Magnetostriction and ferroelectric state in AgCrS$_2$

The band structure calculations in the GGA+U approximation show the presence of additional lattice distortions in the magnetically ordered phase of AgCrS$_2$. The magnetostriction leads to formation of the long and short Cr-Cr bonds in the case when respective Cr ions have the same or opposite spin projections. These changes of the Cr lattice are accompanied by distortions of the CrS$_6$ octahedra, which in its turn leads to development of the spontaneous electric polarization.