A bond-order–bond-length–bond-strength (bond-OLS) correlation mechanism is presented for consistent insight into the origin of the shape-and-size dependence of a nanosolid, aiming to provide guidelines for designing nanomaterials with desired functions. It is proposed that the coordination number imperfection of an atom at a surface causes the remaining bonds of the lower-coordinated surface atom to relax spontaneously; as such, the bond energy rises (in absolute value). The bond energy rise contributes not only to the cohesive energy (ECoh) of the surface atom but also to the energy density in the relaxed region. ECoh relates to thermodynamic properties such as self-assembly, phase transition and thermal stability of a nanosolid. The binding energy density rise is responsible for the changes of the system Hamiltonian and related properties, such as the bandgap, core-level shift, phonon frequency and the dielectrics of a nanosolid of which the surface curvature and the portion of surface atoms vary with particle size. The bond-OLS premise, involving no assumptions or freely adjustable parameters, has led to consistency between predictions and experimental observations of a number of outstanding properties of nanosolids.

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Two-dimensional (2D) ferromagnetic materials with high spin polarization are highly desirable for spintronic devices. 2D Janus materials exhibit novel properties due to their broken symmetry. However, the electronic structure and magnetic properties of 2D Janus magnetic materials with high spin polarization are still unclear. Inspired by the successful synthesis of a ferromagnetic FeCl2 monolayer and 2D Janus MoSSe and WSSe, we systematically study the electronic structure and magnetic properties of Janus FeXY (X, Y = Cl, Br, and I, X ≠ Y) monolayers. Based on the Goodenough–Kanamori–Anderson theory, the ferromagnetism stems from the superexchange interaction mediated by Fe–X/Y–Fe bonds. The band gaps of spin-up channels are large enough (>4 eV) to prevent spin flipping, which is beneficial for spintronic devices. Additionally, the sizable magnetocrystalline anisotropy energy (MAE) indicates that Janus FeXY monolayers are suitable for information storage. More importantly, the half-metallic character is still kept in Janus FeXY monolayers, and their magnetic properties are enhanced by the biaxial compressive strain. The MAE of FeClI and FeBrI increases by 1 order of magnitude, and the Curie temperature of FeXY monolayers enhances by 100%. These results provide an example of the 2D Janus half-metallic materials and enrich the 2D magnetic material library.