{"id":888784,"date":"2026-10-20T11:36:16","date_gmt":"2026-10-20T11:36:16","guid":{"rendered":"https:\/\/www.newsbeep.com\/us\/888784\/"},"modified":"2026-10-20T11:36:16","modified_gmt":"2026-10-20T11:36:16","slug":"a-liquid-crystal-analogue-of-the-skyrmion-hall-effect","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/us\/888784\/","title":{"rendered":"A liquid-crystal analogue of the skyrmion Hall effect"},"content":{"rendered":"<p class=\"c-article-references__text\" id=\"ref-CR1\">Hess, A. J., Poy, G., Tai, J.-S. B., \u017dumer, S. &amp; Smalyukh, I. I. Control of light by topological solitons in soft chiral birefringent media. Phys. Rev. X 10, 031042 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.10.031042\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.10.031042\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.10.031042<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.10.031042\" data-track-item_id=\"10.1103\/PhysRevX.10.031042\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.10.031042\" aria-label=\"Article reference 1\" data-doi=\"10.1103\/PhysRevX.10.031042\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 1\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Control%20of%20light%20by%20topological%20solitons%20in%20soft%20chiral%20birefringent%20media&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.10.031042&amp;volume=10&amp;publication_year=2020&amp;author=Hess%2CAJ&amp;author=Poy%2CG&amp;author=Tai%2CJ-SB&amp;author=%C5%BDumer%2CS&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR2\">Papi\u010d, M. et al. Topological liquid crystal superstructures as structured light lasers. Proc. Natl Acad. Sci. USA 118, e2110839118 <a href=\"https:\/\/doi.org\/10.1073\/pnas.2110839118\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1073\/pnas.2110839118\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1073\/pnas.2110839118<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1073\/pnas.2110839118\" data-track-item_id=\"10.1073\/pnas.2110839118\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1073%2Fpnas.2110839118\" aria-label=\"Article reference 2\" data-doi=\"10.1073\/pnas.2110839118\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 2\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20liquid%20crystal%20superstructures%20as%20structured%20light%20lasers&amp;journal=Proc.%20Natl%20Acad.%20Sci.%20USA&amp;doi=10.1073%2Fpnas.2110839118&amp;volume=118&amp;publication_year=2021&amp;author=Papi%C4%8D%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR3\">Li, Y. et al. Periodic assembly of nanoparticle arrays in disclinations of cholesteric liquid crystals. Proc. Natl Acad. Sci. USA 114, 2137\u20132142 <a href=\"https:\/\/doi.org\/10.1073\/pnas.1615006114\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1073\/pnas.1615006114\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1073\/pnas.1615006114<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1073\/pnas.1615006114\" data-track-item_id=\"10.1073\/pnas.1615006114\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1073%2Fpnas.1615006114\" aria-label=\"Article reference 3\" data-doi=\"10.1073\/pnas.1615006114\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PNAS..114.2137L\" aria-label=\"ADS reference 3\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 3\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Periodic%20assembly%20of%20nanoparticle%20arrays%20in%20disclinations%20of%20cholesteric%20liquid%20crystals&amp;journal=Proc.%20Natl%20Acad.%20Sci.%20USA&amp;doi=10.1073%2Fpnas.1615006114&amp;volume=114&amp;pages=2137-2142&amp;publication_year=2017&amp;author=Li%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR4\">Mertelj, A., Lisjak, D., Drofenik, M. &amp; \u010copi\u010d, M. Ferromagnetism in suspensions of magnetic platelets in liquid crystal. Nature 504, 237\u2013241 <a href=\"https:\/\/doi.org\/10.1038\/nature12863\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nature12863\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nature12863<\/a> (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature12863\" data-track-item_id=\"10.1038\/nature12863\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature12863\" aria-label=\"Article reference 4\" data-doi=\"10.1038\/nature12863\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2013Natur.504..237M\" aria-label=\"ADS reference 4\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 4\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Ferromagnetism%20in%20suspensions%20of%20magnetic%20platelets%20in%20liquid%20crystal&amp;journal=Nature&amp;doi=10.1038%2Fnature12863&amp;volume=504&amp;pages=237-241&amp;publication_year=2013&amp;author=Mertelj%2CA&amp;author=Lisjak%2CD&amp;author=Drofenik%2CM&amp;author=%C4%8Copi%C4%8D%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR5\">Mundoor, H., Senyuk, B. &amp; Smalyukh, I. I. Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions. Science 352, 69\u201373 <a href=\"https:\/\/doi.org\/10.1126\/science.aaf0801\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/science.aaf0801\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/science.aaf0801<\/a> (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.aaf0801\" data-track-item_id=\"10.1126\/science.aaf0801\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aaf0801\" aria-label=\"Article reference 5\" data-doi=\"10.1126\/science.aaf0801\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016Sci...352...69M\" aria-label=\"ADS reference 5\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 5\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Triclinic%20nematic%20colloidal%20crystals%20from%20competing%20elastic%20and%20electrostatic%20interactions&amp;journal=Science&amp;doi=10.1126%2Fscience.aaf0801&amp;volume=352&amp;pages=69-73&amp;publication_year=2016&amp;author=Mundoor%2CH&amp;author=Senyuk%2CB&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR6\">Mundoor, H., Wu, J.