An adaptive computational method for domain wall dynamics (abstract)

The dynamics of magnetic domain walls is a subject of intensive computer simulation of last years. Now it is well understood, that strongly twisted structures (like horizontal Bloch lines) of domain walls can be created. In some cases this HBL can have a very small localization region. Appearance of such inconvenient objects, like HBL, states a new scale for numerical model and it required a significant increase of node number for the uniform grid model. The main idea of the new adaptive computational method for LLG equation for two-dimensional (2D) domain wall dynamics is to inject and delete additional nodes only to the HBL localization region, using a special target function, which is based on the twisting angle of the domain wall. Node injection occurs when HBL is created, and node deleting occurs when HBL is breakthrough. The conjugated gradient method was used for fast demagnetization field computation by two Dirichlet problems for Poisson equations. We show an effective application of this method for 2D computations of domain wall dynamics for bubble film with parameters: Q=4, D=3(l), α=0.2, h=(0,8,−3), (Ms) [Here Q is the quality factor of the film, D the film thickness in characterization units, α the damping parameter, h the external magnetic field in Ms units, 8(Ms) the value of in-plane magnetic field via chirality, −3(Ms) is the driven magnetic field.] We found that HBL has very strong localization in this case. To carry out this computation we need nx×nz=65×162 for uniform grid sytem, and only nx×nz=33×60 for adaptive grid system. A color computer movie was created for this case. The new mechanics of HBL generation and breakthrough is discussed. Here we can see significant asymmetry in HBL generation: two HBL created at one moment at the lower surface of the film, but upper HBL goes to the upper surface of the film and the lower goes to the opposite direction. The next pair of HBL is created at the lower surface of the film at the same place.