ABSTRACT
In this chapter, recent work on the stability of magnetic skyrmions have been reviewed for two types of low-dimensional magnetic nanostructures, that is, nanowires and nanocontact spin-transfer oscillators (NC-STOs) with perpendicular magnetic anisotropy (PMA) and
11 .1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
11 .2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 11 .2 .1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 11 .2 .2 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
11 .3 Skyrmion in a Nanowire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 11 .3 .1 Finite Size Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 11 .3 .2 PMA and DMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 11 .3 .3 Exchange Stiffness and Gilbert Damping Parameter . . . 350
11 .4 Skyrmion in an NC-STO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 11 .4 .1 Varying the Fixed-Layer Parameters . . . . . . . . . . . . . . 352 11 .4 .2 Varying the Spacer Parameters . . . . . . . . . . . . . . . . . . 353 11 .4 .3 Varying the Free-Layer Parameters . . . . . . . . . . . . . . . 355 11 .4 .4 Varying the External Parameters . . . . . . . . . . . . . . . . . 362
11 .5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
11 .6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
Dzyaloshinskii-Moriya interaction (DMI) due to spin-orbit interaction at the interfaces. By means of micromagnetic simulations, various physical and geometrical conditions for stabilizing a skyrmion in low-dimensional nanostructures have been discussed. It is found that a combination of reasonably large PMA and DMI are essential for establishing magnetic skyrmions in a nanowire, especially at elevated temperatures. There are also some dimensional/geometrical constraints of the nanowires for skyrmion stability. A moderate damping parameter (larger than 0.1 for typical interface-induced DMI cases) is a prerequisite for maintaining a skyrmion without relaxing into a ferromagnetic or helical state. In addition, stability of skyrmions in nanodisks have also been briefly discussed. Finally, various perspectives on realistic applications based on skyrmions in low-dimensional systems including memory and microwave generators have been discussed.