-S., Wensink, H. H. &amp; Smalyukh, I. I. Thermally reconfigurable monoclinic nematic colloidal fluids. Nature 590, 268\u2013274 <a href=\"https:\/\/doi.org\/10.1038\/s41586-021-03249-0\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41586-021-03249-0\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41586-021-03249-0<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-021-03249-0\" data-track-item_id=\"10.1038\/s41586-021-03249-0\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-021-03249-0\" aria-label=\"Article reference 6\" data-doi=\"10.1038\/s41586-021-03249-0\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021Natur.590..268M\" aria-label=\"ADS reference 6\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 6\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Thermally%20reconfigurable%20monoclinic%20nematic%20colloidal%20fluids&amp;journal=Nature&amp;doi=10.1038%2Fs41586-021-03249-0&amp;volume=590&amp;pages=268-274&amp;publication_year=2021&amp;author=Mundoor%2CH&amp;author=Wu%2CJ-S&amp;author=Wensink%2CHH&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR7\">Fukuda, J. -i &amp; \u017dumer, S. Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal. Nat. Commun. 2, 246 <a href=\"https:\/\/doi.org\/10.1038\/ncomms1250\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/ncomms1250\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/ncomms1250<\/a> (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/ncomms1250\" data-track-item_id=\"10.1038\/ncomms1250\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fncomms1250\" aria-label=\"Article reference 7\" data-doi=\"10.1038\/ncomms1250\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2011NatCo...2..246F\" aria-label=\"ADS reference 7\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 7\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quasi-two-dimensional%20skyrmion%20lattices%20in%20a%20chiral%20nematic%20liquid%20crystal&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fncomms1250&amp;volume=2&amp;publication_year=2011&amp;author=Fukuda%2CJ-i&amp;author=%C5%BDumer%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR8\">Ackerman, P. J., Trivedi, R. P., Senyuk, B., van de Lagemaat, J. &amp; Smalyukh, I. I. Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics. Phys. Rev. E 90, 012505 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevE.90.012505\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevE.90.012505\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevE.90.012505<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevE.90.012505\" data-track-item_id=\"10.1103\/PhysRevE.90.012505\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevE.90.012505\" aria-label=\"Article reference 8\" data-doi=\"10.1103\/PhysRevE.90.012505\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvE..90a2505A\" aria-label=\"ADS reference 8\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 8\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Two-dimensional%20skyrmions%20and%20other%20solitonic%20structures%20in%20confinement-frustrated%20chiral%20nematics&amp;journal=Phys.%20Rev.%20E&amp;doi=10.1103%2FPhysRevE.90.012505&amp;volume=90&amp;publication_year=2014&amp;author=Ackerman%2CPJ&amp;author=Trivedi%2CRP&amp;author=Senyuk%2CB&amp;author=Lagemaat%2CJ&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR9\">Posnjak, G., \u010copar, S. &amp; Mu\u0161evi\u010d, I. Points, skyrmions and torons in chiral nematic droplets. Sci. Rep. 6, 26361 <a href=\"https:\/\/doi.org\/10.1038\/srep26361\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/srep26361\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/srep26361<\/a> (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/srep26361\" data-track-item_id=\"10.1038\/srep26361\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fsrep26361\" aria-label=\"Article reference 9\" data-doi=\"10.1038\/srep26361\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016NatSR...626361P\" aria-label=\"ADS reference 9\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 9\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Points%2C%20skyrmions%20and%20torons%20in%20chiral%20nematic%20droplets&amp;journal=Sci.%20Rep.&amp;doi=10.1038%2Fsrep26361&amp;volume=6&amp;publication_year=2016&amp;author=Posnjak%2CG&amp;author=%C4%8Copar%2CS&amp;author=Mu%C5%A1evi%C4%8D%2CI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR10\">Smalyukh, I. I., Lansac, Y., Clark, N. A. &amp; Trivedi, R. P. Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids. Nat. Mater. 9, 139\u2013145 <a href=\"https:\/\/doi.org\/10.1038\/nmat2592\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nmat2592\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nmat2592<\/a> (2010).