  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$_8$.
