Pressure-induced softening in bulk modulus due to magneto-elastic coupling in Nd$_2$CoFeO$_6$ double Perovskite

Double perovskite oxide materials have garnered tremendous interest due to their strong spin-lattice-charge coupling. Interesting in their own right, rare-earth-based DPOs have yet to be subjected to high-pressure studies. In this paper, we have investigated the structural response of Nd$_2$CoFeO$_6$ to pressure by XRD and Raman spectroscopic measurements. From XRD data, we have observed pressure-induced structural transition from the orthorhombic phase to the monoclinic phase at about 13.8~\si{\giga\pascal}. An anomalous increase in compressibility at a much lower pressure($\sim$1.1~\si{\giga\pascal}) is seen where no structural transition occurs. At about the same pressure, a sudden drop in the slope of Raman modes is observed. Further investigation at low temperatures reveals that the B$_g$ Raman mode is strongly affected by magnetic interactions. Additional high-pressure Raman experiments with the application of a magnetic field indicated that the mentioned anomaly around 1.1~\si{\giga\pascal} can be explained by a high-spin to low-spin transition of Co$^{3+}$.