General structure factor and dynamic effects of the Dzyaloshinskii–Moriya interaction in S = 1/2 clusters

Understanding the effects of the Dzyaloshinskii-Moriya interaction (DMI) has become increasingly important in the context of nanoscale magnetism and spintronics. In this study, we derive a general structure factor equation for an S = 1/2 dimer and show that the anisotropic ratio $D_z/|J|$ and complex phase $ϕ$ of the DMI control the gap energy and intensity of the $|0,0\rangle \to |1,0\rangle$ transition. {Using exact diagonalization of the Heisenberg spin-spin Hamiltonian that incorporates both isotropic and anisotropic interactions,} as well as the effects of an external magnetic field and an electric field. Our results show that the DM interaction splits energy eigenstates, induces level repulsion, and significantly modifies the spin dimer structure factor. These effects reveal a direct correspondence between thermodynamic anomalies in the heat capacity and spin-resolved selection rules.