Magnetoelectric coupling at the interface of BiFe${\mathrm{O}}_3$/La${}_{0.7}$Sr${}_{0.3}$Mn${\mathrm{O}}_3$ multilayers

Electric-field controlled exchange bias in a heterostructure composed of the ferromagnetic manganite La${}_{0.7}$Sr${}_{0.3}$${\mathrm{MO}}_3$ and the ferroelectric antiferromagnetic BiFe${\mathrm{O}}_3$ has recently been demonstrated experimentally. By means of a model Hamiltonian, we provide a possible explanation for the origin of this magnetoelectric coupling. We find, in agreement with experimental results, a net ferromagnetic moment at the BiFe${\mathrm{O}}_3$ interface. The induced ferromagnetic moment is the result of the competition between the $e_{\mathrm{g}}$-electron double exchange and the $t_{2\mathrm{g}}$-spin antiferromagnetic superexchange that dominates in bulk BiFe${\mathrm{O}}_3$. The balance of these simultaneous ferromagnetic and antiferromagnetic tendencies is strongly affected by the interfacial electronic charge density, which, in turn, can be controlled by the BiFe${\mathrm{O}}_3$ ferroelectric polarization.

Figure 1

Proposed spin order in the BFO-LSMO heterostructure (only half of the structure is shown, the other half is symmetric). The two first ($1,2$) and two last ($11,12$) planes have ionic charge $Z=+2$, and correspond to BFO. Layers $3$ and $10$ define the interface, with $Z=(0.7+2)/2$. The central planes ($4$ to $9$) have $Z=0.7$ and correspond to LSMO.

Figure 2

Main panel: Energy vs canting angle $\theta$ for different values of $J_{\mathrm{AFM}}$. Inset: Value of the magnetization induced at the interfacial plane of BFO vs $J_{\mathrm{AFM}}$, as given by the position of the minima in the main panel.

Figure 3

(a) Electronic charge for canting angles $\theta ~\pi /2$ and $\theta ~3\pi /2$ (the dashed line is the positive charge background). The charge-density distribution depends only slightly on $\theta$. (b) Orbital order described by the expectation value of $\langle {\tau }_z\rangle =n_{x^2-y^2}-n_{3z^2-r^2}$. The $e_g$ orbitals are equally populated ($\langle {\tau }_z\rangle =0$) at the BFO and LSMO bulk layers.

Figure 4

Magnetization induced in BFO ($M_{\mathrm{BFO}}$) as a function of $J_{\mathrm{AFM}}$ and $V_0$ for (a) $V_{\mathrm{offset}}=0$ and (b) $V_{\mathrm{offset}}=0.6t$. (c) Electronic charge in the heterostructure for $V_0=-0.5t$ and $V_0=0.5t$. Inset: charge at layer 2 for $-1t⩽V_0⩽1t$.