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 LandauLifshitsGilbert(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 abinitio 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, YFe, Sm_{2}Fe_{17}, Sm_{2}Co_{17}). We use
firstprinciple linearmuffintinorbital 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
abinitio 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
firstprinciples using the multiplescattering 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 spinglass 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 noncollinear
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.
