Rarefied Band in Spectrum of Two-Magnon States of Heisenberg Ferromagnet of Clock Dial Plate

The Heisenberg isotropic exchange Hamiltonian with the nearest neighbour interactions for the ring of N = 12 nodes (the clock dial plate) with the spin 1/2 has been diagonalized within the manifold of all 66 two-magnon excitations from the ferromagnetic ground state. The spectrum consists of 5 full bands, i.e. bands defined over the whole Brillouin zone, and a single band which is doubly rarefied, i.e. defined only for even values of quasimomentum. The rarefied band is found to be dispersionless outside the centre of the Brillouin zone. It separates two bands of "weakly bounded" spin waves from two other which are "weakly antibounded". The last remaining band is situated below this collection of scattered spin waves, and describes two tightly bounded spin deviations. The spectrum exhibits dispersion, but it is degenerate (singlet and quintet) at the boundary of the Brillouin zone.