  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 N\'eel 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 $\alpha=\frac{d\log T_N}{d\log
V}=-\frac{10}{3} \approx -3.3$, to a $\alpha$ value of -6.0 $\pm$ 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 Ne\'el
temperature, $\alpha$ 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.

Strongly Correlated Electrons;Materials Science