Two-dimensional magnetic materials with magnetic anisotropy can form magnetic order under limited temperature in the single-layer limit. Their macroscopic magnetism is closely related to the number of layers and stacking orders, and their magnetic exchange can be regulated by various external fields. These novel properties have endowed 2D magnetic materials with rich physical connotation and potential application value, which has attracted wide attention of researchers¹.

Currently, two-dimensional magnetic materials reported in experiments mainly include transition metal halides, transition metal sulfides, transition metal carbonitides, transition metal phosphorus sulfides, Mn-Bi-Te family, etc. When the system degree is reduced to the single-layer limit, they usually exhibit significantly different magnetic behavior from that of bulk and less layered samples. These single-layer and few-layer magnetic materials are more easily regulated by external means, such as magnetic field, electric field, strain, light, etc. Therefore, the rich and highly adjustable magnetic phenomena of these two-dimensional magnetic materials indicate that they have broad development prospects in the application of two-dimensional devices.

Although a considerable number of intrinsic two-dimensional magnetic materials have been discovered, the related research on them is still in its infancy. The discovery of new mechanisms of magnetic coupling and magnetic regulation of two-dimensional magnetic materials and the design of intrinsic two-dimensional magnetic materials with high magnetic ordered transition temperatures are still challenging frontier scientific issues.

Ferroelectricity usually exists in a special class of dielectric materials. The spatial inversion symmetry of these materials is broken, so that the positive and negative charge centers of the system are separate, resulting in a spontaneous polarization. The direction of this spontaneous polarization can be reversed by the external electric field, resulting in a hysteresis loop^1-2 similar to ferromagnetic materials, so this kind of property is called ferroelectric in analogy with ferromagnetism. In ferroelectric materials, the two electrical states of the electric polarization vectors before and after flipping can correspond to “0” and “1” in binary language respectively. Because the electrical state can be read and written repeatedly and preserved for a long time, ferroelectric materials are widely used in many fields, such as ferroelectric memory, ferroelectric tunnelling junction(FTJ)³, ferroelectric capacitor and ferroelectric diode. The traditional ferroelectric materials are mainly ABO₃ type perovskite materials⁴.

Under the general trend of miniaturization and integration of electronic equipment, exploring the new ferroelectric materials with small size and foldable properties has become a hot topic in the low dimensional ferroelectricity fields. In traditional ferroelectric materials (ABO₃-type perovskite), when the thickness of the material reduce to several nanometers, the surface depolarization effect is strong, so that the ferroelectric property significantly weakened or even disappeared, corresponding to the ferroelectric critical size. Therefore, how to design and prepare high performance ferroelectric devices with small size has become one of the major challenges in this field.

Multiferroics exhibit more than one primary ferroic ordering, including ferromagnetism, ferroelectricity, or ferroelasticity in the same phase^[1,2]. The terminology is usually extended to include non-primary orderings such as antiferromagnetism, antiferroelectricity, as well as composites of individual ferroics. The concept often used today is referred to magnetoelectric materiasl combing ferroelectric and magnetic behaviors (Fig. 1);. Such a combination of ferroic orders in multiferroics can lead to coupling between them and provide an efficient route to control magnetism by electric fields or vice versa.

Multiferroics can be classified into two categories: type-I mulitferroics refer to the ferroelectricity does not have magnetic origin, which usually leads to an indirect and weak magnetoelectric coupling; Type-II multiferroics are induced by some specific magnetic orders with a strong magnetoelectric coupling but a small electric polarization and thus low transition temperature (T_C). The two types are depicted in Fig. 2^[3]

In geometrically driven ferroelectrics, a small A-site cation permits rotations of its surrounding coordination polyhedral (Fig. 3b), which are either polar in their own right (for example, in BaNiF4^[6]) or couple to a secondary polar distortion (as in YMnO3^[7]). In this case, the polarization is both robust and small in magnitude. In h-RMnO3 (R=Sc, Y, In or Dy-Lu^[8,9]), unit-cell tripling drives the emergence of a ferroelectric order at Tc ≥ 1,200 K with a polarization of 5.6 μC/cm2, followed by a magnetic ordering at the Neel temperature (TN ≤ 120 K).

In magnetically induced ferroelectrics, a non-collinear magnetic ordering, such as a spin spiral, breaks the inversion symmetry and induces a spontaneous polarization. These magnetically induced, so-called improper ferroelectric materials are totally different from displacive ferroelectrics, in which magnetic ordering is inhibited. The most intensely discussed mechanism is the inverse Dzyaloshinskii–Moriya (DM) interaction. Spin-orbit coupling (SOC) is crucial for the inverse DM interaction. The polarization is essentially determined by the optimization of the spin configuration from the point of view of anitsymmetry exchange, expressed by the antisymmetric product S_i × S_j of neighboring spins Si,j (see Fig. 3d). The polarization vector is P ∝ e_ij × ( S_i × S_j), where eij is the unit vector connecting neighboring spins. Multiferroicity of this type was first found in Cr2BeO4^[11].

Manipulating and engineering atom dynamics with single atom precision has long been the ultimate goal in nanoscience and nanotechnology ^[1]. Direct atom manipulation or beam induced structural evolution by scanning transmission electron microscopy (STEM) has several advantages, i.e. much faster speed of atom manipulation (a few tens of seconds) and manipulation at room temperature ^[1]. STEM has been applied in various research, such as, structural defects ^[2], phase transitions ^[3], electron beam lithography ^[4], assembly of atoms ^[5] and single-atom migration ^[6].

When electrons pass through atomically thin 2D materials, energy can be either elastically or inelastically transferred to the targeted atom. During an elastic collision, impinging electrons are scattered to high angles by the recoiling nucleus and energy and momentum are both conserved. During the inelastic scattering process, the incident electron interacts with the electronic system of the target atom resulting in electronic excitation and electrostatic charging ^[1]

Atomic clusters, consisting of a few to a few thousand atoms, have emerged over the past 40 years as the ultimate nanoparticles. Some of these clusters form stable units with atomically precise structures that give rise to collective behaviors that mimic those of traditional atoms, essentially functioning as ‘superatoms’^{[1, 2]}. The ultimate vision is to create materials with tailored and tuneable functions through the judicious design, synthesis and assembly of superatoms. The use of superatoms as building blocks for materials offers opportunities to design materials with tailored functionalities^{[3, 4]}.

However, the reinforcing chemical interaction between atoms (chemical bond)^{[5, 6]}is the main factor that leads to the unstable structure of atomic crystal through the replacement of elements, and the weakening of such interaction is likely to overcome this difficulty. In the superatomic crystal materials with atomic clusters as the basic building unit, the surface saturated atomic clusters can be combined by non-covalent interactions such as weak atom identification, electrostatic interaction^[7] and hydrogen bonding^[8]. It has the potential to maintain structural stability in the regulation of electronic structural properties through continuous cluster (element) replacement, and is also more in line with the needs of large-scale material preparation, with some characteristics of atomic fabrication.

Correlated two-dimensional (2D) layers exhibit varies quantum phases, e.g. unconventional superconductor^{[1, 2]}, quantum spin liquids^{[3, 4]}, Mott and charge-transfer (CT) insulators^[5-7], charge-density ware (CDW)^{[8, 9]} and Wigner crystals^[10-12], have been emerging in correlated systems. The understanding of correlated electronic systems and the phase transitions between those quantum states is very important.