We reinvestigate the pressure dependence of the crystal structure and antiferromagnetic phase transition in MnTe_2 by the rigorous and reliable tool of high pressure neutron powder diffraction. First-principles density functional theory calculations are carried out in order to gain microscopic insight. The measured Néel temperature of MnTe_2 is found to show unusually large pressure dependence of 12 K GPa^-1. This gives rise to large violation of Bloch's rule given by α=d T_N/d V=-10/3≈ -3.3,

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... a α value of -6.0 ± 0.1 for MnTe_2. The ab-initio calculation of the electronic structure and the magnetic exchange interactions in MnTe_2, for the measured crystal structures at different pressures, gives the pressure dependence of the Neél temperature, α to be -5.61, in close agreement with experimental finding. The microscopic origin of this behavior turns to be dictated by the distance dependence of the cation-anion hopping interaction strength.