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nmat2592\" data-track-item_id=\"10.1038\/nmat2592\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnmat2592\" aria-label=\"Article reference 10\" data-doi=\"10.1038\/nmat2592\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 10\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Three-dimensional%20structure%20and%20multistable%20optical%20switching%20of%20triple-twisted%20particle-like%20excitations%20in%20anisotropic%20fluids&amp;journal=Nat.%20Mater.&amp;doi=10.1038%2Fnmat2592&amp;volume=9&amp;pages=139-145&amp;publication_year=2010&amp;author=Smalyukh%2CII&amp;author=Lansac%2CY&amp;author=Clark%2CNA&amp;author=Trivedi%2CRP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR11\">Guo, Y. et al. Cholesteric liquid crystals in rectangular microchannels: skyrmions and stripes. Soft Matter 12, 6312\u20136320 <a href=\"https:\/\/doi.org\/10.1039\/C6SM01190J\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1039\/C6SM01190J\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1039\/C6SM01190J<\/a> (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1039\/C6SM01190J\" data-track-item_id=\"10.1039\/C6SM01190J\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1039%2FC6SM01190J\" aria-label=\"Article reference 11\" data-doi=\"10.1039\/C6SM01190J\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016SMat...12.6312G\" aria-label=\"ADS reference 11\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 11\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Cholesteric%20liquid%20crystals%20in%20rectangular%20microchannels%3A%20skyrmions%20and%20stripes&amp;journal=Soft%20Matter&amp;doi=10.1039%2FC6SM01190J&amp;volume=12&amp;pages=6312-6320&amp;publication_year=2016&amp;author=Guo%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR12\">Ackerman, P. J. &amp; Smalyukh, I. I. Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids. Nat. Mater. 16, 426\u2013432 <a href=\"https:\/\/doi.org\/10.1038\/nmat4826\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nmat4826\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nmat4826<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nmat4826\" data-track-item_id=\"10.1038\/nmat4826\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnmat4826\" aria-label=\"Article reference 12\" data-doi=\"10.1038\/nmat4826\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 12\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Static%20three-dimensional%20topological%20solitons%20in%20fluid%20chiral%20ferromagnets%20and%20colloids&amp;journal=Nat.%20Mater.&amp;doi=10.1038%2Fnmat4826&amp;volume=16&amp;pages=426-432&amp;publication_year=2017&amp;author=Ackerman%2CPJ&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR13\">Voinescu, R., Tai, J.-S. B. &amp; Smalyukh, I. I. Hopf solitons in helical and conical backgrounds of chiral magnetic solids. Phys. Rev. Lett. 125, 057201 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.125.057201\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.125.057201\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.125.057201<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.125.057201\" data-track-item_id=\"10.1103\/PhysRevLett.125.057201\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.125.057201\" aria-label=\"Article reference 13\" data-doi=\"10.1103\/PhysRevLett.125.057201\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvL.125e7201V\" aria-label=\"ADS reference 13\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 13\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Hopf%20solitons%20in%20helical%20and%20conical%20backgrounds%20of%20chiral%20magnetic%20solids&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.125.057201&amp;volume=125&amp;publication_year=2020&amp;author=Voinescu%2CR&amp;author=Tai%2CJ-SB&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR14\">Tai, J.-S. B. &amp; Smalyukh, I. I. Three-dimensional crystals of adaptive knots. Science 365, 1449\u20131453 <a href=\"https:\/\/doi.org\/10.1126\/science.aay1638\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/science.aay1638\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/science.aay1638<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.aay1638\" data-track-item_id=\"10.1126\/science.aay1638\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aay1638\" aria-label=\"Article reference 14\" data-doi=\"10.1126\/science.aay1638\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019Sci...365.1449T\" aria-label=\"ADS reference 14\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 14\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Three-dimensional%20crystals%20of%20adaptive%20knots&amp;journal=Science&amp;doi=10.1126%2Fscience.aay1638&amp;volume=365&amp;pages=1449-1453&amp;publication_year=2019&amp;author=Tai%2CJ-SB&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR15\">Zhao, H., Malomed, B. A. &amp; Smalyukh, I. I. Topological solitonic macromolecules. Nat. Commun. 