Magnon dispersions in quantum Heisenberg ferrimagnetic chains at zero temperature

Within the Dyson-Maleev boson formalism, we study the zero-temperature magnon dispersions in a family of one-dimensional quantum Heisenberg ferrimagnets composed of two different spins $(S_1,S_2)$ in the elementary cell. It is shown that the spin-wave theory can produce precise quantitative results for the low-energy excitations. The spin-stiffness constant ${\rho }_s$ and the optical magnon gap $\mathrm{\Delta }$ of different $(S_1,S_2)$ ferrimagnetic systems are calculated, respectively, to second and third order in the quasiparticle interaction. The spin-wave results are compared with available numerical estimates.