ABSTRACT
Hall Skyrmions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 14 .5 .3 Evidence for Quantum Hall Skyrmions . . . . . . . . . . . . . 459
14 .6 Skyrmions in Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . 460
14 .7 Skyrmions in Cold-Atom Systems . . . . . . . . . . . . . . . . . . . . . . 463
Skyrmions can exist in various condensed matter systems, which is reviewed in this chapter, including the antiferromagnetic (AFM) materials, ferromagnetic bilayers with AFM interface coupling, multiferroic insulators, quantum Hall systems, liquid crystals, and Bose-Einstein condensate (BEC) systems. The basic theory, advantage, and weakness for AFM skyrmions and skyrmions in metallic bilayers with AFM coupling have been examined, which can overcome the skyrmion Hall effect (SkHE) in metallic skyrmion racetrack. Creation and motion of mulitiferroic skyrmion crystals in the magnetic insulator Cu2OSeO3 have also been demonstrated, with the mechanism, nucleation, and dynamic properties summarized, which have no SkHE and can be manipulated by electric potentials. Skyrmions in quantum Hall systems can also be manipulated by electric fields due to the electrical charge carried, whose existence have been confirmed by NMR and other experimental methods. Such unstable skyrmions are mostly found in GaAs and related quantum wells. A 1/4 spiral skyrmion is formed in liquid crystals, where doubletwist cylinders are energetically more favorable than the uniaxial helical structures. On the other hand, a full spiral skyrmion is predicted in coldatom systems, which can be deteriorated due to strong spin-orbit (SO) coupling. While the so-called skyrmions in liquid crystals are far away from a full skyrmion, much work needs to be done before the skyrmions in quantum Hall and cold-atom systems have real applications.
