Nonvolatile electric field control of magnetism in bilayer ${\mathrm{CrI}}_3$ on monolayer ${\mathrm{In}}_2{\mathrm{Se}}_3$

Electrical control of magnetism is of great interest for low-energy-consumption spintronic applications. Here, via first-principles calculations, we propose a van der Waals (vdW) multiferroic heterostructure composed of a magnetic ${\mathrm{CrI}}_3$ bilayer and a ferroelectric α-${\mathrm{In}}_2{\mathrm{Se}}_3$ monolayer substrate. Interestingly, the interlayer magnetism of bilayer ${\mathrm{CrI}}_3$ is switchable between the ferromagnetic and antiferromagnetic coupling by nonvolatile control of the ferroelectric polarization direction of α-${\mathrm{In}}_2{\mathrm{Se}}_3$. The interlayer magnetic coupling of ${\mathrm{CrI}}_3$ bilayer originates from the direct interaction of adjacent I atoms between ${\mathrm{CrI}}_3$ monolayers, which can be tuned by the polarization of ${\mathrm{In}}_2{\mathrm{Se}}_3$, explaining the electrical control of interlayer magnetic phase transition. Our work demonstrates a multiferroelectric material platform by artificially stacking two dimensional vdW layers, providing an effective method for achieving nonvolatile electrical control of atomic-thin vdW ferromagnets.

Figure 1

Top view of (a) HT-BL-$1\times 1 {\mathrm{CrI}}_3$ and (b) $\sqrt{3}\times \sqrt{3} {\mathrm{In}}_2{\mathrm{Se}}_3$ monolayer. Side views of HT-BL-${\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$ heterostructures with the ${\mathrm{In}}_2{\mathrm{Se}}_3$ ferroelectric dipole moment directed (c) upward and (d) downward, respectively. Black rhombuses in (a) and (b) refer to the HT-BL-${\mathrm{CrI}}_3$ unit cell and $\sqrt{3}\times \sqrt{3} {\mathrm{In}}_2{\mathrm{Se}}_3$ supercell.

Figure 2

Atomic decomposed band structures with SOC, the VBM and CBM schematic diagram of HT-BL-${\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$ heterostructures (a),(b) for $P$-up and (d),(e) for $P$-down of ${\mathrm{In}}_2{\mathrm{Se}}_3$, respectively. The induced interlayer magnetic coupling between Cr atom layers switches from (b) AFM to (d) FM. The blue (green) solid circles refer to the Cr atoms at the top (bottom) layer, light brown arrows refer to the spin direction of Cr atoms, and large blue arrows stand for the ferroelectric polarization direction of ${\mathrm{In}}_2{\mathrm{Se}}_3$. The energy difference is defined by $\mathrm{\Delta }E=E_{\mathrm{AFM}}-E_{\mathrm{FM}}$. A negative value indicates that the HT-BL-${\mathrm{CrI}}_3$ prefers an interlayer antiferromagnetic coupling for an upward polarization of ${\mathrm{In}}_2{\mathrm{Se}}_3$ and vice versa.

Figure 3

(a),(c) Spin density (SD) of HT-BL-${\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$ and (b),(d) differential spin density (DSD) between $P$-down and $P$-up HT-BL-${\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$ in FM configuration (left side) and AFM configuration (right side). The yellow and cyan isosurface in (a) and (c) refer to spin-up and -down density, respectively. The increase and decrease of spin density (absolute value) are shown with red and blue isosurface in (b) and (d), respectively. The isosurface value of SD and DSD is $6\times {10}^{\text{−}4}$ and $2\times {10}^{\text{−}6}e/\mathrm{boh}{\mathrm{r}}^3$, respectively. Red and blue arrows stand for the $p_{x/y}-p_z$ and $p_{x/y}-p_{x/y}$ orbital hopping between interlayer I atoms.

Figure 4

The electrostatic potential of (a) HT-BL-${\mathrm{CrI}}_3$ and (b) ML-${\mathrm{In}}_2{\mathrm{Se}}_3$. (c) $\mathrm{PBE}+U$ calculated band alignments between HT-BL-${\mathrm{CrI}}_3$ and ML-${\mathrm{In}}_2{\mathrm{Se}}_3$ with different polarization directions. All the energy levels are shifted relative to the vacuum level of HT-BL-${\mathrm{CrI}}_3$.

Figure 5

Evolution of (a) magnetocrystalline anisotropy energy and (b) energy difference between AFM and FM configurations of HT-BL-${\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$ with $P$-up and $P$-down of ${\mathrm{In}}_2{\mathrm{Se}}_3$ under various I-Se vertical interface distances. The blue arrows denote the equilibrium interfacial spacing position. (c) The energy difference between FM ground state of $P$-down HT-BL-${\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$ and AFM ground state of $P$-up one as a function of the external electric field. The blue and orange region stands for the FM and AFM coupling, respectively.