Abstract
The lifetime of magnetic excitations in finite 1D-supported Heisenberg chains of magnetic atoms is studied theoretically for a model system formed of $S$ $=$ \textonehalf{} spins. Both ferromagnetic and antiferromagnetic cases are considered as well as open chains and rings of atoms. Different chain lengths are considered allowing extrapolation to infinite chains. All the excited magnetic states in the finite chains and rings are studied, not only the spin-wave mode. The magnetic excitations decay by electron-hole pair creation in the substrate. As the main result, for all the systems considered, the decay rate appears to vary approximately proportionally to the excitation energy of the state, with a proportionality constant independent of the strength of the Heisenberg exchange term. In certain finite systems, a stable state is evidenced at low energy, associated with a special spin coupling structure.
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