Griffiths-like phase, large magnetocaloric effect, and unconventional critical behavior in the NdSrCoFeO6 disordered double perovskite

A B-site disordered double perovskite $\mathrm{NdSrCoFe}{\mathrm{O}}₆$ was successfully synthesized by the conventional sol-gel method. Detailed experimental analyses revealed that $\mathrm{NdSrCoFe}{\mathrm{O}}₆$ crystallizes in the orthorhombic $Pnma$ space group, in which ${\mathrm{Co}}^2+/3+$ and ${\mathrm{Fe}}^3+/4+$ ions are randomly distributed at the BB\ensuremath{'} sites, and ${\mathrm{Sr}}²⁺$ and ${\mathrm{Nd}}³⁺$ ions are respectively ordered at the A and A\ensuremath{'} sites in an alternating arrangement along the $c$ direction. $\mathrm{NdSrCoFe}{\mathrm{O}}₆$ has a semimetallic-to-semiconducting transition nature, and a paramagnetic-ferromagnetic (FM) second-order phase transition originating from the complex hybridization between Co $3d$ and O $2p$ states is also found to occur at ${T}_{\mathrm{C}}\ensuremath{\approx}150$ K. Then the spin coupling between ${\mathrm{Fe}}⁴⁺\ensuremath{\leftrightarrow}{\mathrm{Co}}³⁺$ and ${\mathrm{Fe}}³⁺\ensuremath{\leftrightarrow}{\mathrm{Co}}²⁺$ randomly distributed on the B and B\ensuremath{'} sites leads to a FM cluster spin-glass behavior with characteristic parameters of $k=0.01, {T}_{\mathrm{SG}}=82.7$ K, $zv=1.89$, and ${\ensuremath{\tau}}₀=0.46\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ s. Additionally, Griffiths-like phase behavior was observed in the region ${T}_{\mathrm{C}}<T<{T}_{\mathrm{GP}}$, with ${T}_{\mathrm{GP}}=245$ K, consistent with the power law exponent of $\ensuremath{\lambda}=0.74$. The maximum isothermal magnetic entropy change $\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_M^{\mathrm{max}}\ensuremath{\approx}1.84\phantom{\rule{0.16em}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{k}{\mathrm{g}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ and relative cooling power $\ensuremath{\approx}43.8\phantom{\rule{0.16em}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{k}{\mathrm{g}}^{\ensuremath{-}1}$ under a field of 40 kOe also indicate a magnetocaloric coupling wherein fitted critical exponents $\ensuremath{\beta}=1.384, \ensuremath{\gamma}=0.621$, and $\ensuremath{\delta}=1.421$ are far from any conventional universality class. Density functional theory calculations demonstrated spin short- and long-range ordering competitions for Fe/Co at BB\ensuremath{'} sites, which arise predominantly from the stronger negatively charged ligand interaction with Co $3d$ orbitals and the weakest Fe $3d$ orbitals. This unconventional behavior is expected to be the main reason for the experimentally observed magnetic exchange distance decreasing with $J(r)\ensuremath{\approx}{r}^{\ensuremath{-}4.7}$.