Self-consistent approximation for dimerization of ferrimagnets on chains and square lattices

Abstract

We have used nonlinear spin-wave theory to study dimerization of a Heisenberg system with alternating spins ${s}_{1}$ and ${s}_{2}$ on a linear chain and a square lattice for several possible dimerized configurations. It shows that the ground-state energy in both dimensions gets lowered against the dimerization for the three alternating spin systems. In two dimensions the plaquette configuration is found to be the most favorite one among the rest. An ansatz on variable nearest-neighbor exchange coupling gives rise to uniform power law ${\ensuremath{\delta}}^{\ensuremath{\nu}}/|\mathrm{ln}\ensuremath{\delta}|$ for the dependence of magnetic energy gain, energy gap, and magnetization for both the alternating chains as well as square lattices over the entire range of the dimerization parameter $\ensuremath{\delta}$ for the three spin systems. Our calculations using the unexpanded exchange coupling also allows the energy of the gapped excitation spectrum to be $\ensuremath{\delta}$ dependent.