What is a plausible mechanism for the Haber process?

Do you mean the reaction that forms ammonia? If so, it is the Haber Process.

#N_2 + 3H_2 <=> 2NH_3#

A plausible mechanism (that I just thought up, actually) for this is:

#N≡N + H-H -> HN=NH#

#HN=NH + H-H -> H_2N-NH_2#

#H_2N-NH_2 + H-H -> NH_3 + NH_3#

where each step is a reduction step of nitrogen transferring electrons to grab both hydrogen in each step (one N single bond e- pair is donated to a hydrogen, and one e- pair from the hydrogens is donated to break the single bond and bond to the other, cationic nitrogen).

The accepted mechanism is here, though.