Magnetic properties of Fe 2Na 3(PO 4) 3—I. Calculation of magnon dispersion curves in a complex structure

Abstract

A model capable of reproducing the magnon excitations observable in the anti-ferromagnetic phase of Fe 2Na 3(PO 4) 3 is proposed. This model takes into account all the super-super-exchange interactions between the spins of the four Fe 3+ of the unit cell and the neighboring spins. It is assumed that spins are collinear. The calculation method of the magnon dispersion curves is based on Saenz's formalism, and the analytical derivation of the magnon energies is performed for ideal hexagonal symmetry. Numerical calculations of magnon dispersion curves and spin deviations vs exchange interactions are reported, both in the hexagonal and triclinic symmetries. It appears that four modes can be distinguished in the triclinic symmetry. Magnetic structure stability considerations demonstrate that exchange interaction frustrations are consistent with the anti-ferromagnetic structure of the compound; it is shown that magnon dispersion curves are strongly dependent on the presence of frustrated exchange interactions.