The controlled switching between two quasistable Néel states in adsorbed antiferromagnetic Fe chains has recently been achieved by Loth et al. using tunneling electrons from an STM tip. In order to rationalize their data, we evaluate the rate of tunneling electron-induced switching between the Néel states. Good agreement is found with the experiment, permitting us to identify three switching mechanisms: (i) low STM voltage direct electron-induced transitions, (ii) intermediate STM voltage switching via spin-wave-like excitation, and (iii) high STM voltage transitions mediated by domain-wall formation. Spin correlations in the antiferromagnetic chains are the switching driving force, leading to a marked chain-size dependence. © 2013 American Physical Society.