Interlayer Ferromagnetic Coupling In Two-dimensional Van Der Waals Antiferromagnetic Materials

Since 2017,the discovery of magnetism in two-dimensional（2D）layered materials has attracted extensive research interest in physics and related fields.In special,the discovery of the intrinsic magnetic topological insulator Mn Bi₂Te₄provides an ideal platform for investigating novel physical properties such as the quantum anomalous Hall effect（QAHE）and axion insulators.However,its interlayer antiferromagnetic coupling seems to be detrimental to the observation of QAHE in the magnetic topological insulator Mn Bi₂Te₄at zero magnetic field.In addition,2D intrinsic magnetic material Cr I₃has its unique physical properties and has potential applications in the realization of spintronic devices.In the experimentally prepared thin layer samples of Cr I₃,the monolayer exhibits intralayer ferromagnetic coupling,however,the bilayer exhibited interlayer antiferromagnetic coupling.This has also hindered the application of this novel 2D magnetic semiconductor in some ways.Therefore,for the above two types of 2D magnetic materials,it is necessary to realize interlayer ferromagnetic coupling for their further development and application.In this paper,we focus on the intrinsic magnetic topological insulator Mn Bi₂Te₄and the intrinsic magnetic material Cr I₃to achieve interlayer ferromagnetic coupling.Specifically,our studies include the following two aspects based on the first-principles calculations.1.Electronic structure,magnetic properties and topological properties of the p-doped Mn Bi₂Te₄system were studied.In two septuple layers system,the interlayer ferromagnetic coupling appears by doping nonmagnetic elements（e.g.,N,P,As,Na,Mg,K,and Ca）,due to the redistribution of orbital occupations of Mn.We further find that Mg and Ca elements are the most suitable candidates because of their low formation energy.Although,the p-doped two septuple layers exhibit topologically trivial band structure,the increase of layer thickness to three（four）septuple layers with Ca（Mg）dopants leads to the formation of the quantum anomalous Hall effect.Our proposed p-doping strategy without introducing additional magnetic disorder not only makes Mn Bi₂Te₄doped with Mg and Ca elements become an ideal platform to realize the high-temperature quantum anomalous Hall effect without external magnetic field,but also can compensate the electrons from the intrinsic n-type defects in Mn Bi₂Te₄.2.For the monoclinic phase Cr I₃with interlayer antiferromagnetic coupling,recent study confirmed that it can realize the transition from interlayer antiferromagnetic to interlayer ferromagnetic coupling by the gate voltage regulation,and the intrinsic mechanism of realizing this transformation is speculated to be related to the formation of magnetic polaron.In this study,we explore the electronic structure and magnetic properties of the nonmagnetic elements including O,S,Se,N,P,As and C,doped bilayer or triple-layer Cr I₃systems through first-principles calculations.Our results demonstrate that O,P,S,As,and Se doped Cr I₃bilayer can realize interlayer ferromagnetic coupling.Especially for the As doped system,the Curie temperature is estimated to 220K and it can be improved with the increased doping concentration.Further analysis shows that the interlayer ferromagnetic coupling in the elements doped few-layer Cr I₃is related to the formation of the magnetic polaron.Our work provides a new evidence that the interlayer ferromagnetic coupling in Cr I₃ultrathin films can be realized by the formation of magnetic polaron,and it also provides an alternative scheme for the realization of 2D Cr I₃based ferromagnetic semiconductor with high-temperature insulating ferromagnetism.