Thermal Conductivity of Localized Electrons on Magnetic Ordered Monolayer Graphene

We study the thermal conductivity of a spin-1/2 two-dimensional anisotropic antiferromagnet on honeycomb lattice in the presence of antiferromagnetic long range ordering. The conductivity has been studied along zigzag direction. Next nearest neighbor exchange coupling has been added to the model Hamiltonian. The possible effects of spin-orbit coupling are investigated by adding Dzyaloshinskii-Moriya interaction to the model Hamiltonian. Such interaction creates anisotropic effects in the model Hamiltonian. The original antiferromagnetic model hamiltonian is mapped to a bosonic model via linear spin wave theory in the context of Holstein Primakoff transformations. The Green's function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. We have found the temperature dependence of static thermal conductivity in the magnetic long range ordering phase for various next nearest neighbor coupling constant and anisotropy parameter. Furthermore we have studied the temperature dependence of the static thermal conductivity for various Dzyaloshinskii-Moriya interaction strength and next nearest neighbor coupling constants.