Examining Magnetic Properties and Multiferroicity in the Isostructural Cu₂TSiS₄ (T = Mn and Fe) System Based on the DFT Approach and the Orbital Interaction Analysis

In the experiment, despite their structural and electronic similarities, Cu₂MnSiS₄ exhibits AFM ordering characterized by a propagation vector k = (1/2, 0, 1/2), while Cu₂FeSiS₄ has a different type of AFM ordering with a propagation vector k = (1/2, 1/2, 1/2). To unravel how these differences arise, we investigated magnetic properties of Cu₂TSiS₄ (T = Mn and Fe) based on the DFT calculation and an orbital interaction analysis. We suggest that the Cu⁺ ion plays an important role in exhibiting different magnetic structures for the isostructural and pseudoisoelectronic Cu₂TSiS₄ (T = Mn and Fe) compounds. In detail, participation of Cu⁺ ions into spin exchange interaction J₅, which is a spin exchange interaction along the b-direction, is critical for exhibiting AFM coupling of J₅, and the strength of this effect should be responsible for exhibiting different magnetic structures of Cu₂MnSiS₄ and Cu₂FeSiS₄. We also explored the ferroelectric polarization of the Cu₂TSiS₄ (T = Mn and Fe) system on the basis of DFT + U and DFT + U + SOC calculation. Our result reveals that the ferroelectric polarization of the Cu₂TSiS₄ (T = Mn and Fe) system is mainly governed by its geometric structure rather than its magnetic order and the spin-orbit coupling effect.