  We perform a comparative study of the KCr3As3 and the K2Cr3As3 quasi 1D
compounds, and show that the strong interplay between the lattice and the spin
degrees of freedom promotes a new collinear ferrimagnetic ground state within
the chains in presence of intrachain antiferromagnetic couplings. We propose
that the interchain antiferromagnetic coupling in KCr3As3 plays a crucial role
for the experimentally observed spin-glass phase with low critical temperature.
In the same region of the parameter space, we predict K2Cr3As3 to be
non-magnetic but on the verge of the magnetism, sustaining interchain
ferromagnetic spin fluctuations while the intrachain spin fluctuations are
antiferromagnetic.
