Most theoretical studies of chiral magnetism, and the resulting spin textures, have focused on 3D systems with broken bulk inversion symmetry, where skyrmions are stabilized by easy-axis anisotropy. In this talk I will describe our results on 2D and quasi-2D systems with broken surface inversion, where we find  that skyrmion crystals are much more stable than in 3D, especially for the case of easy-plane anisotropy. These results are of particular interest for thin films, surfaces, and oxide interfaces , where broken surface-inversion symmetry and Rashba spin-orbit coupling naturally lead to both the chiral Dzyaloshinskii-Moriya (DM) interaction and to easy-plane compass anisotropy. I will then turn to systems that break both bulk and surface inversion, resulting in two distinct DM terms arising from Dresselhaus and Rashba spin-orbit coupling. I will describe  the evolution of the skyrmion structure and of the phase diagram as a function of the ratio of Dresselhaus and Rashba terms, which can be tuned by varying film thickness and strain.
 S. Banerjee, J. Rowland, O. Erten, and M. Randeria, PRX 4, 031045 (2014).
 S. Banerjee, O. Erten, and M. Randeria, Nature Phys. 9, 626 (2013).
 J. Rowland, S. Banerjee and M. Randeria, (unpublished).
Mohit Randeria, Sumilan Banerjee, and James Rowland, "Skyrmions in quasi-2D chiral magnets with broken bulk and surface inversion symmetry (Presentation Recording)," Proc. SPIE 9551, Spintronics VIII, 95511A (Presented at SPIE Nanoscience + Engineering: August 11, 2015; Published: 5 October 2015); https://doi.org/10.1117/12.2186435.4519370538001.
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