiral spin density $\tilde{\mathbf{M}}\left(\mathbf{r}\right)=\mathbf{M}\left(\mathbf{r}\right)+\mathbf{s}\left(\mathbf{r}\right)$ in a FM near a FM/FE interface $\left(z=0\right)$. The intrinsic FM magnetization $\mathbf{M}\left(\mathbf{r}\right)$ (i.e., for $z\gg 1$) is (a) normal to the interface $\mathbf{M}\parallel {\mathbf{e}}_z$ or (b) in the interface plane. The induced surface spin density $\mathbf{s}\left(\mathbf{r}\right)$, consisting of the adiabatic term $\left({\mathbf{s}}_{\parallel }\right)$ along $\mathbf{M}$ and normal deviations $\left({\mathbf{s}}_{\perp }\right)$, is illustrated. The two exponential decay functions $e^{-z/\sqrt{2D_0{\tau }_{ex}}}$ and $e^{-z/\sqrt{D_0{\tau }_{sf}}}$, describing respectively the spatial distribution of ${\mathbf{s}}_{\parallel }$ and ${\mathbf{s}}_{\perp }$, are derived in the main text. ${\mathbf{P}}_{\mathrm{FE}}^z$ indicates the ferroelectric polarization in the FE part of the interface.