Anomalous spin excitation spectra in honeycomb systems Na_2+xM₂TeO₆ (M=Co and Ni) with zig-zag magnetic ordering

The role played by the magnetic frustration arising from competing exchange interactions on the magnetic properties of honeycomb systems continues to be the subject of intense research. Competition between first, second and third neighbor exchange interactions results in rich magnetic phase diagrams that include Néel, zigzag, stripy, and spiral orders. Anisotropic exchange interactions that arise from spin-orbit coupling can lead to various exotic quantum-disordered states. Here we discuss the results of neutron scattering measurements performed on the honeycomb systems Na_2+xM₂TeO₆ (M=Co and Ni). The diffusive Na atoms provide an effective control of the interlayer magnetic couplings, and therefore a route for tuning the lattice dimensionality. The changes in the static magnetic order and spin-dynamics for samples with different Na content are discussed. We also show that spin-wave excitation spectra obtained from stoichiometric powder samples cannot be well described using a simple isotropic Heisenberg spin Hamiltonian. An alternative model with anisotropic exchange coupling is evaluated and discussed.