  MCrS2 compounds (M=Li, Na, K, Cu, Ag, and Au) with triangular Cr layers show
large variety of magnetic ground states ranging from 120-degree
antiferromagnetic order of Cr spins in LiCrS2 to double stripes in AgCrS2,
helimagnetic order in NaCrS2, and, finally, ferromagnetic Cr layers in KCrS2.
On the base of ab-initio band structure calculations and an analysis of various
contributions to exchange interactions between Cr spins we explain this
tendency as originating from a competition between antiferromagnetic direct
nearest-neighbor d-d exchange and ferromagnetic superexchange via S p states
which leads to the change of the sign of the nearest neighbor interaction
depending on the radius of a M ion. It is shown that other important
interactions are the third-neighbor interaction in a layer and interlayer
exchange. We suggest that strong magneto-elastic coupling is most probably
responsible for multiferroic properties of at least one material of this
family, namely, AgCrS2.
