Correspondência entre ondas de spin de um ferromagneto em uma rede favo de mel e a banda de energia do grafeno

Abstract

Spin waves are collective excitations that occur in magnetic materials. These excitations are caused by disturbances in the magnetic system. For example, a small change in temperature causes the precession of a magnetic dipole moment that interacts with neighboring leading to the spread of this disorder. This disturbance has wave character, and can propagate in the direction of any of the nearest neighbors. These waves of spin can be observed by some experimental methods, such as: the inelastic neutron scattering, inelastic scattering of light including Raman and Brillouin scattering, to name a few. The importance of spin waves emerges clearly when magnetoelectronic devices are operated at low frequencies. This situation, the generation of spin waves can sing in a significant loss of energy of these systems, because the excitation of such waves consumes a small part of the energy of the system, becoming important in the innovation process of electronic systems. These waves can be studied using mathematical models like the Heisenberg, Ising, among others. In this model, we can calculate the dispersion relation of the spin waves. The Heisenberg model can be written in terms of operators of creation and destruction through the Holstein-Primakoff transformations. The Hamiltonian that describes the spin waves is now written in terms of bosonic operators. This mathematical description is similar to Tight-Binding Hamiltonian for fermions. This Hamiltonian described, for example, graphene, a material that has recently been discovered and is being treated with much optimism for having a two-dimensional structure that leads to amazing properties. Many possibilities of applications for it have been studied. Our goal here is to make an analogy between the graphene and a magnetic system on a honeycomb lattice. In the magnetic system, we use the Heisenberg model to find the dispersion relations and understand the behavior of the spin waves of the same. While in graphene, we used the Tight-Binding model to find the energy spectrum. Underscoring we use a mathematically identical method for both and found that the curves for power modes have similar behaviors, respecting the particularities of each. Then, we calculate how these modes behave introduction of impurities in substitution sites on one or two lines of the crystal lattice.