1 Direct Demonstration of Topological Stability of Magnetic Skyrmions via 2 Topology Manipulation 3 Soong-Geun Je,†,‡,§,|| Hee-Sung Han,¶ Se Kwon Kim,** Sergio A. Montoya,†† Weilun Chao,† "#- 4 Sun Hong,‡‡ $ri% $. &ullerton,§§,|||| Ki-Suk 'ee,¶ Kyung-Jin 'ee,‡‡,¶¶ Mi-(oung Im,†,‡,¶,* and 5 Jung-Il Hong‡,* 6 † enter for X-ray O-ti%., Lawrence Ber#eley National Laboratory, Ber#eley, CA 94720, USA. 7 ‡8epartment of Emerging Material. S%ience, DGIS9, Daegu 42988, Korea. 8 § enter for Spin-,rbitroni% Material., Korea Uni;ersity, Seoul 02841, Korea. 9 ||8epartment of P!y.i%., Chonnam National Uni;ersity, Gwang>u 61186, Korea 10 ¶S%hool of Material. S%ience and $ngineering, 7l.an 0ational Institute of S%ience and 11 9e%hnology, Ul.an 44919, Korea. 12 **8epartment of P!y.i%. and A.tronomy, Uni;ersity of Mi..ouri, Columbia, M, 65211, USA. 13 ††Spa%e and Na;al War*are Sy.tem. Center Pa%iA%, San Diego, CA 92152, USA. 14 ‡‡K7-KIS9 Graduate S%hool of on;erging S%ience and 9e%hnology, Korea 7ni;ersity, Seoul 15 02841, Korea. 16 §§ enter *or Memory and Be%ording Be.ear%h, 7ni;ersity of ali*ornia–San 8iego, 'a Jolla, 17 A 92093, USA. 18 ||||8epartment of Ele%tri%al and Computer Engineering, 7ni;ersity of ali*ornia–San 8iego, La 19 Jolla, CA 92093, USA. 20 ¶¶8epartment of Material. S%ience and Engineering, Korea Uni;ersity, Seoul 02841, Korea. 21 *e-mailE mimFlbl.go;G >ihong@)gi.t.a%.kr 1 1 Abstract 2 9opologi%al prote%tion pre%lude. a continuous de*ormation between topologi%ally ineHui;alent 3 %onfigurations in a %ontinuum. Moti;ate) 1y thi. %once-t, magneti% .#yrmions, topologi%ally 4 nontrivial .pin texture., are expe%te) to exhibit the topologi%al .ta1ility, there1y offering a 5 prospe%t a. a nanometer-.%ale non-;olatile information %arrier. In real material., howe;er, 6 atomi% .pins are %onfigure) a. not %ontinuous but di.%rete di.tribution, whi%! rai.e. a 7 *undamental Hue.tion i* the topologi%al .tability i. indee) pre.er;e) *or real magneti% 8 .#yrmions. Answering t!i. Hue.tion ne%e..itate. a dire%t %ompari.on between topologi%ally 9 nontrivial and trivial .pin texture., but the dire%t %ompari.on in one .ample under the .ame 10 magneti% Ael). ha. been %hallenging. Here we report how to .ele%ti;ely a%hie;e either a 11 .#yrmion .tate or a topologi%ally trivial bubble .tate in a .ingle .pe%imen and there1y 12 experimentally .how how robust t!e .#yrmion .tru%ture i. in %ompari.on wit! the bubble.. 13 We demonstrate that topologi%ally nontrivial magneti% .#yrmions .how longer li*etime. than 14 trivial bubble .tructure., evi)encing the topologi%al .tability in a real di.%rete .y.tem. ,ur 15 wor# %orroborate. the -!y.i%al importance of the topology in the magneti% material., whi%! 16 ha. hitherto been .ugge.te) 1y mathemati%al argument., provi)ing an important .te- towar). 17 e;er-dense and more-.table magneti% de;i%e.. 18 Keywor).E topology manipulation, topologi%al .tability, topologi%al prote%tion, magneti% 19 .#yrmion, magneti% bubble, li*etime, FeG) 20 2 1 9opology<,5 %onstitute. profound viewpoint. in modern -!y.i%. on re;ealing ;arious robust 2 .tate. exi.ting in many -!y.i%al .y.tem. including topologi%al insulators,3,3 ultra%ol) atom.,@ 3 topologi%al insulator la.ers? and topologi%al me%hani%al metamaterial..4 9opology ha. al.o 4 been .uc%e..*ul in repre.enting ;arious magneti% phenomena.1,8-<: In a %ontinuum de.%ri-tion 5 of magneti% .y.tem., the topologi%al prote%tion mean. t!at a %ontinuous de*ormation between 6 .pin .tructure. wit! diJerent topologie. i. not allowe).1,5 9hi. im-lie. eI%e-tional .tability of 7 .pin texture. with nontrivial topology again.t colla-.e to a uni*orm spin configuration. 8 A %om-elling eIam-le of .uc! topologi%al .-in .tru%ture. i. t!e magneti% .#yrmion. It i. a 9 .wirling .pin .tructure K&igure 1aL pos.e..ing a HuantiMe) topologi%al %harge deAne) 1y < 10 = = m Q 3 π ∫ m ∙ ( ∂x m× ∂y m ) dxdy <, whi%! mea.ure. how many time. winds t!e unit .phere 11 within a %lose) .ur*a%e, where m i. the unit ;e%tor of magnetiMation. In term. of topologi%al 12 %harge, the .#yrmion .tru%ture i. topologi%ally di.tinct from a uni*orm *erromagneti% .tate 13 with Q=6, hence chara%teriMed a. a topologi%ally nontrivial s-in texture. 