Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature

Bogdanov, A. & Yablonskii, A. Thermodynamically stable ‘vortices’ in magnetically ordered crystals. JETP Lett. 68, 101–103 (1989).

Bogdanov, A. N. & Rößler, U. K. Chiral symmetry breaking in magnetic thin films and multilayers. Phys. Rev. Lett. 87, 037203 (2001).

Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nature Nanotech. 8, 152–156 (2013).

Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nature Nanotech. 8, 899–911 (2013).

Braun, H. B. Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons. Adv. Phys. 61, 1–112 (2012).

Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).

Huang, S. X. & Chien, C. L. Extended skyrmion phase in epitaxial FeGe(111) thin films. Phys. Rev. Lett. 108, 267201 (2012).

Ritz, R. et al. Formation of a topological non-Fermi liquid in MnSi. Nature 497, 231–234 (2013).

Kiselev, N. S., Bogdanov, A. N., Schäfer, R. & Rößler, U. K. Chiral skyrmions in thin magnetic films: new objects for magnetic storage technologies? J. Phys. D 44, 392001 (2011).

Neubauer, A. et al. Topological Hall effect in the α phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009).

Pappas, C. et al. Chiral paramagnetic skyrmion-like phase in MnSi. Phys. Rev. Lett. 102, 197202 (2009).

Tonomura, A. et al. Real-space observation of skyrmion lattice in helimagnet MnSi thin samples. Nano Lett. 12, 1673–1677 (2012).

Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).

Tokunaga, Y. et al. A new class of chiral materials hosting magnetic skyrmions beyond room temperature. Nature Commun. 6, 7238 (2015).

Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nature Phys. 7, 713–718 (2011).

Romming, N. et al. Writing and deleting single magnetic skyrmions. Science 341, 636–639 (2013).

Fert, A. & Levy, P. M. Role of anisotropic exchange interactions in determining the properties of spin-glasses. Phys. Rev. Lett. 44, 1538–1541 (1980).

Chen, G., Mascaraque, A., N'Diaye, A. T. & Schmid, A. K. Room temperature skyrmion ground state stabilized through interlayer exchange coupling. Appl. Phys. Lett. 106, 242404 (2015).

Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science 349, 283–286 (2015).

Baltz, V., Marty, A., Rodmacq, B. & Dieny, B. Magnetic domain replication in interacting bilayers with out-of-plane anisotropy: application to Co∕Pt multilayers. Phys. Rev. B 75, 014406 (2007).

Malozemoff, A. P. & Slonczewski, J. C. in Magnetic Domain Walls in Bubble Materials (ed. Wolfe, R.) Ch. II, III (Academic Press, 1979).

Moutafis, C., Komineas, S. & Bland, J. A. C. Dynamics and switching processes for magnetic bubbles in nanoelements. Phys. Rev. B 79, 224429 (2009).

Moutafis, C. et al. Magnetic bubbles in FePt nanodots with perpendicular anisotropy. Phys. Rev. B 76, 104426 (2007).

Büttner, F. et al. Dynamics and inertia of skyrmionic spin structures. Nature Phys. 11, 225–228 (2015).

Sampaio, J., Cros, V., Rohart, S., Thiaville, A. & Fert, A. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures. Nature Nanotech. 8, 839–844 (2013).

Kabanov, Y. P. et al. In-plane field effects on the dynamics of domain walls in ultrathin Co films with perpendicular anisotropy. IEEE Trans. Magn. 46, 2220–2223 (2010).

Hrabec, A. et al. Measuring and tailoring the Dzyaloshinskii–Moriya interaction in perpendicularly magnetized thin films. Phys. Rev. B 90, 020402 (2014).

Yang, H., Thiaville, A., Rohart, S., Fert, A. & Chshiev, M. Anatomy of Dzyaloshinskii–Moriya interaction at Co/Pt interfaces. Preprint at http://arxiv.org/abs/1501.05511 (2015).

Franken, J. H., Herps, M., Swagten, H. J. M. & Koopmans, B. Tunable chiral spin texture in magnetic domain walls. Sci. Rep. 4, 5248 (2014).

Donahue, M. J. & Porter, D. G. OOMMF User's Guide Version 1.0. Interagency Report NISTIR 6376 (National Institute of Standards and Technology, 1999).

Vansteenkiste, A. et al. The design and verification of MuMax3. AIP Adv. 4, 107133 (2014).

Eyrich, C. et al. Effect of substitution on the exchange stiffness and magnetization of Co films. Phys. Rev. B 90, 235408–235419 (2015).

Pizzini, S. et al. Chirality-induced asymmetric magnetic nucleation in Pt/Co/AlOx ultra-thin microstructures. Phys. Rev. Lett. 113, 047203 (2014).

Hiramatsu, R., Kim, K.-J., Nakatani, Y., Moriyama, T. & Ono, T. Proposal for quantifying the Dzyaloshinskii–Moriya interaction by domain walls annihilation measurement. Jpn. J. Appl. Phys. 53, 108001 (2014).

Belmeguenai, M. et al. Interfacial Dzyaloshinskii–Moriya interaction in perpendicularly magnetized Pt/Co/AlOx ultrathin films measured by Brillouin light spectroscopy. Phys. Rev. B 91, 180405(R) (2015).

Tetienne, J.-P. et al. The nature of domain walls in ultrathin ferromagnets revealed by scanning nanomagnetometry. Nature Commun. 6, 6733 (2015).

Rohart, S. & Thiaville, A. Skyrmion confinement in ultrathin film nanostructures in the presence of Dzyaloshinskii–Moriya interaction. Phys. Rev. B 88, 184422 (2013).

Romming, N., Kubetzka, A., Hanneken, C., von Bergmann, K. & Wiesendanger, R. Field-dependent size and shape of single magnetic skyrmions. Phys. Rev. Lett. 114, 177203 (2015).

Braun, H. B. Fluctuations and instabilities of ferromagnetic domain–wall pairs in an external magnetic field. Phys. Rev. B 50, 16485 (1995).

Woo, S. et al. Observation of room temperature magnetic skyrmions and their current-driven dynamics in ultrathin Co films. Preprint at http://arxiv.org/abs/1502.07376 (2015).