Ferroelectric-controlled magnetoelectric effect at the CrI3/HfO2 interface

The effective manipulation magnetic properties of two-dimensional magnets through electric field presents profound implications for spintronics. In this study, we investigate the ferroelectric-controlled magnetoelectric coupling within the $\mathrm{Cr}{\mathrm{I}}_{3}/\mathrm{Hf}{\mathrm{O}}_{2}$(111)/$\mathrm{Cr}{\mathrm{I}}_{3}$ heterostructure by using first-principles calculations. It is found that the magnetic moments of $\mathrm{Cr}{\mathrm{I}}_{3}$ are notably responsive to the polarization orientation---either directed towards (${P}_{\mathrm{in}}$) or away (${P}_{\mathrm{out}}$) from the interface. The polarization of $\mathrm{Hf}{\mathrm{O}}_{2}$ triggers the accumulation (depletion) of screening electrons at the ${P}_{\mathrm{in}}$ (${P}_{\mathrm{out}}$) interface, which affects the relative population of the exchange-split spin bands at the interface and thus results in the enhanced (reduced) total magnetic moments of the monolayer $\mathrm{Cr}{\mathrm{I}}_{3}$. The easy magnetization axis of $\mathrm{Cr}{\mathrm{I}}_{3}$ switches from an out-of-plane (${P}_{\mathrm{out}}$ state) to an in-plane (${P}_{\mathrm{in}}$ state) direction by the reversal of ferroelectric polarization of $\mathrm{Hf}{\mathrm{O}}_{2}$. Additionally, the Curie temperature (${T}_{C}$) of monolayer $\mathrm{Cr}{\mathrm{I}}_{3}$ is enhanced by 78% in the ${P}_{\mathrm{out}}$ state. This work provides useful guidelines for the study of interfacial magnetoelectric coupling and design of multiferroic devices.