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SKYRMIONS and the V = 1 QUANTUM HALL FERROMAGNET

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SKYRMIONS and the V = 1 QUANTUM HALL FERROMAGNET o 9 (1997 ACA YSICA OŁOICA A Νo oceeigs o e I Ieaioa Scoo o Semicoucig Comous asowiec 1997 SKYMIOS A E v = 1 QUAUM A EOMAGE M MAA GOEG e o ysics oso Uiesiy oso MA 15 USA EIE A K WES e aoaoies uce ecoogies Muay i 797 USA ece eeimea a eoeica iesigaios ae esue i a si i ou uesaig o e v = 1 quaum a sae ee ow eiss a wea o eiece a e eciaio ga a e esuig quasiaice secum a v = 1 ae ue prdntl o e eomageic may-oy ecage ieacio A gea aiey o eeimeay osee coeaios a v = 1 nnt e icooae io a euaie easio aou e sige-aice moe a sceme og oug o escie e iega qua- um a eec a iig aco 1 eoiss ow ee o e v = 1 sae as e quaum a eomage I is ae we eiew ece eoei- ca a eeimea ogess a eai ou ow oica iesigaios o e v = 1 quaum a egime e ecique o mageo-asoio sec- oscoy as oe o e oweu a oe o e occuacy o e owes aau ee i e egime o 7 v 13 aou e si ga Aiioay we ae eome simuaeous measuemes o e asoio oou- miescece a ooumiescece eciaio seca o e v = 1 sae i oe o euciae e oe o ecioic a eaaio eecs i oica secoscoy i e quaum a egime ACS umes 73Ηm 7-w 73Mí 717Gm 73 1 Ioucio Some iee yeas ae e iscoey o e acioa quaum a e- ec [1] e suy o woimesioa eeco sysems (ES coie o e owes aau ee ( coiues o e a eie aoaoy o e iesiga- io o may-oy ieacios e oieaio o eeimeay osee ac- ioa a saes [] e iscoey o comosie emios a a-iig [3] a e ossiiiy o eoic si-uoaie acioa gou saes [] ae u a ew eames o e aomaies a coiue o caege ou uesaig o sog eeco—eeco coeaios i e eeme mageic quaum imi ecey e v = 1 quaum a sae a egio oug o e we-uesoo wii e (1 622 M.J. Manfra et al. sige-aice moe o e iega quaum a eec (IQE as ee ae o caaog o saes wose ysics is omiae y may-oy ieacios e imoace o e may-oy ecage couig o eemiig e secum a v = 1 ca e see i a aiy iuiie mae y ookig a e eea eegy scaes e aicaio o a age eeicua mageic ie is- ceies e sige aice saes o ee eecos i wo imesios io aau ees seaae i eegy y e cycoo ga Eac aau ee is massiey egeeae aowig may eecos o ae e same oia eegy Eac oia aau ee is ue si io a si-u a si-ow sae y e eema couig o e eecos si o e eea mageic ie iig aco v = 1 coesos o aig eacy oe eeco o eac aaiae sae i e owes eegy si-u aau ee Gie e age mageic ies yicay ecessay o osee e v = 1 quaum a sae (5 Τ B < 1 i may a is aea o o ca is sae e quaum a eomage eomageism is usuay associae wi e soaeous aigme o sis i e asece o a eea ie u a v = 1 a e eecos sae a commo quaie kieic eegy wic is coeioay cose as e eo o emegy e ga o e e oia aau ee is yicay o e oe o K i uis o emeaue us a ow em- eaues e eecos kieic eegy is esseiay oe ou a oes o aec e sysems yamics e wo emaiig eegy scaes ae e sige-aice eema eegy a may-oy ecage I GaAs sysems e eema siig is oy o oe K wie e yica eeco-eeco ieacio scae is aou 1 K A sige si eesa wic is e owes eegy sige-aice eciaio coss a gea ea i eomageic ecage eegy wic is owee y keeig eigoig sis aige us i may e a e ysics o eecos ieac- ig wii a sige oia aau ee wi suc a sma eema couig may o e aeciay iee om a o a eomage i e esece o a sma symmey eakig ie is is e essece o mos ece eoeica aoaces o e quaum a eec a v = 1 e oio o e quaum a eomage was is aace i e semi- a wok o Soi e a [5] is aoac icooae e use o e oiea σ moe (Νσ o isooic eomages io e suy o e = 1 quaum a eec e Νσ moe as ee eesiey suie a is eemeay eciaios ae kow o ossess igy oiia og-age si oe ese quasiaices ae cae skymios a cosis o a aia si esiy a is eese a e cee u gauay eas o e eomageic ackgou oe may mageic egs O couse ea quaum a eomages ossess a sma u iie eema couig wic mus e icue o eaisic cacuaios o eege- ics a si oaiaio A eee aee—ock eoy o quaum a skymioms was eeoe y eig a cowokes [] a oies a quaiaie asis o comaiso wi eeime e eegeics a si o ea quaum a skymios o cage si eue eciaios (CSEs ae agey ee- mie y e aamee 9 = gμB Β/(e 2 /ε0l0 e aio o e eema eegy o e Couom ieacio scae e eema em aos sma skymios wie e Couom em ies o maimie e sie o e si eue o yica sames ue iesigaio 9 ≈ 15 o is aue o 9 e CSE is aways owe i Skyrmions and the v = 1 Quantum Hall Ferromagnet 3 eegy a e sige si i eciaio a ioes e eesa o aoi- maey 3 sis I is e eciaio o skymios a is esosie o e ai suessio o e si oaiaio o ecusios away om v = 1. 