Examining\nMagnetic Properties and Multiferroicity\nin the Isostructural Cu<sub>2</sub>TSiS<sub>4</sub> (T = Mn and Fe)\nSystem Based on the DFT Approach and the Orbital Interaction Analysis

In\nthe experiment, despite their structural and electronic\nsimilarities,\nCu<sub>2</sub>MnSiS<sub>4</sub> exhibits AFM ordering characterized\nby a propagation vector <i>k</i> = (1/2, 0, 1/2), while\nCu<sub>2</sub>FeSiS<sub>4</sub> has a different type of AFM ordering\nwith a propagation vector <i>k</i> = (1/2, 1/2, 1/2). To\nunravel how these differences arise, we investigated magnetic properties\nof Cu<sub>2</sub>TSiS<sub>4</sub> (T = Mn and Fe) based on the DFT\ncalculation and an orbital interaction analysis. We suggest that the\nCu<sup>+</sup> ion plays an important role in exhibiting different\nmagnetic structures for the isostructural and pseudoisoelectronic\nCu<sub>2</sub>TSiS<sub>4</sub> (T = Mn and Fe) compounds. In detail,\nparticipation of Cu<sup>+</sup> ions into spin exchange interaction <i>J</i><sub>5</sub>, which is a spin exchange interaction along\nthe b-direction, is critical for exhibiting AFM coupling of <i>J</i><sub>5</sub>, and the strength of this effect should be\nresponsible for exhibiting different magnetic structures of Cu<sub>2</sub>MnSiS<sub>4</sub> and Cu<sub>2</sub>FeSiS<sub>4</sub>. We\nalso explored the ferroelectric polarization of the Cu<sub>2</sub>TSiS<sub>4</sub> (T = Mn and Fe) system on the basis of DFT + <i>U</i> and DFT + <i>U</i> + SOC calculation. Our result\nreveals that the ferroelectric polarization of the Cu<sub>2</sub>TSiS<sub>4</sub> (T = Mn and Fe) system is mainly governed by its geometric\nstructure rather than its magnetic order and the spin–orbit\ncoupling effect.