Micromagnetics simulation and study of magnetic structure

       Magnetic nano-elements have great potential for technological applications, like magnetic disks and Magnetic sensors. The formation of domains and the specific domain structure plays a crucial role in all applications. As the size of the element decreases into the nanometer regime, detailed predictions of their magnetic behaviour can only be possible using micromagnetic equations.
       The experimental research work on thin film and nanocrystalline magnetic materials in IIT Bombay, has also lead to some interesting properties. These properties cannot be explained by the conventional domain theory, which works very well for bulk magnetic materials. It may be possible to explain some of the observed results by the micromagnetic theory.
       Micromagnetic equations:
       The theoretical treatment of the magetic dynamics starts from the Gilbert equation.
       which describes the physical path of the magnetic polarasation, J towards equilibrium. The effective field Heff is given by the negative gradient of the total magnetic Gibbs free energy. This is given by the sum of the exchange field, anisotropy field, external applied field and the demagnetisation field. The calculation of the demagnetization field is itself complicated, and is determined by solving for the potentials which obey Poisson equation inside the magnetic particle and Laplace equation in the infinite region external to the magnetic particle.
       Numerical Solution:
       The solution method is divided into two main steps:
       Determination of magnetostatic energy , which is obtained by solving for the potentials mentioned above. Several approaches have been reported: FEM, BEM and hybrid FEM/BEM. Each approach has its advantages as well as limitations. The investigators have experience in FEM/ BEM for electrical engineering and related applications and the algorithms already developed will be used to tackle this problem
       Time discretisation of Gilbert equation: Both backward difference method and forward difference method have been reported in the literature. Explict as well as implict schemes have been reported. The investigators have developed algorithms for time stepping using FDTD for the Maxwell?s equation. The algorithms developed in this connection will be applied to solve the time stepping in the Gilbert equation and the time evolution of the magnetic polarization will be obtained. The vector plots/ contour plots of the evolution process at different time steps will also be plotted to visualize the processes taking place. The switching behaviour (the critical external field at which the magnetic domain changes its direction of magnetization) will also be studied. These have applications in recording and sensors as well as it will give insight into the fundamental properties of magnetic nanoparticles.
       The method of solution mentioned above has several problems. Most of the techniques that work for bulk materials will not work in the nanocrystalline regime. The space discretisation for FEM will necessitate the nodes to be very fine. When the size of the element becomes comparable to the atomic dimensions the nodes cannot be arbitrarily chosen but must be constrained to be at the locations of the atoms. The BEM discretisation leads to a large system of equations, which are not sparse or symmetric. Special techniques will be needed to tackle these issues. Finally the time discretisation of the Gilbert equations lead to stiff equations that can cause instability, during the time stepping. Special techniques will have to be developed for solving these equations.