14 It i. anti%i-ate) that magneti% s#yrmions wit! eI%e-tionally .mall .iMe. remain robust and can 15 be dri;en 1y ele%tri% %urrent. ea.ily without being interru-te) or annihilate) 1y .y.tem 16 di.orders suc! a. structural de*e%t..<2,5: There*ore, it i. considere) a. a promi.ing candi)ate for 17 information %arrier in the appli%ations *or ultrahigh density data .torage,<9,20,52 logi%,D6 and 18 neuromor-!i%D<,D5 te%hnologie.. A. the .uc%e..*ul im-lementation of .#yrmion-ba.e) 19 appli%ations %rucially relie. on the retention of .#yrmion .tructure., the topologi%ally 20 prote%ted property of the s#yrmions i. the most important prereHui.ite. 21 In real material., howe;er, magneti% moment. are localiMe) on atom. in a di.%rete latti%e that 22 the %olla-.e of magneti% .#yrmions i. plausible 1y o;er%oming a Anite energy barrier in an 23 atomi.ti% length s%ale, where the topologi%al argument i. nulliAe). Thi. reali.ti% situation thus 24 naturally rai.e. *undamentally and te%hnologi%ally important Hue.tionsE ". the topologi%al 25 prote%tion .till a viable %once-t to guarantee the .#yrmion .tability and how .trong i. the 26 %onstraint in t!e real di.%rete sy.temN 27 onsiderable eJort. ha;e been de;ote) to addre..ing the i..ue. on the .#yrmion .ta1ility in a 28 real .y.tem, but they .till remain %ontro;ersial.DD 9heoreti%al wor#. !a;e .ugge.te) that there 29 are alternati;e .#yrmion de%ay pat!. along whi%! the energy barrier i. lower than that of 3 1 atomi.ti%-.hrinking of .#yrmions34-D4 or the entropy ha. an important role in the .#yrmion 2 li*etime.D7-D2 A *ew experimental wor#.30-35 ha;e dealt wit! the .#yrmion .tability 1y 3 mea.uring t!e li*etime. Howe;er, the la%# of dire%t experimental %ompari.on of topologi%ally 4 trivial and nontrivial .pin .tru%ture. under the identi%al environment .uc! a. within the .ame 5 .pe%imen lea;e. the i..ue of ambiguity be%ause the .#yrmion li*etime i. highly dependent not 6 only on the topologi%al eJe%t but al.o on other fa%tors including material propertie.. 7 A re-re.entati;e of the topologi%ally trivial %ounterpart to the .#yrmion i. a bubble of Q=6 8 a. .%hemati%ally depi%te) in &igure <1. 9he boundary of a bubble %on.i.t. of a pair of hal* 9 %ir%le. wit! winding .pins in the opposite dire%tion and the two hal* %ir%le. are >oine) 1y 10 Bloc! line.. Since it. topologi%al %!arge Q eHual. to 0, the topologi%al eJe%t doe. not 11 parti%ipate in t!e annihilation of the bubble. 12 13 FIG. 1. Schematic illustration of a topologically nontrivial skyrmion and a topologically trivial bubble. KaL 14 /loch-type s#yrmion with |Q∨¿<. (1L Bubble with Q=6. The B' re*er. to the Bloch line. 15 16 9he experimental diO%ultie. hindering a thorough a..e..ment of the topologi%al eJe%t to the 17 .#yrmion .ta1ility i. twofol). &irstly, experimental mea.urement of .ub-100 nm .pin 18 .tru%ture. wit! a .uffi%iently high temporal re.olution to dete%t t!e .#yrmion li*etime i. 19 te%hni%ally a %hallenging i..ue. Se%ondly and more importantly, tailoring the topology,3D,33 20 there1y .ele%ti;ely preparing either .#yrmions or bubble. in the .ame material, i. another 21 %hallenging i..ue that ha. not been *ully explore). A mea.urable -!y.i%al Huantity to e.timate 22 the topologi%al eJe%t i. the li*etime, whi%! howe;er ;arie. dra.ti%ally depending on material 23 propertie.. 9here*ore, re.olving the .e%ond i..ue i. parti%ularly important to dire%tly %ompare 24 the stabilitie. of topologi%ally nontrivial and trivial stru%ture. on an eHual footing. 25 ,;er%oming the two %!allenge. mentione) abo;e, we experimentally demonstrate the .tability 26 of magneti% .#yrmions roote) in topology. /y %hoosing diJerent magneti% Ael) pathway., we 27 are able to .ele%ti;ely rea%! eit!er a magneti% .#yrmion .tate or a bubble .tate in the .ame 4 1 .pe%imen under the .ame magneti% Ael) .trength, provi)ing a ;ersatile route towar). the 2 topology manipulation and *air %ompari.on of the topologi%al eJe%t. 9he li*etime. of bot! 3 .#yrmions and bubble. are t!en .tudie) u.ing t!e *ull-fiel) transmi..ion .oft I-ray 4 mi%ros%opy KM9+ML %ombine) wit! pul.e) magneti% Ael). of ;arious durations to enhance 5 the time re.olution. We And that magneti% .#yrmions exhi1it muc! longer li*etime than 6 bubble.