14, 4581 <a href=\"https:\/\/doi.org\/10.1038\/s41467-023-40335-5\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-023-40335-5\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-023-40335-5<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-023-40335-5\" data-track-item_id=\"10.1038\/s41467-023-40335-5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-023-40335-5\" aria-label=\"Article reference 15\" data-doi=\"10.1038\/s41467-023-40335-5\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023NatCo..14.4581Z\" aria-label=\"ADS reference 15\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 15\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20solitonic%20macromolecules&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-023-40335-5&amp;volume=14&amp;publication_year=2023&amp;author=Zhao%2CH&amp;author=Malomed%2CBA&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR16\">Fert, A., Cros, V. &amp; Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152\u2013156 <a href=\"https:\/\/doi.org\/10.1038\/nnano.2013.29\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nnano.2013.29\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nnano.2013.29<\/a> (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nnano.2013.29\" data-track-item_id=\"10.1038\/nnano.2013.29\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnnano.2013.29\" aria-label=\"Article reference 16\" data-doi=\"10.1038\/nnano.2013.29\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2013NatNa...8..152F\" aria-label=\"ADS reference 16\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 16\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Skyrmions%20on%20the%20track&amp;journal=Nat.%20Nanotechnol.&amp;doi=10.1038%2Fnnano.2013.29&amp;volume=8&amp;pages=152-156&amp;publication_year=2013&amp;author=Fert%2CA&amp;author=Cros%2CV&amp;author=Sampaio%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR17\">Nagaosa, N. &amp; Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899\u2013911 <a href=\"https:\/\/doi.org\/10.1038\/nnano.2013.243\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nnano.2013.243\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nnano.2013.243<\/a> (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nnano.2013.243\" data-track-item_id=\"10.1038\/nnano.2013.243\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnnano.2013.243\" aria-label=\"Article reference 17\" data-doi=\"10.1038\/nnano.2013.243\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2013NatNa...8..899N\" aria-label=\"ADS reference 17\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 17\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20properties%20and%20dynamics%20of%20magnetic%20skyrmions&amp;journal=Nat.%20Nanotechnol.&amp;doi=10.1038%2Fnnano.2013.243&amp;volume=8&amp;pages=899-911&amp;publication_year=2013&amp;author=Nagaosa%2CN&amp;author=Tokura%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR18\">Sutcliffe, P. Hopfions in chiral magnets. J. Phys. A 51, 375401 <a href=\"https:\/\/doi.org\/10.1088\/1751-8121\/aad521\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/1751-8121\/aad521\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/1751-8121\/aad521<\/a> (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1751-8121\/aad521\" data-track-item_id=\"10.1088\/1751-8121\/aad521\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1751-8121%2Faad521\" aria-label=\"Article reference 18\" data-doi=\"10.1088\/1751-8121\/aad521\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 18\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Hopfions%20in%20chiral%20magnets&amp;journal=J.%20Phys.%20A&amp;doi=10.1088%2F1751-8121%2Faad521&amp;volume=51&amp;publication_year=2018&amp;author=Sutcliffe%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR19\">M\u00fcller, G. P., Rybakov, F. N., J\u00f3nsson, H., Bl\u00fcgel, S. &amp; Kiselev, N. S. Coupled quasimonopoles in chiral magnets. Phys. Rev. B 101, 184405 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevB.101.184405\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevB.101.184405\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevB.101.184405<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.101.184405\" data-track-item_id=\"10.1103\/PhysRevB.101.184405\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.101.184405\" aria-label=\"Article reference 19\" data-doi=\"10.1103\/PhysRevB.101.184405\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvB.101r4405M\" aria-label=\"ADS reference 19\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 19\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Coupled%20quasimonopoles%20in%20chiral%20magnets&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.101.184405&amp;volume=101&amp;publication_year=2020&amp;author=M%C3%BCller%2CGP&amp;author=Rybakov%2CFN&amp;author=J%C3%B3nsson%2CH&amp;author=Bl%C3%BCgel%2CS&amp;author=Kiselev%2CNS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR20\">Kent, N. et al. Creation and observation of hopfions in magnetic multilayer systems. Nat. Commun. 12, 1562 <a href=\"https:\/\/doi.org\/10.1038\/s41467-021-21846-5\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-021-21846-5\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-021-21846-5<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-021-21846-5\" data-track-item_id=\"10.1038\/s41467-021-21846-5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-021-21846-5\" aria-label=\"Article reference 20\" data-doi=\"10.1038\/s41467-021-21846-5\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021NatCo..12.1562K\" aria-label=\"ADS reference 20\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 20\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Creation%20and%20observation%20of%20hopfions%20in%20magnetic%20multilayer%20systems&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-021-21846-5&amp;volume=12&amp;publication_year=2021&amp;author=Kent%2CN\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR21\">Li, L. et al. Electrically writing a magnetic heliknoton in a chiral magnet. Nat. Mater. 