| Ferroelectric and ferromagnetic materials are a special class of materials that exhibit spontaneous polarization（magnetization）and can be controlled by external electric（magnetic）fields,thus having wide application prospects in data storage,sensors,spin electronic devices,and other fields.In recent years,with the deepening of two-dimensional materials research,two-dimensional ferroelectricity and ferromagnetism have been confirmed in van der Waals materials.Compared with bulk materials,two-dimensional ferroic materials have stronger external field responsivity,tunability,and higher integration,thus having enormous potential for designing new electronic devices with high density,high processing speed,multifunctionality,and low energy consumption.In addition,the concept of ferrovalley materials based on valley degree of freedom has been proposed.Similar to spontaneous polarization in ferroelectric materials or spontaneous magnetization in ferromagnetic materials,ferrovalley materials exhibit spontaneous valley polarization.With the discovery of these various two-dimensional ferroic orders,their coexistence and coupling have begun to attract widespread attention.In these materials with multiple ferroic coexistence,there may be coupling effects between different ferroic orders,such as magneto-electric coupling,magneto-valley coupling,and electro-valley coupling.These coupling effects provide a basis for achieving magneto-electric cross-control and external field control of energy valleys.Therefore,studying the coexistence and coupling of multiple ferroic orders in individual two-dimensional materials is of great significance for the study of spin electronics and valley electronics.This article employs various techniques,such as first-principles calculations,atomic spin dynamics simulations,Monte Carlo simulations,and symmetry analysis,to demonstrate the coexistence and coupling of multiple ferroic orders in two-dimensional ferroic materials with broken inversion symmetry,and to reveal the effect of external fields on these orders.The main research contents are as follows:（1）The article demonstrates the spin-dependent ferroelectricity and ferrovalley effects induced by spin-orbit coupling in some two-dimensional ferromagnetic materials with broken inversion symmetry.It confirms the coexistence and coupling of ferroelectricity,ferromagnetism,and ferrovalley in single-phase materials.The article reveals that spin-induced ferroelectricity arises from the modification of p-d hybridization by spin-orbit coupling,and some polarization components involve high-order perturbations of spin-orbit coupling.The article also demonstrates through atomic spin dynamics simulations that the coupling between spin and polarization,as well as the coupling between spin and valley,allows the electronic degree of freedom to be cross-controlled by external fields.（2）We investigated the structural stability,magnetism,and spin-induced ferroelectricity of three structural phases of monolayer Fe I2.The influence of the U value on the stability of the structural phases and the ground state structure was revealed.We focused on the differences in magnetism and spin-induced ferroelectricity between two structural phases（P-6m2 and P-4m2 phases）with inversion symmetry breaking.The ground state of the P-6m2 phase is ferromagnetic,while the ground state of the P-4m2 phase is antiferromagnetic.We calculated the dependence of the ferroelectric polarization components induced in different spin planes on the spin direction by combining symmetry analysis and first-principles methods,and derived an expression for the polarization components through model analysis,which can well explain the theoretical results.This study contributes to the design and implementation of two-dimensional multiferroic materials with intrinsic magnetoelectric coupling effects. |
