The mixed spin-1/2 and spin-1 Ising model for CuInP₂S₆ ferrielectrics

DOI: 10.62564/M4-YV1553

Ruslan Yevych, Vitalii Liubachko, Viacheslav Hryts, Mykola Medulych, Anton Kohutych, Yulian Vysochanskii

Institute for Solid State Physics and Chemistry, Uzhhorod National University, Ukraine


The temperature behavior of Sn₂P₂S₆ ferroelectrics was previously explained using the Blume-Capel model with pseudospin S=1, which is related to the local three-well potential for spontaneous polarization fluctuations [1-3]. For CuInP₂S₆ crystals, the mixed Ising model [4,5] can be applied, which uses spins s=1/2 and S=1. These spins are related to the ordering dynamics of Cu⁺ cations in the double-well potential (pseudospins s=1/2) and to the displacive dynamics of In³⁺ cations in the three-well local potential (pseudospins S=1). The quantum anharmonic oscillator model was used to accomplish this task. Additionally, data from a light scattering study is incorporated. Based on the temperature dependence of the pseudospin fluctuations spectra, it can be concluded that the In³⁺ cations experience anharmonic disordering/displacements in the local asymmetric three-well potential at temperatures below 150K. This leads to specific lattice anharmonicity phenomena, which alter the temperature behavior of the lattice vibrations and cause the thermal expansion coefficient to change sign. Additionally, a dipole glassy appearance is observed in the deeply cooled ferrielectric phase. The contribution of Cu⁺ cations to the calculated pseudospin fluctuation spectra is found to evolve with heating above 150K, supporting the activation of ionic conductivity in CuInP₂S₆ crystals. Notably, the same species, namely copper cations, participate in both spontaneous polarization and ionic conductivity creation. The variation of the pseudospin fluctuation spectra upon heating to 150K is consistent with the softening of the Raman low-frequency spectral lines related to the cationic sublattice dynamics of indium and a broadening of the spectral line above this temperature due to the disorder in the copper sublattice.

Keywords
ferrielectrics, CuInP2S6, mixed Ising model, quantum anharmonic oscillator model

Acknowledgments
We acknowledge support from the Horizon Europe Framework Programme (HORIZON-TMA-MSCA-SE), project № 101131229, Piezoelectricity in 2D-materials: materials, modeling, and applications (PIEZO 2D).

References
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