25, 950\u2013955 <a href=\"https:\/\/doi.org\/10.1038\/s41563-025-02450-0\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41563-025-02450-0\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41563-025-02450-0<\/a> (2026).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41563-025-02450-0\" data-track-item_id=\"10.1038\/s41563-025-02450-0\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41563-025-02450-0\" aria-label=\"Article reference 21\" data-doi=\"10.1038\/s41563-025-02450-0\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 21\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Electrically%20writing%20a%20magnetic%20heliknoton%20in%20a%20chiral%20magnet&amp;journal=Nat.%20Mater.&amp;doi=10.1038%2Fs41563-025-02450-0&amp;volume=25&amp;pages=950-955&amp;publication_year=2026&amp;author=Li%2CL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR22\">Volovik, G. E. Linear momentum in ferromagnets. J. Phys. C: Solid State Phys. 20, L83 <a href=\"https:\/\/doi.org\/10.1088\/0022-3719\/20\/7\/003\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/0022-3719\/20\/7\/003\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/0022-3719\/20\/7\/003<\/a> (1987).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/0022-3719\/20\/7\/003\" data-track-item_id=\"10.1088\/0022-3719\/20\/7\/003\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F0022-3719%2F20%2F7%2F003\" aria-label=\"Article reference 22\" data-doi=\"10.1088\/0022-3719\/20\/7\/003\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1987JPhC...20L..83V\" aria-label=\"ADS reference 22\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 22\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Linear%20momentum%20in%20ferromagnets&amp;journal=J.%20Phys.%20C%3A%20Solid%20State%20Phys.&amp;doi=10.1088%2F0022-3719%2F20%2F7%2F003&amp;volume=20&amp;publication_year=1987&amp;author=Volovik%2CGE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR23\">Schulz, T. et al. Emergent electrodynamics of skyrmions in a chiral magnet. Nat. Phys. 8, 301\u2013304 <a href=\"https:\/\/doi.org\/10.1038\/nphys2231\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys2231\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys2231<\/a> (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys2231\" data-track-item_id=\"10.1038\/nphys2231\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys2231\" aria-label=\"Article reference 23\" data-doi=\"10.1038\/nphys2231\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 23\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Emergent%20electrodynamics%20of%20skyrmions%20in%20a%20chiral%20magnet&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys2231&amp;volume=8&amp;pages=301-304&amp;publication_year=2012&amp;author=Schulz%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR24\">Litzius, K. et al. Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy. Nat. Phys. 13, 170\u2013175 <a href=\"https:\/\/doi.org\/10.1038\/nphys4000\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys4000\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys4000<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys4000\" data-track-item_id=\"10.1038\/nphys4000\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys4000\" aria-label=\"Article reference 24\" data-doi=\"10.1038\/nphys4000\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 24\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Skyrmion%20Hall%20effect%20revealed%20by%20direct%20time-resolved%20X-ray%20microscopy&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys4000&amp;volume=13&amp;pages=170-175&amp;publication_year=2017&amp;author=Litzius%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR25\">Jiang, W. et al. Direct observation of the skyrmion hall effect. Nat. Phys. 13, 162\u2013169 <a href=\"https:\/\/doi.org\/10.1038\/nphys3883\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys3883\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys3883<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys3883\" data-track-item_id=\"10.1038\/nphys3883\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys3883\" aria-label=\"Article reference 25\" data-doi=\"10.1038\/nphys3883\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 25\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Direct%20observation%20of%20the%20skyrmion%20hall%20effect&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys3883&amp;volume=13&amp;pages=162-169&amp;publication_year=2017&amp;author=Jiang%2CW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR26\">Ackerman, P. J., Boyle, T. &amp; Smalyukh, I. I. Squirming motion of baby skyrmions in nematic fluids. Nat. Commun. 8, 673 <a href=\"https:\/\/doi.org\/10.1038\/s41467-017-00659-5\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-017-00659-5\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-017-00659-5<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-017-00659-5\" data-track-item_id=\"10.1038\/s41467-017-00659-5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-017-00659-5\" aria-label=\"Article reference 26\" data-doi=\"10.1038\/s41467-017-00659-5\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017NatCo...8..673A\" aria-label=\"ADS reference 26\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 26\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Squirming%20motion%20of%20baby%20skyrmions%20in%20nematic%20fluids&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-017-00659-5&amp;volume=8&amp;publication_year=2017&amp;author=Ackerman%2CPJ&amp;author=Boyle%2CT&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR27\">Sohn, H. R. O. et al. Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals. Phys. Rev. E 97, 052701 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevE.97.052701\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevE.97.052701\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevE.97.052701<\/a> (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevE.97.052701\" data-track-item_id=\"10.1103\/PhysRevE.97.052701\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevE.97.052701\" aria-label=\"Article reference 27\" data-doi=\"10.1103\/PhysRevE.97.052701\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018PhRvE..97e2701S\" aria-label=\"ADS reference 27\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 27\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dynamics%20of%20topological%20solitons%2C%20knotted%20streamlines%2C%20and%20transport%20of%20cargo%20in%20liquid%20crystals&amp;journal=Phys.%20Rev.%20E&amp;doi=10.1103%2FPhysRevE.97.052701&amp;volume=97&amp;publication_year=2018&amp;author=Sohn%2CHRO\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR28\">Sohn, H. R. O. &amp; Smalyukh, I. I. Electrically powered motions of toron crystallites in chiral liquid crystals. Proc. Natl Acad. Sci. USA 117, 6437\u20136445 <a href=\"https:\/\/doi.org\/10.1073\/pnas.1922198117\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1073\/pnas.1922198117\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1073\/pnas.1922198117<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1073\/pnas.1922198117\" data-track-item_id=\"10.1073\/pnas.1922198117\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1073%2Fpnas.1922198117\" aria-label=\"Article reference 28\" data-doi=\"10.1073\/pnas.1922198117\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PNAS..117.6437S\" aria-label=\"ADS reference 28\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 28\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Electrically%20powered%20motions%20of%20toron%20crystallites%20in%20chiral%20liquid%20crystals&amp;journal=Proc.%20Natl%20Acad.%20Sci.%20USA&amp;doi=10.1073%2Fpnas.1922198117&amp;volume=117&amp;pages=6437-6445&amp;publication_year=2020&amp;author=Sohn%2CHRO&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR29\">Coelho, R. C. V., Zhao, H., Tasinkevych, M., Smalyukh, I. I. &amp; Telo da Gama, M. M. Sculpting liquid crystal skyrmions with external flows. Phys. Rev. Res. 5, 033210 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevResearch.5.033210\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevResearch.5.033210\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevResearch.5.033210<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevResearch.5.033210\" data-track-item_id=\"10.1103\/PhysRevResearch.5.033210\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.5.033210\" aria-label=\"Article reference 29\" data-doi=\"10.1103\/PhysRevResearch.5.033210\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 29\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Sculpting%20liquid%20crystal%20skyrmions%20with%20external%20flows&amp;journal=Phys.%20Rev.%20Res.&amp;doi=10.1103%2FPhysRevResearch.5.033210&amp;volume=5&amp;publication_year=2023&amp;author=Coelho%2CRCV&amp;author=Zhao%2CH&amp;author=Tasinkevych%2CM&amp;author=Smalyukh%2CII&amp;author=Telo%20da%20Gama%2CMM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR30\">Tai, J.-S. B. &amp; Smalyukh, I. I. Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers, and their hybrids in chiral nematics. Phys. Rev. E 101, 042702 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevE.101.042702\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevE.101.042702\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevE.101.042702<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevE.101.042702\" data-track-item_id=\"10.1103\/PhysRevE.101.042702\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevE.101.042702\" aria-label=\"Article reference 30\" data-doi=\"10.1103\/PhysRevE.101.042702\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvE.101d2702T\" aria-label=\"ADS reference 30\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 30\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Surface%20anchoring%20as%20a%20control%20parameter%20for%20stabilizing%20torons%2C%20skyrmions%2C%20twisted%20walls%2C%20fingers%2C%20and%20their%20hybrids%20in%20chiral%20nematics&amp;journal=Phys.%20Rev.%20E&amp;doi=10.1103%2FPhysRevE.101.042702&amp;volume=101&amp;publication_year=2020&amp;author=Tai%2CJ-SB&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR31\">Amaral, G. N. C. et al. Liquid crystal torons in Poiseuille-like flows. Sci. Rep. 15, 2684 <a href=\"https:\/\/doi.org\/10.1038\/s41598-024-83294-7\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41598-024-83294-7\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41598-024-83294-7<\/a> (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41598-024-83294-7\" data-track-item_id=\"10.1038\/s41598-024-83294-7\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41598-024-83294-7\" aria-label=\"Article reference 31\" data-doi=\"10.1038\/s41598-024-83294-7\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025NatSR..15.2684A\" aria-label=\"ADS reference 31\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 31\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Liquid%20crystal%20torons%20in%20Poiseuille-like%20flows&amp;journal=Sci.