Properties Of Spin Waves In Monolayer And Bilayer Magnetic Graphene Structures

In this paper,the quantum Green's function method and the Heisenberg model are used to study the spin-wave frequencies,the spin-wave density of states,and the spatial distribution of spin waves in magnetic monolayer graphene structures,magnetic asymmetric and symmetric bilayer graphene structure.The effects of temperatures,interlayer exchange coupling and external magnetic field,anisotropy on the properties of spin waves has been investigated.For the monolayer graphene structure,there is only one spin-wave spectra.When the temperature increases,the spin-wave frequencies decrease.The spin-wave frequencies increase with increasing the external magnetic field and the anisotropy,the anisotropy has less effect on the spin-wave frequency.The peaks of the spin-wave density of states in the monolayer graphene structure decrease with increasing the temperature,and increase with increasing the external magnetic field and the anisotropy.For magnetic asymmetric bilayer graphene structures,there are two spin spectra.We have discovered a special wave vector.When the wave vector is greater than or equal to the special wave vector,two spin waves propagate in two different layers of the bilayer graphene structure,respectively.We define this special wave vector as the critical wave vector k_c,the interlayer exchange coupling has a greater influence on the critical wave vector k_c.In order to study the spatial distribution of two spin waves in the bilayer asymmetric graphene structure in different spin-wave frequency ranges,we divided the spin-wave frequency into four special ranges.In a frequency range,two spin wave propagate in different layers,respectively.In another frequency range,two spin waves can propagate in layer 1 as well as layer 2.Therefore,in this range,the interference of two spin waves with same frequency and different wavelength can be achieved in layer 1 or layer 2 of the magnetic asymmetric bilayer graphene structure.The frequency range of spin wave interference increases with increasing the interlayer exchange coupling and the external magnetic field,and decreases with increasing the temperature.When the interlayer exchange coupling and the intralayer exchange coupling are equal,the frequency range of spin wave interference is the widest.The interference frequency range of spin waves propagating along Y-direction is the same as that of spin wave propagating along X-direction.For magnetic symmetric bilayer graphene structure,two spin waves have the same spatial distribution in layer 1 and layer 2,due to the symmetry of the system structure.Therefore,the spin-wave frequency range can be divided into three parts.In a frequency range,two spin waves can propagate in layer 1 as well as layer 2 of the bilayer graphene structure.Consequently,in this frequency range,the interference of two spin waves with same frequency and different wavelength can be achieved in layer 1 or layer 2 of the magnetic symmetric bilayer graphene structure.The frequency range of spin wave interference increases with increasing the interlayer exchange coupling,and decreases with increasing the temperature and the external magnetic field.The interference frequency range of spin waves propagating along Y-direction is greater than that of spin wave propagating along X-direction.The results of this paper are useful for understanding the propagation properties of spin waves in a graphene structures,and are beneficial to the study of spin-wave logic devices.