Giant magnetoelectric effect in pure manganite-manganite heterostructures

Obtaining strong magnetoelectric couplings in bulk materials and heterostructures is an ongoing challenge. We demonstrate that manganite heterostructures of the form (Insulator) $/{\left({\mathrm{LaMnO}}_3\right)}_{\mathrm{n}}/\mathrm{Interface}/{\left({\mathrm{CaMnO}}_3\right)}_{\mathrm{n}}/\left(\mathrm{Insulator}\right)$ show strong multiferroicity in magnetic manganites where ferroelectric polarization is realized by charges leaking from ${\mathrm{LaMnO}}_3$ to ${\mathrm{CaMnO}}_3$ due to repulsion. Here, an effective nearest-neighbor electron-electron (electron-hole) repulsion (attraction) is generated by cooperative electron-phonon interaction. Double exchange, when a particle virtually hops to its unoccupied neighboring site and back, produces magnetic polarons that polarize antiferromagnetic regions. Thus a striking giant magnetoelectric effect ensues when an external electrical field enhances the electron leakage across the interface.

Figure 1

Schematic showing the symmetric $\left(\mathrm{Insulator}\right)/{\left({\mathrm{LaMnO}}_3\right)}_{\mathrm{N}}/\mathrm{Interface}/{\left({\mathrm{CaMnO}}_3\right)}_{\mathrm{N}}/\left(\mathrm{Insulator}\right)$ heterostructure. Each of the labeled $N$ layers on both LMO (${\mathrm{LaMnO}}_3$) and CMO (${\mathrm{CaMnO}}_3$) sides contain manganese-oxide (MO) layers.

Figure 2

Electronic charge density $n\left(z_N\right)$ and per-site magnetization $m\left(z_N\right)$ (of $t_{2\mathrm{g}}$ spins normalized to unity) in various manganese-oxide layers of a $\left(\mathrm{Insulator}\right)/{\left({\mathrm{LaMnO}}_3\right)}_2/\mathrm{Interface}/{\left({\mathrm{CaMnO}}_3\right)}_2/\left(\mathrm{Insulator}\right)$ heterostructure for $a=4\AA$, $\epsilon =20$, and $C_1=0.24$. Figures are for (a) $n(E_{\mathrm{ext}}=0\mathrm{kV}/\mathrm{cm})$; (b) $\mathrm{\Delta }n=n(E_{\mathrm{ext}}=300/400\mathrm{kV}/\mathrm{cm})-n(E_{\mathrm{ext}}=0\mathrm{kV}/\mathrm{cm})$; and (c) $m\left(z_N\right)$ at $E_{\mathrm{ext}}=0,300$, and $400\mathrm{kV}/\mathrm{cm}$. MO layer 1 on the LMO side undergoes spin reversal when $E_{\mathrm{ext}}=400\mathrm{kV}/\mathrm{cm}$ is applied.

Figure 3

Electronic charge density $n\left(z_N\right)$ and per-site magnetization $m\left(z_N\right)$ (of normalized-to-unity $t_{2\mathrm{g}}$ spins) in various manganese-oxide layers of an $\left(\mathrm{Insulator}\right)/{\left({\mathrm{LaMnO}}_3\right)}_2/\mathrm{Interface}/{\left({\mathrm{CaMnO}}_3\right)}_2/\left(\mathrm{Insulator}\right)$ heterostructure for $a=4\AA$, $\epsilon =20$, and $C_1=0.31$. Plots pertain to (a) $n(E_{\mathrm{ext}}=0\mathrm{kV}/\mathrm{cm})$, (b) $\mathrm{\Delta }n=n(E_{\mathrm{ext}}=100\mathrm{kV}/\mathrm{cm})-n(E_{\mathrm{ext}}=0\mathrm{kV}/\mathrm{cm})$, and (c) $m\left(z_N\right)$ at $E_{\mathrm{ext}}=0$ and $100\mathrm{kV}/\mathrm{cm}$. The LMO side becomes completely ferromagnetic when $E_{\mathrm{ext}}=100\mathrm{kV}/\mathrm{cm}$ is applied.

Figure 4

Layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged per-site magnetization $\langle m\left(I\right)\rangle$ (of $t_{2\mathrm{g}}$ spins normalized to unity) for a symmetric $12\times 8$ LMO-CMO lattice when electron-phonon interaction is zero; $J_z=0.01t$ and $J_{xy}/J_z=1.39$; $T=0.001t$; and when (a) external electric field $E_{\mathrm{ext}}=0$ and (b) $400\mathrm{kV}/\mathrm{cm}$.

Figure 5

Layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged per-site magnetization $\langle m\left(I\right)\rangle$ (of $t_{2\mathrm{g}}$ spins normalized to unity) for a symmetric $12\times 8$ LMO-CMO lattice when electron-phonon interaction $g=0$; superexchange $J_z=0.02t$ and coupling ratio $J_{xy}/J_z=1.39$; $T=0.001t$; and when (a) $E_{\mathrm{ext}}=0$ and (b) $400\mathrm{kV}/\mathrm{cm}$.

Figure 6

Layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged per-site magnetization $\langle m\left(I\right)\rangle$ (of normalized-to-unity $t_{2\mathrm{g}}$ spins) for a symmetric $12\times 8$ LMO-CMO lattice when $g=0$; $J_z=0.01t$ and $J_{xy}/J_z=1.39$; enhanced temperature $T=0.01t$; and when (a) $E_{\mathrm{ext}}=0$ and (b) $400\mathrm{kV}/\mathrm{cm}$.

