Non-equilibrium Critical Dynamics In Magnetic Systems Based On Landau-Lifshtiz-Gilbert Equation

The next-generation magnetic memory devices and magnetic logic devices based on magnetic domain and domain wall dynamics in magnetic materials are characterized by high density and low power consumption.In these devices,the information are recorded by the magnetic domains and domain walls.An understanding of the magnetic domain and domain wall motion properties and how to effectively control their motion are important issues in theory and application.Previously,the Ising model based on Monte Carlo simulation and the elastic string model were used to study the dynamic properties of magnetic domains and domain walls.These models are general,but do not capture the unique properties of magnetic materials,such as spin waves,Walker breakdown,and the driving effects of the current.Based on the elastic string model,the domain wall is sup-posed to be described by a single-valued elastic string.and detailed microscopic structures is not concerned.So it is impossible to describe microstructures such as overhangs and islands.The Ising model based on Monte Carlo simulation overcomes the shortcomings of the elastic string model,but it can not describe the real dynamic process.The Landau-Lifshitz-Gilbert(LLG)equation is a basic equation describing the dynamics of a magnetic system.The motion of the domain wall,the propagation of spin waves,and the dynamics of the Skyrmion can be investigated based on this equation.In this paper,we introduce the numerical simulation method of the LLG equation at zero temperature and the finite temperature.The order-disorder phase transition caused by temperature and the magnetization reversal caused by external magnetic field near the Curie temperature are carefully investigated.Besides,We study the pinning-depinning phase transition of the domain wall motion driven by the current and the external magnetic field at zero temperature,as well as the thermal rounding of the domain wall at the finite temperature in the disordered magnetic film.The reversal process of magnetic domains in magnetic materials is an important topic.How to reduce the coercivity and switching the magnetic domain more efficiently is of great significance for magnetic memory devices.It is known that the coercivity can be greatly reduced near the Curie temperature,so that a small driving force can switching the magnetic domain.We used the stochastic LLG equation to investigate the ordered-disorder phase transition of the magnetic film.The Curie temperature and the critical exponents are accurately determined based on the dynamic approach.The results are consistent with the experimental measurements.Besides,the process of magnetization reversal caused by external magnetic field near the Curie temperature are simulated,and the critical exponent,which describes the response the external magnetic field,are obtained.The pinning phenomenon of the magnetic domain wall caused by defects is a hotspot in theory and experiment,and the understanding of this phenomenon provides a guidance in the application of magnetic devices.After introducing the domain wall motion in the absence of defects,the LL-G equation are simulated to study the pinning-depinning phase transition of domain wall motion driven by the current and the external magnetic field in the presence of defect.At zero temperature,we measured the phase transition point and critical exponents of the pinning-depinning phase tran-sition,and compared them with other models.The thermal rounding of the domain wall activated by finite temperatures is investigated.The thermal rounding exponent agrees well with the exper-imental one.More importantly,we find the adiabatic spin-transfer torque caused by the current plays a distinct role in the domain-wall depinning phase transition,while the non-adiabatic spin-transfer torque may suppress the adiabatic spin-transfer torque,and behaves somewhat similar to the external magnetic field.Besides,the phase diagram of the(u,h)plane is predicted.Our innovation is that performing large-scale numerical simulations for the order-disorder phase transition and the pinning-depinning phase transition with LLG equation in the magnetic system.Based on the non-equilibrium/stationary dynamics approach,the critical points and the critical exponents are accurately measured without suffering critical slowing.The results agrees well with the experimental one,and also predict the phenomenon that the experiment has not yet discovered.