Ionic Radius Ratio versus Tolerance Factor to Design Metal Formate Framework Chiral Magnets

The observation of topologically protected spin phase objects, such as spin solitons and skyrmions, hinges on the ability to control the chiral space group and crystal system. The space group is of particular significance with regard to chiral spin structures. In this context, the study of chiral crystal systems has become a significant area of interest. The use of a tolerance factor has been proposed as a means of predicting the crystal space group and crystal system. This study demonstrates the inaccuracy of the tolerance factor in predicting crystalline systems and its limitations in the design of high-dimensional chiral crystalline systems from a newly synthesized compound. In order to enhance the efficacy of the prediction methodology, a comprehensive investigation was conducted on the novel synthesized chiral magnetic crystals and reported crystal structures. A strong correlation was identified between the crystal systems and the ionic radii ratios of the metal components. The crystallization of small A⁺ cations (small A⁺ radii/M²⁺ radii ratio) into a cubic crystal system is enabled by their smaller size. Conversely, large A⁺ cations (large A⁺ radii/M²⁺ radii ratio) facilitate the formation of lower symmetry crystal systems, including monoclinic and hexagonal structures. The findings of this study provide a foundation for the development of more symmetrical chiral magnetic materials.