%20Rep.&amp;doi=10.1038%2Fs41598-024-83294-7&amp;volume=15&amp;publication_year=2025&amp;author=Amaral%2CGNC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR32\">Foster, D. et al. Two-dimensional skyrmion bags in liquid crystals and ferromagnets. Nat. Phys. 15, 655\u2013659 <a href=\"https:\/\/doi.org\/10.1038\/s41567-019-0476-x\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41567-019-0476-x\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41567-019-0476-x<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-019-0476-x\" data-track-item_id=\"10.1038\/s41567-019-0476-x\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-019-0476-x\" aria-label=\"Article reference 32\" data-doi=\"10.1038\/s41567-019-0476-x\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 32\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Two-dimensional%20skyrmion%20bags%20in%20liquid%20crystals%20and%20ferromagnets&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-019-0476-x&amp;volume=15&amp;pages=655-659&amp;publication_year=2019&amp;author=Foster%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR33\">Thiele, A. A. Steady-state motion of magnetic domains. Phys. Rev. Lett. 30, 230 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.30.230\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.30.230\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.30.230<\/a> (1973).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.30.230\" data-track-item_id=\"10.1103\/PhysRevLett.30.230\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.30.230\" aria-label=\"Article reference 33\" data-doi=\"10.1103\/PhysRevLett.30.230\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1973PhRvL..30..230T\" aria-label=\"ADS reference 33\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 33\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Steady-state%20motion%20of%20magnetic%20domains&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.30.230&amp;volume=30&amp;publication_year=1973&amp;author=Thiele%2CAA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR34\">G\u00f6bel, B., Mertig, I. &amp; Tretiakov, O. A. Beyond skyrmions: review and perspectives of alternative magnetic quasiparticles. Phys. Rep. 895, 1\u201328 <a href=\"https:\/\/doi.org\/10.1016\/j.physrep.2020.10.001\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1016\/j.physrep.2020.10.001\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1016\/j.physrep.2020.10.001<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.physrep.2020.10.001\" data-track-item_id=\"10.1016\/j.physrep.2020.10.001\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.physrep.2020.10.001\" aria-label=\"Article reference 34\" data-doi=\"10.1016\/j.physrep.2020.10.001\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhR...895....1G\" aria-label=\"ADS reference 34\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4199839\" aria-label=\"MathSciNet reference 34\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 34\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Beyond%20skyrmions%3A%20review%20and%20perspectives%20of%20alternative%20magnetic%20quasiparticles&amp;journal=Phys.%20Rep.&amp;doi=10.1016%2Fj.physrep.2020.10.001&amp;volume=895&amp;pages=1-28&amp;publication_year=2021&amp;author=G%C3%B6bel%2CB&amp;author=Mertig%2CI&amp;author=Tretiakov%2COA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR35\">Zhang, S. &amp; Li, Z. Roles of nonequilibrium conduction electrons on the magnetization dynamics of ferromagnets. Phys. Rev. Lett. 93, 127204 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.93.127204\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.93.127204\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.93.127204<\/a> (2004).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.93.127204\" data-track-item_id=\"10.1103\/PhysRevLett.93.127204\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.93.127204\" aria-label=\"Article reference 35\" data-doi=\"10.1103\/PhysRevLett.93.127204\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2004PhRvL..93l7204Z\" aria-label=\"ADS reference 35\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 35\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Roles%20of%20nonequilibrium%20conduction%20electrons%20on%20the%20magnetization%20dynamics%20of%20ferromagnets&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.93.127204&amp;volume=93&amp;publication_year=2004&amp;author=Zhang%2CS&amp;author=Li%2CZ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR36\">Coelho, R. C. V., Tasinkevych, M. &amp; da Gama, M. M. T. Dynamics of flowing 2D skyrmions. J. Phys. Cond. Mat. 34, 034001 <a href=\"https:\/\/doi.org\/10.1088\/1361-648x\/ac2ca9\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/1361-648x\/ac2ca9\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/1361-648x\/ac2ca9<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1361-648x\/ac2ca9\" data-track-item_id=\"10.1088\/1361-648x\/ac2ca9\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1361-648x%2Fac2ca9\" aria-label=\"Article reference 36\" data-doi=\"10.1088\/1361-648x\/ac2ca9\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022JPCM...34c4001C\" aria-label=\"ADS reference 36\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 36\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dynamics%20of%20flowing%202D%20skyrmions&amp;journal=J.