Excitation of finite chains of magnetic atoms adsorbed on a surface by tunneling electrons from a scanning tunneling microscope tip is studied using a Heisenberg Hamiltonian description of the magnetic couplings along the chain and a strong coupling approach to inelastic tunneling. 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 tunneling electrons are determined from the results on the finite chains. Both ferromagnetic and antiferromagnetic couplings are considered, leading to very different results. In particular, in the antiferromagnetic case, excitations linked to the entanglement of the chain ground state are evidenced.
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