References
- Bogdanov A, Hubert A. Thermodynamically stable magnetic vortex states in magnetic crystals. J Magn Magn Mater. 1994;138(3):255–269.
- Nagaosa N, Tokura Y. Topological properties and dynamics of magnetic skyrmions. Nat Nanotechnol. 2013;8(12):899.
- Göbel B, Mertig I, Tretiakov OA. Beyond skyrmions: review and perspectives of alternative magnetic quasiparticles. Phys Rep. 2021;895:1–28.
- Tokura Y, Kanazawa N. Magnetic skyrmion materials. Chem Rev. 2020;121:2857–2897.
- Fert A, Reyren N, Cros V. Magnetic skyrmions: advances in physics and potential applications. Nature Rev Mater. 2017;2(7):1–15.
- Büttner F, Lemesh I, Beach GS. Theory of isolated magnetic skyrmions: from fundamentals to room temperature applications. Sci Rep. 2018;8:1–12.
- Wu H, Groß F, Dai B, et al. Ferrimagnetic skyrmions in topological insulator/ferrimagnet heterostructures. Adv Mater. 2020;32(34):2003380. DOI:10.1002/adma.202003380
- Pöllath S, Aqeel A, Bauer A, et al. Ferromagnetic resonance with magnetic phase selectivity by means of resonant elastic x-ray scattering on a chiral magnet. Phys Rev Lett. 2019;123(16):167201.
- Luo S, You L. Skyrmion devices for memory and logic applications. APL Mater. 2021;9(5):050901.
- Muhlbauer S, Binz B, Jonietz F, et al. Skyrmion lattice in a chiral magnet. Science. 2009;323(5916):915–919.
- Yu XZ, Kanazawa N, Onose Y, et al. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat Mater. 2011;10(2):106–109.
- Münzer W, Neubauer A, Adams T, et al. Skyrmion lattice in the doped semiconductor Fe1-xCoxSi. Phys Rev B. 2010;81:041203.
- Kézsmárki I, Bordács S, Milde P, et al. Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8. Nat Mater. 2015;14(11):1116–1122. DOI:10.1038/nmat4402
- Fujima Y, Abe N, Tokunaga Y, et al. Thermodynamically stable skyrmion lattice at low temperatures in a bulk crystal of lacunar spinel GaV4Se8. Phys Rev B. 2017;95(18):180410.
- Kurumaji T, Nakajima T, Ukleev V, et al. Néel-type skyrmion lattice in the tetragonal polar magnet VOSe2O5. Phys Rev Lett. 2017;119(23):237201.
- Seki S, Yu XZ, Ishiwata S, et al. Observation of skyrmions in a multiferroic material. Science. 2012;336(6078):198–201.
- White JS, Levatić I, Omrani A, et al. Electric field control of the skyrmion lattice in Cu2OSeO3. J Phys. 2012;24(43):432201. DOI:10.1088/0953-8984/24/43/432201
- Qian F, Bannenberg LJ, Wilhelm H, et al. New magnetic phase of the chiral skyrmion material Cu2OSeO3. Sci Adv. 2018;4(9):eaat7323. DOI:10.1126/sciadv.aat7323
- Chacon A, Heinen L, Halder M, et al. Observation of two independent skyrmion phases in a chiral magnetic material. Nat Phys. 2018;14:936–941.
- Bannenberg LJ, Wilhelm H, Cubitt R, et al. Multiple low-temperature skyrmionic states in a bulk chiral magnet. Npj Quantum Mater. 2019;4:1–8.
- Takagi R, Yamasaki Y, Yokouchi T, et al. Particle-size dependent structural transformation of skyrmion lattice. Nat Commun. 2020;11(1):1–7.
- Aqeel A, Sahliger J, Taniguchi T, et al. Microwave spectroscopy of the low-temperature skyrmion state in Cu2OSeO3. Phys Rev Lett. 2021;126:017202.
- Schwarze T, Waizner J, Garst M, et al. Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets. Nat Mater. 2015;14:478–483.
- Mochizuki M, Seki S. Dynamical magnetoelectric phenomena of multiferroic skyrmions. J Phys. 2015;27:503001.
- Stirling W, Cooper M. X-ray magnetic scattering. J Magn Magn Mater. 1999;200:755–773.
- Kortright J, Awschalom D, Stöhr J, et al. Research frontiers in magnetic materials at soft x-ray synchrotron radiation facilities. J Magn Magn Mater. 1999;207:7–44.
