  We investigate electronic and magnetic structures of the Mn chains supported
on the CuN surface using first-principle LSDA and LDA+U calculations. The
isotropic exchange integrals and anisotropic Dzyaloshinskii-Moriya interactions
between Mn atoms are calculated using Green function formalism. It is shown
that the account of lattice relaxation and on-site Coulomb interaction are
important for accurate description of magnetic properties of the investigated
nanosystems. We predict a weak ferromagnetism phenomenon in the Mn
antiferromagnetic nanochains on the CuN surface. The value of a net magnetic
moment and direction of spin canting are calculated. We show that some
experimental features may be explained using anisotropic exchange interactions.
