# Characteristic temperatures of a triplon system of dimerized quantum magnets

## TL;DR

This paper investigates the thermodynamic behavior of triplon systems in dimerized quantum magnets, introducing the inversion temperature concept and analyzing phase transitions related to Bose-Einstein condensation under magnetic fields.

## Contribution

It introduces the inversion temperature for dimerized quantum magnets and explores its relation to BEC and phase transitions in these systems.

## Key findings

- Inversion temperature is finite and exceeds the BEC critical temperature in 3D dimerized magnets.
- Below the inversion temperature, triplons can form a liquid phase transitioning to a superfluid.
- Calculated the dependence of inversion temperature on magnetic field for specific quantum magnets.

## Abstract

Exploiting the analogy between ultracold atomic gases and the system of triplons, we study magneto-thermodynamic properties of dimerized quantum magnets in the framework of Bose -Einstein condensation (BEC). Particularly, introducing the inversion (or Joule - Thomson) temperature $T_{JT}$ as the point where Joule - Thomson coefficient of an isenthalpic process changes its sign, we show that for a simple paramagnet, this temperature is infinite, while for three-dimensional (3D) dimerized quantum magnets it is finite and always larger than the critical temperature $T_c$ of BEC. Below the inversion temperature $T<T_{JT}$ the system of triplons may be in a liquid phase, which undergoes a transition into a superfluid phase at $T\le T_c<T_{JT}$. The dependence of the inversion temperature on the external magnetic field $T_{JT} (H)$ has been calculated for quantum magnets of TlCuCl$_3$ and Sr$_3$Cr$_2$O$_8$.