- Ament LJ, Van Veenendaal M, Devereaux TP, et al. Resonant inelastic x-ray scattering studies of elementary excitations. Rev Mod Phys. 2011;83:705.
- Vettier C. Resonant elastic x-ray scattering: where from? where to? Eur Phys J Spec Top. 2012;208:3–14.
- Fink J, Schierle E, Weschke E, et al. Resonant elastic soft x-ray scattering. Rep Prog Phys. 2013;76:056502.
- Ohsumi H, Arima TH. Novel insight into structural magnetism by polarized synchrotron x-ray scattering. Adv Phys X. 2016;1:128–145.
- Kortright JB. Resonant soft x-ray and extreme ultraviolet magnetic scattering in nanostructured magnetic materials: fundamentals and directions. J Electron Spectros Relat Phenomena. 2013;189:178–186.
- Mulders AM, Lawrence SM, Princep AJ, et al. Circularly polarized soft x-ray diffraction study of helical magnetism in hexaferrite. Phys Rev B. 2010;81:092405.
- Yamasaki Y, Morikawa D, Honda T, et al. Dynamical process of skyrmion-helical magnetic transformation of the chiral-lattice magnet fege probed by small-angle resonant soft x-ray scattering. Phys Rev B. 2015;92:220421.
- Ueda H, Skoropata E, Burian M, et al. Conical spin order with chiral quadrupole helix in CsCuCl3. Phys Rev B. 2022;105:144408.
- Durr H, Dudzik E, Dhesi S, et al. Chiral magnetic domain structures in ultrathin FePd films. Science. 1999;284:2166–2168.
- Zhang S, Bauer A, Berger H, et al. Resonant elastic x-ray scattering from the skyrmion lattice in Cu2OSeO3. Phys Rev B. 2016;93:214420.
- Zhang S, van der Laan G, Hesjedal T. Direct experimental determination of spiral spin structures via the dichroism extinction effect in resonant elastic soft x-ray scattering. Phys Rev B. 2017;96:094401.
- Zhang S, Van Der Laan G, Hesjedal T. Direct experimental determination of the topological winding number of skyrmions in Cu2OSeO3. Nat Commun. 2017;8:1–7.
- Chauleau JY, Legrand W, Reyren N, et al. Chirality in magnetic multilayers probed by the symmetry and the amplitude of dichroism in x-ray resonant magnetic scattering. Phys Rev Lett. 2018;120:037202.
- Legrand W, Chauleau JY, Maccariello D, et al. Hybrid chiral domain walls and skyrmions in magnetic multilayers. Sci Adv. 2018;4:eaat0415.
- Okamura Y, Yamasaki Y, Morikawa D, et al. Emergence and magnetic-field variation of chiral-soliton lattice and skyrmion lattice in the strained helimagnet Cu2OSeO3. Phys Rev B. 2017;96:174417.
- Ukleev V, Yamasaki Y, Morikawa D, et al. Coherent resonant soft x-ray scattering study of magnetic textures in FeGe. Quantum Beam Sci. 2018;2:3.
- Ukleev V, Yamasaki Y, Morikawa D, et al. Element-specific soft x-ray spectroscopy, scattering, and imaging studies of the skyrmion-hosting compound Co8Zn8Mn4. Phys Rev B. 2019;99:144408.
- Burn D, Zhang S, Wang S, et al. Helical magnetic ordering in thin fege membranes. Phys Rev B. 2019;100:184403.
- Burn DM, Wang S, Wang W, et al. Field and temperature dependence of the skyrmion lattice phase in chiral magnet membranes. Phys Rev B. 2020;101:014446.
- Ukleev V, Yamasaki Y, Utesov O, et al. Metastable solitonic states in the strained itinerant helimagnet FeGe. Phys Rev B. 2020;102:014416.
- Langner M, Roy S, Mishra S, et al. Coupled skyrmion sublattices in Cu2OSeO3. Phys Rev Lett. 2014;112:167202.
- Zhang S, van der Laan G, Müller J, et al. Reciprocal space tomography of 3D skyrmion lattice order in a chiral magnet. Proc Nat Acad Sci. 2018;115:6386–6391.
- Zhang S, Burn DM, Jaouen N, et al. Robust perpendicular skyrmions and their surface confinement. Nano Lett. 2020;20:1428–1432.