Figure 7

In a $12\times 8$ symmetric lattice, when the electron-phonon interaction strength $g=2.0$, (a) when the external electric field $E_{\mathrm{ext}}=0$, the layer-averaged profiles of charge density $\langle n\left(I\right)\rangle$ and magnetization $\langle m\left(I\right)\rangle$ (of the $t_{2\mathrm{g}}$ spins normalized to unity); (b) when the external electric field $E_{\mathrm{ext}}=0$, schematic occupation-number representation of ground-state charge configuration in the lattice; (c) when a large external electric field $E_{\mathrm{ext}}=300\mathrm{kV}/\mathrm{cm}$ is applied, modified layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged magnetization $\langle m\left(I\right)\rangle$ (of the $t_{2\mathrm{g}}$ spins normalized to unity) for various layers in the lattice; and (d) when $E_{\mathrm{ext}}=300\mathrm{kV}/\mathrm{cm}$, reorganized ground-state charge configuration.

Figure 8

Charge modulation due to Coulomb interaction $H_{\mathrm{coul}}$ in a one-dimensional symmetric LMO-CMO lattice. The number of neutral layers/sites is $x$.

Figure 9

Total magnetization as a function of temperature for various $E_{\mathrm{ext}}$ in a $12\times 8$ lattice when electron-phonon coupling $g=2.0$. Figure shows that an enhancement in magnetization occurs for electric fields $E_{\mathrm{ext}}\gtrsim 300$ kV/cm, whereas below this threshold value, total magnetization does not change from its value at $E_{\mathrm{ext}}=0$ kV/cm. The magnetoelectric effect is reasonably large at temperatures below $0.5\mathrm{t}{e}^{-g^2}$ ($\sim 10$ K).

Figure 10

Result of enhanced electron-phonon coupling $g=2.2$ and zero electric field, in a symmetric $12\times 8$ lattice, on (a) layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged magnetization $\langle m\left(I\right)\rangle$ (of the $t_{2\mathrm{g}}$ spins normalized to unity), and (b) ground-state charge configuration.

Figure 11

In a symmetric $12\times 6$ lattice, for enhanced coupling $g=2.2$, (a) at zero electric field, layer-averaged charge density $\langle n\left(I\right)\rangle$, and layer-averaged magnetization $\langle m\left(I\right)\rangle$ of $t_{2\mathrm{g}}$ spins normalized to unity; (b) at $E_{\mathrm{ext}}=0$, ground-state configuration; (c) at strong external electric field $E_{\mathrm{ext}}=400\mathrm{kV}/\mathrm{cm}$, layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged magnetization $\langle m\left(I\right)\rangle$ of $t_{2\mathrm{g}}$ spins normalized to unity; (d) at $E_{\mathrm{ext}}=400\mathrm{kV}/\mathrm{cm}$, charge configuration in the ground state.

Figure 12

In a symmetric $12\times 6$ lattice, for reduced coupling $g=2.0$ and for the heterostructure $\mathrm{Ins}./{\left(\mathrm{LaO}\text{−}{\mathrm{MnO}}_2\right)}_{\mathrm{n}}/\left({\mathrm{La}}_{1/2}{\mathrm{Ca}}_{1/2}\mathrm{O}\right)/{\left({\mathrm{MnO}}_2\text{−}\mathrm{CaO}\right)}_{\mathrm{n}}/\mathrm{Ins}.$ with $Z_j=0.75$ ($Z_j=0.25$) for the layer adjacent to interface on the LMO (CMO) side, (a) at zero electric field, layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged magnetization $\langle m\left(I\right)\rangle$ of $t_{2\mathrm{g}}$ spins normalized to unity; (b) at $E_{\mathrm{ext}}=0$, ground-state configuration; (c) at strong external electric field $E_{\mathrm{ext}}=400\mathrm{kV}/\mathrm{cm}$, layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged magnetization $\langle m\left(I\right)\rangle$ of $t_{2\mathrm{g}}$ spins normalized to unity; and (d) at $E_{\mathrm{ext}}=400\mathrm{kV}/\mathrm{cm}$, charge configuration in the ground state.

Figure 13

In asymmetric heterostructure defined on a $12\times 8$ lattice with two layers of LMO and six layers of CMO, when coupling $g=2.0$, (a) at $E_{\mathrm{ext}}=0$, layer-averaged charge density $\langle n\left(I\right)\rangle$ and layer-averaged magnetization $\langle m\left(I\right)\rangle$ of normalized-to-unity $t_{2\mathrm{g}}$ spins; (b) at $E_{\mathrm{ext}}=0$, ground-state configuration; (c) at $E_{\mathrm{ext}}=300\mathrm{kV}/\mathrm{cm}$, layer-averaged charge profile $\langle n\left(I\right)\rangle$ and layer-averaged magnetization profile $\langle m\left(I\right)\rangle$ of normalized-to-unity $t_{2\mathrm{g}}$ spins; and (d) at $E_{\mathrm{ext}}=300\mathrm{kV}/\mathrm{cm}$, ground-state configuration.

Figure 14

In asymmetric $12\times 8$ lattice with six layers of LMO and two layers of CMO, when electron-phonon interaction $g=2.0$, (a) at external electric field $E_{\mathrm{ext}}=0$, layer-averaged electron density $\langle n\left(I\right)\rangle$ and layer-averaged magnetization $\langle m\left(I\right)\rangle$ of $t_{2\mathrm{g}}$ spins normalized to unity; (b) at $E_{\mathrm{ext}}=0$, ground-state electronic configuration; (c) at $E_{\mathrm{ext}}=300\mathrm{kV}/\mathrm{cm}$, layer-averaged electron density $\langle n\left(I\right)\rangle$ and layer-averaged magnetization $\langle m\left(I\right)\rangle$ of $t_{2\mathrm{g}}$ spins normalized to unity; and (d) at $E_{\mathrm{ext}}=300\mathrm{kV}/\mathrm{cm}$, the ground state.