Energy spectrum of magnetic quantum wires

Recent technology of polymers allows to form short chains of magnetic metal ions (e.g. Cr8, Fe8, Fe10, Mn12, etc.). These structures can be considered as magnetic quantum nanowires. Quantum properties of such systems are strictly described by Heisenberg model of chains with finite number of nodes. The quantum solutions of finite nanomagnets are different from those of mesoscopic and infinite lengths. The Bethe hypothesis is extremely useful in exact solving of the problem. In the paper we apply the Bethe theory to wire nanomagnets consisting of spin in each node for the length N = 6 and 8. The complete set of eigenfunctions and eigenvalues was derived by this method. The scattering and bounded states of the system were selected. The structure of energy bands is discussed as a function of total spin S as well as a quasimomentum k of spin waves. The shape of energy bands in the Brillouin zone is the same as for asymptotic case. The spin representation fulfills rotational model.