  Excitation of finite chains of magnetic atoms adsorbed on a surface by
tunnelling electrons from an STM (Scanning Tunnelling Microscope) tip is
studied using a Heisenberg Hamiltonian description of the magnetic couplings
along the chain and a strong coupling approach of inelastic tunnelling. The
excitation probability of the magnetic levels is very high and the excitation
spectra in chains of different lengths are very similar. The excitations in
finite chains can be considered as spin waves quantized in the finite object.
The energy and momentum spectra of the spin waves excited in the idealized
infinite chain by tunnelling electrons are determined from the results on the
finite chains. Both ferro- and antiferromagnetic couplings are considered,
leading to very different results. In particular, in the anti-ferromagnetic
case, excitations linked to the entanglement of the chain ground state are
evidenced.
