8/3/2019 S. Brazovski and N. Kirova- Topological coupling of dislocations and magnetization vorticity in Spin Density Waves

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azXlw;omif"bav- zsoz (I 2 Z:-s,H(I,

Ini IE4zsoz-z4 Z 9 zsoz

Pe see vhav plvhli zsoz vheze ls im tezlbeivzloan nap juv zavhez vhe azeamie gmz vhe flsnmoavlmi eiez`|) Av naz`e flsvaioes vhe svaifazf I " nap lszesvmzef juv eihaioef as 1-:i ) Vhe equlnljzlub plvh zesteov vm a``ze`avlmimg eneovzmis vm vhe FN ls omivzmnef j| vhe ohebloan tmveivlan F 2 H(I,-I)Zesunvli` F mg a sli`ne F"nmmt ls fzmpi sohebavloann| av Gl`) 1) Heze vhefashef nlie omzzestmifs vm vhe ba`ievlo wmzvex nmmt) Vhe liiez ze`lmi mg vhesmnlf nlie fesozljes vhe F"nmmt av shmzvesv flsvaioes pheze vhe Omunmbj gmzoesaze imv lbtmzvaiv |ev)

?) Ombjlief vmtmnm`loan fegeovs li _FP)

Li _FP vhe Omunmbj eihaioebeiv mg vhe flsnmoavlmi eiez`| tna|s a tzli"oltan zmne vm jzli` vm nlge a steolan ombjlief vmtmnm loan mjkeov) Vhls ls vhehang"live`ez flsnmoavlmi aoombtailef j| 184m zmvavlmi M mg vhe sva``ezef ba`"ievl{avlmi b) Lifeef. vhe _FP mzfez tazabevez annmps gmz vhe gmnnmpli` vhzeev|tes mg seng"battli` ) (Vhe battli` ls a `eiezan zequlebeiv mg vmtmnm`l"oan omiieovlwlv| phloh seneovs vhe annmpef omifi`uzavlmis S5.7R),l) imzban flsnmoavlmi; # :. b b3ll) imzban b wmzvex; b M: b. 3lll) ombjlief mjkeov ; # . b M b 2 b)

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8/3/2019 S. Brazovski and N. Kirova- Topological coupling of dislocations and magnetization vorticity in Spin Density Waves

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Z

Ohebloan tmveivlan

Gl`uze 1; Vhe ohebloan tmveivlan F 2 P-I mg vhe F"nmmt) Fashef nlieomzzestmifs vm vhe bmfen plvhmuv Omunmbj livezaovlmis aif vm vhe wmzvex nmmt)

A ieoesslv| mg sebl"wmzvloes li omiweivlmian aivlgezzmba`ievs li tzeseioe mg gzm{ei"li hmsv navvloe flsnmoavlmis has jeei zeanl{ef anzeaf| li S0R) Li _FP vhe sebl"

wmzvloes jeombe vhe mjkeovs mg vhe nmpesv eiez`| ozeavef li vhe omuzse mg T_ tzm"oess) Lifeef. imv gaz jenmp Vo av i 1 vhe enasvlo bmfunl zenavef vm vhe thaseflstnaoebeivs aif vm ba`ievl{avlmi zmvavlmis aze mg vhe sabe mzfez) Heioe annvhzee mjkeovs hawe slblnaz eiez les) Plvh nmpezli` V vhe eiez`| mg vhe mjkeovll) ls imv affleovef jeoause ohaz`es aze imv tezvuzjef sm vhav Omunmbj gmzoes azeimv liwmnwef) Gmz mjkeovs l) aif lll) vhe bakmz eiez`| 1-:i ls assmolavef vmflsvmzvlmis mg sm vhav vhe eiez`| mg b zmvavlmi li oase lll) ba| je ie`neovef) Vmombtaze vhe bali omivzljuvlmis vm vhe eiez`les mg mjkeovs l) aif lll) pe zeblifvhav av `lwei Z vhe FN eiez`| feteifs mi lvs plifli` iubjez P as P:.pheze P 2 1-: gmz "FN aif aif P 2 1 gmz :"FN) Pe busv ombtaze vhelz ei"

ez`les av vhe `lwei iubjez mg aooubunavef eneovzmis :I) Gmz shmzviess omislfezmin| vhe naz`esv (sozeeief, sl{es mg FNs) Gmz vhe F"nmmt aif vhe F"nlie pe haweomzzestmifli`n|

I P Z:. F (P:Z ni Z,-(P Z:, P?-:-I1-:

I P Z. F (P: ni Z,-(P Z, P:-I

Li jmvh oases vhe nmpesv eiez`| tez eneovzmi ls `lwei j| ai mjkeov plvh sbannesv

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8/3/2019 S. Brazovski and N. Kirova- Topological coupling of dislocations and magnetization vorticity in Spin Density Waves

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P 2 1-: l)e) j| vhe ombjlief mie) Vhus li _FP vhe imzban flsnmoavlmi busvstnlv livm vpm mjkeovs mg vhe ombjlief vmtmnm`|) Attazeivn| vhe| plnn hawe vhe

sabe sl`i mg vhe flstnaolwe hang"live`ez plifli` iubjezs aif mttmslve sl`is mgvhe hang"live`ez stli zmvavlmi iubjezs) Li Gl`): pe tzeseiv vhe weovmz fienf mg vhenmoan _FP ba`ievlsavlmi gmz suoh a h|bez) Vhe ohali axls ls hmzl{mivan) Fue

Gl`uze :; Vhe weovmz"fienf gmz hang"FN ombjlief plvh sebl"wmzvex) _mnlf nlieslifloave omisvaiv thases azmuif vhe hang"FN)

vm vhe tzeseioe mg vhe hang"live`ez FN. vhe iubjez mg slves ohai`es jevpeei vheuttez aif vhe nmpez zmps gzmb :)5 tezlmfs (7#7#?, vm : tezlmfs (0#5,)

Li vhe tzeseioe mg stli ailsmvzmt| gmz ann vhzee mzleivavlmis. vhe gzee zmvavlmi

mg stlis ls tzmhljlvef av naz`e flsvaioes gzmb vhe FN) Vhei vhe vpm mjkeovs plnnje jmuif j| a svzli` phloh ls vhe Ieen fmbali pann) Lv oai je shmpi vm svzevohanmi` vhe livezohali flzeovlmi) Usuann| vhe stli ailsmvzmt| ls imvloeajne min| gmzmie mzleivavlmi aif ohazaovezl{ef j| vhe stli"mt fienf Hsg 1V) Lv pmunfmzl`liave vhe svzli` mg vhe nei`vh 4)1b) Av hl`hez ba`ievlo fienfs min| asbann li"tnaie ailsmvzmt| ls negv sm vhav vhe svzli` nei`vh ba| zeaoh vhe sabtneplfvh)

Pe omionufe vhav vhe snlfli` _FP shmunf `eiezave h|bezs; vhe ombjliefvmtmnm`loan mjkeovs pheze vhe stli zmvavlmis aze omutnef vm vhe FP flstnaoebeivs)

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8/3/2019 S. Brazovski and N. Kirova- Topological coupling of dislocations and magnetization vorticity in Spin Density Waves

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Vhe h|bezs aze svajne nmpezli` vhe FN Omunmbj eiez |) Vhls ombjliavlmieffleovlwen| zefuoes vhe _FP tezlmf annmpli` e)`) gmz vhe vploe feozease li vhe

IJI gzequeio|. phloh ls ai lbtmzvaiv flstuvajne quesvlmi S8.