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Griffiths phase-like behaviour and spin-phonon coupling in double perovskite Tb$_{2}$NiMnO$_{6}$

The Griffiths phase-like features and the spin-phonon coupling effects observed in Tb$_2$NiMnO$_6$ are reported. The double perovskite compound crystallizes in monoclinic $P2_1/n$ space group and exhibits a magnetic phase transition at $T_c \sim$ 111 K as an abrupt change in magnetization. A negative deviation from ideal Curie-Weiss law exhibited by 1/$χ(T)$ curves and less-than-unity susceptibility exponents from the power-law analysis of inverse susceptibility are reminiscent of Griffiths phase-like features. Arrott plots derived from magnetization isotherms support the inhomogeneous nature of magnetism in this material. The observed effects originate from antiferromagnetic interactions which arise from inherent disorder in the system. Raman scattering experiments display no magnetic-order-induced phonon renormalization below $T_c$ in Tb$_2$NiMnO$_6$ which is different from the results observed in other double perovskites and is correlated to the smaller size of the rare earth. The temperature evolution of full-width-at-half-maximum for the {\it stretching} mode at 645 cm$^{-1}$ presents an anomaly which coincides with the magnetic transition temperature and signals a close connection between magnetism and lattice in this material.