A multi-scale model of domain wall velocities based on ab initio parameters

Abstract

A new approach is presented to evaluate the velocity of field-driven domain walls by means of ab initio parameters. This approach makes intensive use of multi-scaling by means of (a) mapping of domain wall formation energies obtained in terms of a fully relativistic method onto a Landau–Ginzburg-type expression, and (b) applying the Landau–Lifshitz–Gilbert equation to evaluate the time needed to move domain walls. In comparison with the “classical” expression for the domain wall velocity originally proposed by Landau and Lifshitz, according to which the velocity increases with increasing width of the domain wall, three different types of magnetic alloys, namely permalloy (Ni₈₅Fe₁₅), Co _x Ni_1−x and Co _x Pd_1−x , are analyzed. It is shown that the Landau–Lifshitz expression for the velocity seems to be valid whenever the slopes of the exchange and the anisotropy energy with respect to the concentration are either both increasing or both decreasing.

Keywords:

• domain wall velocities
• magnetism
• magnetization
• magnetization dynamics
• domain structure

Acknowledgements

This work has been supported by the Deutsche Forschungsgemeinschaft in the framework of the project B3 of the SFB 668 and the Cluster of Excellence “Nanospintronics”.

Notes

Note

1. This can easily be seen considering the quantity , the “spin-polarized current density”, which is only quantum mechanically well-defined in the (non-relativistic) case of collinear magnetic structures. In principle for non-collinear magnetic structures this term has to be replaced by the so-called polarization density, introduced in Ref. 24.