  We report on a theoretical study of the lifetime of the first excited state
of spin chains made of an odd number of Fe atoms on Cu2N/Cu(100). Yan et al
(Nat. Nanotech. 10, 40 (2015)) recently observed very long lifetimes in the
case of Fe3 chains. We consider the decay of the first excited state induced by
electron-hole pair creation in the substrate. For a finite magnetic field, the
two lowest-lying states in the chain have a quasi-N\'eel state structure. Decay
from one state to the other strongly depends on the degree of entanglement of
the local spins in the chain. The entanglement in the chain accounts for the
long lifetimes that increase exponentially with chain length. Despite their
apparently very different properties, the behaviour of odd and even chains is
governed by the same kind of phenomena, in particular entanglement effects. The
present results account quite well for the lifetimes recently measured by Yan
et al on Fe3
