Cluster spin-glass state with magnetocaloric effect in open framework structure of the Prussian blue analog molecular magnet K2x/3Cu[Fe(CN)

We report on the existence of cluster spin-glass behavior and magnetocaloric properties of potassium-ion-intercalated copper hexacyanoferrate open framework material ${\mathrm{K}}_{2x/3}\mathrm{Cu}{[\mathrm{Fe}{(\mathrm{CN})}_{6}]}_{2/3}\ifmmode\cdot\else\textperiodcentered\fi{}n{\mathrm{H}}_{2}\mathrm{O}\phantom{\rule{4pt}{0ex}}(x=0$ and 0.3) synthesized using a coprecipitate method. The structural properties are investigated using room-temperature powder x-ray and neutron diffraction measurements. The results derived from the fitted x-ray and neutron diffraction data using the Rietveld refinement method reveal that both compounds are in pure single-nanocrystalline phase with face-centered cubic crystal structure of space group $Fm\text{\ensuremath{-}}3m$. The room-temperature M\"ossbauer spectroscopy reveals the presence of a low-spin (LS) state of ${\mathrm{Fe}}^{\mathrm{III}}$ for compound $x=0$, whereas for compound $x=0.3$, LS states of ${\mathrm{Fe}}^{\mathrm{II}}$ and ${\mathrm{Fe}}^{\mathrm{III}}$ are evident. The chemical and M\"ossbauer studies reveal stoichiometries of compounds as ${\mathrm{Cu}}^{\mathrm{II}}{[{\mathrm{Fe}}^{\mathrm{III}}{(\mathrm{CN})}_{6}]}_{2/3}\ifmmode\cdot\else\textperiodcentered\fi{}3.75\phantom{\rule{0.16em}{0ex}}{\mathrm{H}}_{2}\mathrm{O}\phantom{\rule{4pt}{0ex}}(x=0)$ compound (1) and ${\mathrm{K}}_{0.2}{\mathrm{Cu}}^{\mathrm{II}}{[{\mathrm{Fe}}_{0.3}^{\mathrm{II}}{\mathrm{Fe}}_{0.7}^{\mathrm{III}}{(\mathrm{CN})}_{6}]}_{2/3}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}\phantom{\rule{4pt}{0ex}}(x=0.3)$. The dc magnetization measurement shows a magnetic phase transition from a paramagnetic to a ferromagneticlike state below the magnetic ordering temperatures of $\ensuremath{\sim}18.6$ and $\ensuremath{\sim}16.3$ K for the compounds (1) and (2), respectively. The positive value of Curie constants obtained from the fitting of the Curie-Weiss law in the paramagnetic region confirms the presence of ferromagnetic interaction in both compounds. The spin-only effective paramagnetic moments are found to be $\ensuremath{\sim}2.3$ and $\ensuremath{\sim}1.9\phantom{\rule{0.16em}{0ex}}\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ for compounds (1), and (2), respectively. The analysis of ac susceptibility measurements as a function of frequency shows that the spin dynamics follows the Vogel-Fulcher and the power law. The best fitted values of ${\ensuremath{\tau}}_{o}=4.037\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ s and $3.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ s for compounds (1) and (2), respectively, confirm a cluster spin-glass behavior of both compounds. A neutron depolarization study further validates the cluster spin-glass nature of both compounds. The magnetocaloric effect for both the compounds is further investigated and found to be higher for compound (1) than compound (2). The maximum magnetic entropy change---$\mathrm{\ensuremath{\Delta}}{S}_{M}$ under a magnetic field of 50 kOe is found to be $\ensuremath{\sim}6.61$ and $2.95\phantom{\rule{0.16em}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{k}{\mathrm{g}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ for compounds (1) and (2), respectively. The relative cooling power is found to be $78.3\phantom{\rule{0.16em}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{k}{\mathrm{g}}^{\ensuremath{-}1}$ for compound (1) and $40\phantom{\rule{0.16em}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{k}{\mathrm{g}}^{\ensuremath{-}1}$ for compound (2).