The Detection Principle Of Spin Waves Propagating In Domain Wall

The traditional CMOS devices has hit a bottleneck after decades of development due to the contradiction between low energy consumption and high integration.However,the spin waves are highly expected in the field of information transmission or data processing because of its excellent characteristics such as Joule-heat-free during propagation in magnetic insulator and nanometer-scale wavelength range.Similar to electromagnetic waves,it is necessary to prepare a corresponding magnetic structure to guide the propagation of the spin wave,that is,the spin-wave waveguide.At present,it is a good choice to use the magnetic domain walls as spin-wave waveguides for the following two reasons:?1?The magnetic domain wall is equivalent to a potential well,which means the spin waves will be bounded in the domain wall with low energy consumption when the frequency is appropriate;?2?The magnetic domain wall can be moved only by a small external magnetic field.This feature provides a more convenient manipulation on spin waves.Currently,Micro-focused Brillouin Light Scattering?BLS?is widely used to image the spin waves.However,there are some drawbacks,for example,expensive and large optical equipments.If the spin waves are defined in the magnetic domain wall,it is hardly to be detected form outside the wall.Therefore,the main content of this paper is to propose a method to detect the information of the spin wave propagating in the magnetic domain wall.The main work of this paper is divided into two directions:one is to theoretically calculate the spin-wave nonlinear effect of three-magnon to obtain the method of detection;the other is to use the method of micromagnetic simulation to verifify the theory proposed by us.Firstly,we give a basic model with Ne?el type magnetic domain wall,whose static Walker solution is obtained by our next calculation.In the mean time,we set two spin waves,i.e.,??_i,k_i?in left domains and??_b,k_b?in the domain wall,of which the dispersion relations are obtained by considering some small parameters in the main direction of magnetic moment and the LLG equation.Next,we focus on the nonlinear process of three-magnon.In the calculation,we obtain the theoretical formula of the conluence process and the splitting process respectively by taking the energy conservation and momentum conservation into consideration.In a word,the spin waves scattered into a nother domains in the confluence process are satisified the following equations:?=?_i+?_b andk=k_i+k_b;Similarily,the conditions of the spin waves generated from the splitting process are respectively?=?_i-?_b andk=?|k _i|²-2|k_b|²?^1/2e_?-k_b,where e_?represents the direction of the vertical magnetic domain wall.The second part of the paper is mainly to numerically verify our theory above by using the micromagnetic simulation software Mumax3.We first give the dispersion relations of the two spin waves which agree excellently with analytical formula.To further confirm the existence of the bounded spin waves,we show two figures about spin-wave propagation with two different frequency,i.e.,one is higher than the gap and the other is lower.Next,we use Matlab to perform FFT analysis on the simulated data,which verifies the three-magnon theory including the confluence process and the splitting process.Finally,we discuss the relationship between the amplitude of the microwave field that excites the spin waves both in domains and domain walls and the three-magnon intensity,and then we further illustrate the low energy consumption characteristics of the magnetic domain walls as the waveguides by comparing the power of the two microwave fields.