Research And Application Of Gauss-Seidel Projection Methods In Micromagnetic Simulation

Micromagnetic simulation is an important tool to study various dynamic be-haviours of magnetic order in magnetic materials.The underlying model of the fer-romagnets is the Landau-Lifshitz-Gilbert equation.In equation,the magnetization dynamics is driven by the gyromagnetic torque term and Gibert damping term which control the different behaviours of the magnetic moments.Compared with ferromag-netic counterpart,antiferromagnetic and ferrimagnetic materials are considerd as the outstanding candicate materials in the future of spintronic applications,since these ma-terials display ultrafast dynamics and are robust against the magnetic perturbation.Unlike ferromagnetic materials,there are(at least)two sets of magnetic moments in antiferromagnets and ferrimagnets with antiparallel direction,and their dynamics are modeled by the coupled Landau-Lifshitz-Gilbert equation system with the additional fileds origanited from interlattice exchange effects in effective field.Numerically,one of the most popular methods is the Gauss-Seidel projection method devoloped by Xiao-Ping Wang,Carlos Garcia-Cervera and Weinan E for fer-romagnets in 2001.The gyromagnetic torque term and damping term are treated differently and since the time splitting method,the vector field equation are decoupled through the Gauss-Seidel manner,and it needs to solve equation system with constant coefficients 7 times in one time step.Based on the Gauss-Seidel projection method,we deal with the gyromagnetic term and damping term simultaneously by different update strategies,so there are two improved schemes.The two improved schemes de-duce the time costs since only equation system with constant coefficients 5 times and 3 times to be solved,respectively.These methods are verified to be unconditionally sta-ble through comparing with the original Gauss-Seidel projection method numerically.Micromagnetie simulation is also presented with same hysteresis loops.Furthermore,we apply three Gauss-Seidel projection methods to the antiferro-magnetic and ferrimagnetic Landau-Lifshitz-Gilbert equation system,and verify the unconditionally stable with respect to the meshgrid and sublattice exchange parame-ters numerically.In terms of micromagnetic simulations,femtosecond dynamics,Neel wall structure,and phase transition in presence of an external magnetic field for anti-ferromagnets are provided with the femtosecond stepsize.Numerical simulations are consistent with physical experiments.In addition to experiments,the proposed meth-ods open up an alternative way to understand femtosecond magnetization dynamics in antiferromagnetic and ferrimagnetic materials.