%20Phys.%20Cond.%20Mat.&amp;doi=10.1088%2F1361-648x%2Fac2ca9&amp;volume=34&amp;publication_year=2021&amp;author=Coelho%2CRCV&amp;author=Tasinkevych%2CM&amp;author=Gama%2CMMT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR37\">Ericksen, J. L. Hydrostatic theory of liquid crystals. Arch. Ration. Mech. Anal. 9, 371\u2013378 <a href=\"https:\/\/doi.org\/10.1007\/bf00253358\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1007\/bf00253358\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1007\/bf00253358<\/a> (1962).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"noopener nofollow\" data-track-label=\"10.1007\/bf00253358\" data-track-item_id=\"10.1007\/bf00253358\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/link.springer.com\/doi\/10.1007\/bf00253358\" aria-label=\"Article reference 37\" data-doi=\"10.1007\/bf00253358\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=137403\" aria-label=\"MathSciNet reference 37\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 37\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Hydrostatic%20theory%20of%20liquid%20crystals&amp;journal=Arch.%20Ration.%20Mech.%20Anal.&amp;doi=10.1007%2Fbf00253358&amp;volume=9&amp;pages=371-378&amp;publication_year=1962&amp;author=Ericksen%2CJL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR38\">Leslie, F. M. &amp; Green, A. E. Some thermal effects in cholesteric liquid crystals. Proc. R. Soc. Lond. A 307, 359\u2013372 <a href=\"https:\/\/doi.org\/10.1098\/rspa.1968.0195\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1098\/rspa.1968.0195\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1098\/rspa.1968.0195<\/a> (1968).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1098\/rspa.1968.0195\" data-track-item_id=\"10.1098\/rspa.1968.0195\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1098%2Frspa.1968.0195\" aria-label=\"Article reference 38\" data-doi=\"10.1098\/rspa.1968.0195\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1968RSPSA.307..359L\" aria-label=\"ADS reference 38\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 38\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Some%20thermal%20effects%20in%20cholesteric%20liquid%20crystals&amp;journal=Proc.%20R.%20Soc.%20Lond.%20A&amp;doi=10.1098%2Frspa.1968.0195&amp;volume=307&amp;pages=359-372&amp;publication_year=1968&amp;author=Leslie%2CFM&amp;author=Green%2CAE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR39\">Stewart, I. W. The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction (CRC Press, 2019).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR40\">Kleman, M. &amp; Lavrentovich, O. D. Soft Matter Physics (Springer, 2003).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR41\">Kr\u00fcger, T. et al. The Lattice Boltzmann Method: Principles and Practice (Springer International Publishing, 2016).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR42\">Succi, S. The Lattice Boltzmann Equation: For Complex States of Flowing Matter (Oxford Univ. Press, 2018).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR43\">Turk, J. &amp; Sven\u0161ek, D. Backflow-mediated domain switching in nematic liquid crystals. Phys. Rev. E 89, 032508 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevE.89.032508\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevE.89.032508\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevE.89.032508<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevE.89.032508\" data-track-item_id=\"10.1103\/PhysRevE.89.032508\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevE.89.032508\" aria-label=\"Article reference 43\" data-doi=\"10.1103\/PhysRevE.89.032508\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvE..89c2508T\" aria-label=\"ADS reference 43\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 43\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Backflow-mediated%20domain%20switching%20in%20nematic%20liquid%20crystals&amp;journal=Phys.%20Rev.%20E&amp;doi=10.1103%2FPhysRevE.89.032508&amp;volume=89&amp;publication_year=2014&amp;author=Turk%2CJ&amp;author=Sven%C5%A1ek%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n","protected":false},"excerpt":{"rendered":"Hess, A. J., Poy, G., Tai, J.-S. B., \u017dumer, S. &amp; Smalyukh, I. I. Control of light by&hellip;\n","protected":false},"author":2,"featured_media":888785,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[2362,2361,2366,2365,47654,257,31205,2360,2363,2364,199,79,2359],"class_list":["post-888784","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-atomic","tag-classical-and-continuum-physics","tag-complex-systems","tag-condensed-matter-physics","tag-fluid-dynamics","tag-general","tag-liquid-crystals","tag-mathematical-and-computational-physics","tag-molecular","tag-optical-and-plasma-physics","tag-physics","tag-science","tag-theoretical"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/888784","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/comments?post=888784"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/888784\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media\/888785"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media?parent=888784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/categories?post=888784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/tags?post=888784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}