The Influence Of Interfacial Dzyaloshinskii–Moriya Interaction And Its Boundary Effect On Magnetic Dynamics

The novel spintronic devices based on heavy metal(HM)/ferromagnet(FM)composite generally have a small size,high processing speed,and low power dissipation,which make them important parts of information devices in the "Beyond Moore" era.Owing to the asymmetric interfacial structure of the FM layer,the anisotropic exchange coupling named the interfacial Dzyaloshinskii–Moriya(DM)interaction is generated at the HM/FM interface.This DM interaction plays a fundamental role in stabilizing non-trivial topological magnetic solitons,such as magnetic skyrmions and chiral domain walls(DWs).On the other hand,the DM interaction also influences the magnetic dynamics including ferromagnetic resonance(FMR),spin wave,and the motion of chiral DWs and skyrmions.These magnetic dynamics behaviors are the physical fundermental of novel magnetic information device.Therefore,the influence of DM interaction on the magnetic dynamics has attracted wide attention in recent years.Nevertheless,the DM interaction in the inner part of FM medium and that at the boundary coexist.It is challenging to distinguish their respective contributions to the magnetic dynamics.The magnetic dynamics at a nanometer scale in a very short time(ns)range is hard to characterize in experiments but can be simulated using the micromagnetic calculation.Therefore,during my working experience as a Ph.D.student,I have studied the influence of interfacial DM interaction on the magnetic dynamics through micromagnetic calculation,concentrating on differentiating the influence of DM boundary effect and the inner DM interaction on the magnetic dynamics.The investigation contains the following aspects:Firstly,the influence of DM interaction on the spin wave diffraction has been studied by micromagnetic simulation.By setting a boundary layer with a high damping coefficient,the spin wave can be absorbed at the boundary.Therefore,the influence of DM boundary effect on the diffraction of spin wave can be safely neglected.The results demonstrate that the diffraction pattern is symmetric about the slit center when the incident wave is Damon-Eschbach(DE)wave.The DM interaction changes the wavelength of the incident wave,thereby manipulates the diffraction angle.On the other hand,when backward volume spin wave is injected,the diffraction pattern is no longer symmetric.The strongest diffracted beam deviates from the slit center and the sine of the deflection angle is proportional to the DM interaction constant for a spin wave at a high frequency.The dipole-dipole interaction has negligible influence.The result of theoretical analysis is consistent with that of the simulation.This provides a possible new method for probing the DM interaction strength.Secondly,the effect of interfacial DM interaction on ferromagnetic resonance(FMR)was studied using micromagnetic simulation.The influence of DM interaction on FMR in a perpendicular-magnetized nanodisk with the radius less than 50 nanometers was studied.Unlike the in-plane-magnetized medium,the vortex is not generated in a perpendicular-magnetized film with a small area.The mode for magnetostatic resonance is absent as well.Therefore,the influence of DM interaction on FMR mainly comes from the DM interaction boundary effect.The simulation results indicate that the DM interaction boundary effect introduces a new characteristic oscillation mode: counterclockwise rotation mode.The characteristic frequency of this mode can be manipulated by the DM interaction and the size of FM medium,which provides possible route for measuring the DM interaction constant.Thirdly,the influence of DM interaction boundary effect on the motion of a chiral domain wall(DW)in a nanowire with width smaller than 500 nm was numerically investigated.The main results are as following:(i).The tilting of the Dzyaloshinskii DW driven by spin-orbit-torque(SOT)is originated from the antisymmetric DW structure at the upper and lower boundary of the nanowire.Owing to this antisymmetric DW structure,the velocity for the SOT-induced rotation of magnetic moments at the two boundaries is different,resulting in the difference of local DW velocities at two boundaries.On the other hand,the relaxation time for stabilizing DW tilting is a cubic function of the width of ferromagnetic nanowire.The turning point of the function corresponds to a critical width,and the microscopic process of DW tilting above and below this critical width is obviously different.(ii).When alternating magnetic field is applied,the DM interaction boundary effect leads to the motion of DW with periodic deformation.The traditional CCM based on rigid model fails to predict this sort of mode.(iii).Considering the possible deformation of DW,the shape of the DW under direct current(DC)magnetic field has been investigated based on the variational method.It has been proved that the final stable shape of DW under the DC magnetic field must be a slanted straight line due to the DM interaction boundary effect.The analytical solution of the DW tilting angle versus the external DC magnetic field has been derived,and it can be extended to anisotropic Dzyaloshinskii DW.Finally,two methods have been proposed to suppress the DW tilting induced by the DM boundary effect based on the interlayer ferromagnetic/antiferromagnetic exchange coupling.(i).The DW tilting can be suppressed through the interlayer ferromagnetic coupling of an anisotropic Dzyaloshinskii DW and an isotropic one.The velocity of the coupled DWs driven by SOT can be enhanced and the minimum spacing between the neighboring DWs can be reduced.(ii).The DW tilting can also be depressed by the interlayer antiferromagnetic coupling.The coupled DWs move at a high velocity under the gradient of anisotropic energy induced by electric field.Also,the Walker breakdown can be effectively suppressed.