- Burn D, Brearton R, Ran K, et al. Periodically modulated skyrmion strings in Cu2OSeO3. Npj Quantum Mater. 2021;6:1–8.
- Renaud G, Lazzari R, Leroy F. Probing surface and interface morphology with grazing incidence small angle x-ray scattering. Surf Sci Rep. 2009;64:255–380.
- Fasolino A, Carra P, Altarelli M. X-ray resonant magnetic scattering from surfaces. Phys Rev B. 1993;47:3877.
- Flewett S, Burgos-Parra E, Strelow MG, et al. General treatment of off-specular resonant soft x-ray magnetic scattering using the distorted-wave born approximation: numerical algorithm and experimental studies with hybrid chiral domain structures. Phys Rev B. 2021;103:184401.
- Zhang S, Stasinopoulos I, Lancaster T, et al. Room-temperature helimagnetism in FeGe thin films. Sci Rep. 2017;7:1–10.
- Huang H, Lee SJ, Kim B, et al. Detection of the chiral spin structure in ferromagnetic SrRuO3 thin film. ACS Appl Mater Interfaces. 2020;12:37757–37763.
- Li W, Bykova I, Zhang S, et al. Anatomy of skyrmionic textures in magnetic multilayers. Adv Mater. 2019;31:1807683.
- Léveillé C, Flewett S, Burgos-Parra E, et al. Chiral spin spiral in synthetic antiferromagnets probed by circular dichroism in x-ray resonant magnetic scattering. Phys Rev B. 2021;104:L060402.
- Kachel T, Eggenstein F, Follath R. A soft x-ray plane-grating monochromator optimized for elliptical dipole radiation from modern sources. J Synchrotron Radiat. 2015;22:1301–1305.
- Abrudan RM, Radu F. Alice: a diffractometer/reflectometer for soft x-ray resonant magnetic scattering at bessy ii. J Large Scale Res Facil JLSRF. 2016;2:A69.
- Aqeel A, Sahliger J, Li G, et al. Growth and helicity of noncentrosymmetric Cu2OSeO3 crystals. Phys Status Solidi B. 2022;259:2100152.
- Aqeel A, Vera-Marun IJ, van Wees BJ, et al. Surface sensitivity of the spin Seebeck effect. J Appl Phys. 2014;116:153705.
- Arnold T, Böhm G, Fechner R, et al. Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook. Nucl Instrum Methods Phys Res A. 2010;616:147–156.
- Zhang S, Bauer A, Burn D, et al. Multidomain skyrmion lattice state in cu2oseo3. Nano Lett. 2016;16:3285–3291.
- Milde P, Köhler L, Neuber E, et al. Field-induced reorientation of helimagnetic order in Cu2OSeO3 probed by magnetic force microscopy. Phys Rev B. 2020;102:024426.
- Izyumov YA. Modulated, or long-periodic, magnetic structures of crystals. Soviet Phys Uspekhi. 1984;27:845.
- Honda T, Yamasaki Y, Nakao H, et al. Topological metastability supported by thermal fluctuation upon formation of chiral soliton lattice in CrNb3S6. Sci Rep. 2020;10:1–12.
- Grigoriev S, Maleyev S, Okorokov A, et al. Field-induced reorientation of the spin helix in MnSi near Tc. Phys Rev B. 2006;73:224440.
- Dyadkin V, Prša K, Grigoriev S, et al. Chirality of structure and magnetism in the magnetoelectric compound Cu2OSeO3. Phys Rev B. 2014;89:140409.
- Eisebitt S, Lörgen M, Eberhardt W, et al. Polarization effects in coherent scattering from magnetic specimen: implications for x-ray holography, lensless imaging, and correlation spectroscopy. Phys Rev B. 2003;68:104419.
- Tokunaga Y, Yu XZ, White JS, et al. A new class of chiral materials hosting magnetic skyrmions beyond room temperature. Nat Commun. 2015;6:1–7.
- Nayak AK, Kumar V, Ma T, et al. Magnetic antiskyrmions above room temperature in tetragonal heusler materials. Nature. 2017;548:561–566.
- Takagi R, Yu XZ, White JS, et al. Low-field bi-skyrmion formation in a noncentrosymmetric chimney ladder ferromagnet. Phys Rev Lett. 2018;120:037203.
- Karube K, Peng L, Masell J, et al. Room-temperature antiskyrmions and sawtooth surface textures in a non-centrosymmetric magnet with S4 symmetry. Nat Mater. 2021;20:335–340.