Invited:
Ordering/displacive ferrielectricity in 2D CuInP₂S₆.

Van der Waals crystals CuInP₂S(Se)₆ demonstrate ferrielectric and antiferroelectric ordering at thickness lowering till several structural layers which provide possibilities of their applications [1-3]. With the DFT-based molecular dynamical simulation of the Cu⁺ and In³⁺ cations flipping dynamics temperature dependence in the crystal lattice of CuInP₂S₆ we clarify the dipole ordering in these ferrielectrics. The second order Jahn-Teller effects determine the double-well local potential for Cu⁺ cations and the three-well potential for In³⁺ cations inside the structural layers. The quantum anharmonic oscillators model was also used for description of Cu⁺ and In³⁺ cations space distribution temperature dependence. It was found that In³⁺ cations play a decisive role in character of polar ordering which is determined by the energy of side wells in respect to the central well in their local potential. At normal and for positive pressures, the first order transition occurs, which is determined by the higher energy of side wells in respect to the central well of the In³⁺ local potential. With the rise of negative compression, the named side wells are stabilized and ferrielectric transition can evolve to the second order.

Results of modeling are discussed together with a mean-field analysis of dielectric and acoustic properties, entropy and heat capacity anomalies for CuInP₂S₆ and Ag_0.1Cu_0.9InP₂S₆ within the frame of the early proposed [4] approach. Finally, we compare our new evidence concerning the role of Cu⁺ and In³⁺ cations in the ferrielectric ordering with the prediction of the spin model [5] about the phase diagram topology.

1. A. Belianinov et al., Nano Lett., 2015, 15, 3808.

2. F. Liu et al., Nat. Commun., 2016, 7, 12357.

3. A. Dziaugys et al., Nat. Commun., 2020, 11, 3623.

4. A.N. Morozovska et al., Phys. Rev. B, 2021, 104, 054102.

5. Sumedha and S. Mukherjee, Phys. Rev. E, 2020, 101, 042125.