# Theoretical Study of the Phonon Energy and Specific Heat of Ion-Doped LiCsSO4—Bulk and Nanoparticles

## TL;DR

This paper studies how ion doping and nanoparticle size affect the phonon energy and specific heat of LiCsSO4, focusing on temperature-dependent behavior and phase transitions.

## Contribution

The novel contribution is the theoretical analysis of spin–phonon interactions and their impact on phonon modes and specific heat in ion-doped LiCsSO4 nanoparticles.

## Key findings

- The first phonon mode increases with temperature while the second decreases, due to differing anharmonic spin–phonon interaction signs.
- Doping with K, Rb, and NH4 ions enhances the ferroelastic phase transition temperature TC, whereas doping with Na, K, or Rb on the Li site reduces it.
- Specific heat decreases with smaller nanoparticle size and increases with higher K doping concentration.

## Abstract

Using a microscopic model, the temperature dependence of two phonon modes, ω0 = 32 cm−1 and 72 cm−1, and their damping of the ferroelastic LiCsSO4 compound, are calculated within Green’s function technique. It is observed that the first mode increases whereas the second one decreases with increasing temperature T. This different behavior is explained with different sign of the anharmonic spin–phonon interaction constant. At the ferroelastic phase transition temperature TC, there is a kink in both modes due to the spin–phonon interaction. The phonon damping increases with T, and again shows an anomaly at TC. The contributions of the spin–phonon and phonon–phonon interactions are discussed. TC is reduced by decreasing the nanoparticle size, and can be enhanced by doping with K, Rb and NH4 ions at the Cs site. TC decreases by doping with Na, K or Rb on the Li site. The specific heat Cp also shows a kink at TC. Cp decreases with decreasing nanoparticle size and the peak disappears, whereas Cp increases with increasing K ion doping concentration.