Synthesis and Magnetic Properties of the Multiferroic [C(NH2)3]Cr(HCOO)3 Metal–Organic Framework: The Role of Spin–Orbit Coupling and Jahn–Teller Distortions

We report for the first time the synthesis of [C(NH₂)₃]Cr(HCOO)₃ stabilizing Cr²⁺ in formate perovskite, which adopts a polar structure and orders magnetically below 8 K. We discuss in detail the magnetic properties and their coupling to the crystal structure based on first-principles calculations, symmetry, and model Hamiltonian analysis. We establish a general model for the orbital magnetic moment of [C(NH₂)₃]M(HCOO)₃ (M = Cr, Cu) based on perturbation theory, revealing the key role of the Jahn-Teller distortions. We also analyze their spin and orbital textures in k-space, which show unique characteristics.