  A comprehensive study of thermodynamic properties of three samples of
bimetallic molecular magnets
[Co$^{\mathrm{II}}$(pyrazole)$_{4}$]$_{2x}$[Fe$^{\mathrm{II}}$(pyrazole)$_{4}$]$_{2(1-x)}$[Nb$^{\mathrm{IV}}$(CN)$_{8}$]$\cdot$4H$_{2}$O
with $x$=0 (Co$_{2}$Nb), 0.5 (CoFeNb), and 1 (Fe$_{2}$Nb) is reported. The
three samples display the same crystallographic structure crystallizing in the
tetragonal system with space group $I4_1/a$. Their heat capacities are measured
in the temperature range 0.36-100 K without applied field as well as in the
field of $\mu_0 H$ = 0.1, 0.2, 0.5, 1, 2, 5, and 9 T. The results imply the
presence of the second-order phase transitions to magnetically ordered phases
at 4.87(8) K, 7.1(2) K, and 8.44(3) K for $x$=0, 0.5, and 1, respectively. The
corresponding thermodynamic functions are analyzed to discuss the stability of
the mixed compound and the magnetocaloric effect (MCE). The Gibbs energy of
mixing is found to be positive but smaller in magnitude than the energy of
thermal fluctuations indicating that the mixed sample is marginally stable in
the full detected temperature range. The enthalpy of mixing is negative, which
points to an ordered arrangement of the Co(II) and Fe(II) ions in the solid
solution CoFeNb. The negative values of the entropy of mixing are explained by
considering the enhanced rigidity of the crystal lattice of the solid solution
sample. To extract the magnetic contribution to the heat capacity an approach
based on a reasonable frequency spectrum is adopted. Taking advantage of the
in-field heat capacity measurements MCE was described in terms of the
isothermal entropy change $\Delta S_\mathrm{M}$ and the adiabatic temperature
change $\Delta T_\mathrm{ad}$. The magnitudes of these quantities are typical
for the class of molecular magnets.
