I am not perfectly sure, but let me try to give a guess anyway.
In short: Your are doing it right and the programs behaves correctly. If you make a carbon wire as it would be in nature,
it would be spin-unpolarized, hence if you make a carbon wire with the correct lattice constant as you do, you will
end up with the true ground state of the atomic chain.
If the atoms in the atomic chain is very long from one another, then the physics is sudden gone, since instead of atomic chain
you will have a string of very weakly, almost independent, atoms, and this system can be made spin-polarized,
and due to the very weak interaction between the atoms it will preserve the initial spin-configuration and can therefore have
a magnetoresistance