Micromagnetic simulations

The following is the list of some of magnetic simulation techniques and methods that was developed by Renat Sabirianov at the University of Nebraska and can be used for this project.

• In order to address the above problems the micromagnetic simulation will be performed using Landau-Lifshits-Gilbert(LLG) type equation and multiscale approach. Currently, we have access to public micromagnetic code from R. McMichaels and M. J. Donahue(NIST). The code allows us to calculate the hysteresis loop, magnetization curve, domain structure, and BH curve for the thin films of arbitrary shape.
• The exchange term is derived from the ab-initio calculations of exchange parameters. The method of calculations of exchange parameters have been developed by us and applied to a number of transition metal based compounds (Fe,Co,Ni alloys, amorphous Fe, Co, Y-Fe, Sm₂Fe₁₇, Sm₂Co₁₇). We use first-principle linear-muffin-tin-orbital method in atomic sphere approximation. Using eigenvalues and eigenvectors we calculate the Green's function(GF). GF contains a wealth information. Many properties can be derived knowing the GF of the systems including the local moments, interatomic exchange parameters and magnetocrystaline anisotropy. We use mainly the infinitesimal angle approach where the rotation of the local moment is considered. The energy variation due to the rotation is considered in the limit of the zero angle and Heisenberg pair exchange parameters are obtained.
• The exchange stiffness constant (known from experiment) is reproduced quite well by ab-initio methods. However, the effect of the surface (steps, islands) and defects("grain boundary"-like formations or other extended defects like small cracks) cannot be directly addressed from experiment. These effects may be considered from first-principles using the multiple-scattering formalism for the calculation of exchange parameters cited above. We applied this method to the layered composites of hard and soft magnet phases (so called exchange spring magnets) to study the variation of the exchange at the interface and find the optimal thickness of soft phase using micromagnetic analysis. Finally, we used this approach to study the effect of impurities on the magnetic properties of Fe.
• The statistical Monte Carlo method is used to calculate the temperature dependent magnetization, susceptibility and other static thermodynamic properties. It gives the magnetic phase transition temperatures like the Curie temperature, superparamagnetic blocking temperature, and spin-glass transition temperature.
• We recently employed the embedded cluster method. This method allows us to study monoparticles and interface areas with different degrees of disorder at a large scale of several hundred atoms. The idea is to consider the imperfection as an impurity in the ideal matrix. This perturbation can be solved using Dyson equations. This method gives a full description of the magnetic properties of perturbed crystal, particularly local magnetic moments and exchange interactions. The method can be used for non-collinear structures. This is used for finite angle rotation determination of exchange interaction between atoms, clusters or layers in multilayered structures. In the final angle rotation approach the rotation of the arbitrary choice of angles is considered (usually all ranges of rotations). Then, the variation of energy as a function of the angle of rotation is analyzed in terms of exchange interactions. Performing the Fourier transformation, the Heisenberg interactions are extracted as well as higher power spin interactions (like biquadratic). We plan to use this method to calculate the effect of the extended defects and surface on the exchange coupling and use this information in realistic micromagnetic simulations.
• Even knowing the exchange at the areas of interest (surface and defects) it is difficult to perform simulations at the atomic scale. We should further advance the micromagnetic simulations by separating the area of interest(which is described on the atomic scale) and the rest that can be described in continuous LLG model (microscale). This can be done using multiscale procedures where the continuous media is "glued" by the boundary conditions to the atomic scale at the interface. The other and somewhat similar approach is to consider the coarse graining of the sample where the area of interest is considered again on the atomic scale and the area further apart from this area is considered at larger and larger scales. The coupled equations of motion can be written for this situation.