1.1. Experimental verification of skyrmions ee ow eiss a eesie is o eeimea esus [7-1] a oi uamiguousy o eisece o skymios as e owes-yig cage eciaio o e si-oaie v = 1 quaum a sae e iiia aa measuig e si oaiaio as a ucio o iig aco came om aes oicay-ume M suies [7] is measueme o e Kig si wic is ooioa o e egee o eeco si oaiaio sows a ai a quasi-symmeici ecay o e si oaiaio o ecusios away om v = 1. is aa iicae a eac uamea eciaio cosiss o aoimaey 3 si is a cou o e eaie wii e coe o ay sige-aice moe A simia eoa- iaio was eie i e mageoasoio aa o Aie e a [9] Eiece o skymios as aso ee ou i aso Scmee e a [] emoye a ie-ie mageoaso measueme o e eegy ga a v = 1. y iig e same i a mageic ie wie keeig e iig aco cosa e aio o e eema eegy o e Couom eegy ca e aie Scmee measue e aciaio ga as a ucio o iig age e aciaio eegy is sesi- ie o e og-waeeg cage eciaios o e sysem a is aiaio imie cage aso meiae y quasiaices cayig age si quaum umes A o ese eay measuemes oie o e omia oe aye y eomageic ecage a wee i goo ageeme wi eoy a icooae skymios as e uamea eciaio o e sysem Oica eecio o skymios Ou eemiaio o e si oaiaio o e v = 1 sae is ase o oaiaio-esoe mageoasoio secoscoy e ES esies a e ieace o a sige-sie -mouaio oe A1GaAs—GaAs sige quaum we (SQW e we ickess is 5 Α wi a eeco esiy o 6 Ν s = 1 1 11 cm- a moiiy μ = 1 cm / ( s I oe o eom asoio measuemes e sames wee moue sai-ee a ie o i 5 μm wi a e-ecig ecique Coimae ig ceee a m is asse o a coece om e same oug a ie oic sysem a is i a e3 eigeao moue i a 1 mage oaiaio aaysis is oe in situ wi a cicua aaye ace immeiaey oowig e same eesig e iecio o e mageic ie eaie o e iecio o oagaio o ig aows o e ieee moioig o e e cicuay oaie (C a ig cicuay oaie (C seca Mageoasoio secoscoy as seea aaages a make i a uique oe o e si oaiaio o e ES isy e iegae aso- io iesiy is iecy ooioa o e aaiae esiy o saes i e owes aau ee a o eee o ay comicae eaaio eecs Aiiom- ay e agua momeum saes o e iiia a ia saes ae we-eie 624 M.J. Manfra t al. so a y moioig o e C asiio a e C asiio we ca independently moio e ouaios o e wo si as o e owes aau ee as e emi ee swees oug v = Ι A eame o e asoio seca as a ucio o mageic ie i eac oaiaio is sow i ig 1 As e emi ee moes oug v = 1 e asoio o e owe eegy si-u sae queces cocomia wi a eakig o e asoio io e ige eegy si-ow sae is is ceay see i e ise o ig 1 wee e asoio coeicie α = —1/ w (I(/I( (L is e quaum we wi a Ι e measue asmissio iesiy is oe as a ucio o Β i e eigooo o v = 1 o eac oaiaio ese aa iicae e aiy cagig ouaios o e wo si saes o o e ig a ow e sies o v = Ι Ou eemiaio o e si oaiaio om e asoio seca o- ows om emis goe ue wic eaes e iegae asoio iesiy o e aaiae esiy o saes i eac si a a o a sime sum ue wic eoces aice coseaio wee NT(!) is e ume o si-u (ow eecos i e owes aau ee is ca e ecas as wee NA↑(↓) is e aaiae esiy o saes i e si-u (ow a o e owes aau ee e sum ue cosais e oa aaiae esiy o saes a ay gie mageic ie We ocee wi e cacuaio o Sz y is iiig e Skyrmions and the v - 1 Quantum Hall Ferromagnet 5 iegae eak asoio i eac oaiaio y e cacuae oica mai eemes e esuig quaiy is ooioa o e aaiae esiy o saes wee /i is e iegae asoio j is e oica mai eeme a C is e cosa o ooioaiy o e eemie Sice e e a ig cicuay oaie seca oie wo suc ieee equaios — oe o eac si a — e aiioa cosai eoce y ( aows o e eimiaio o e cosa o ooioaiy C a e eemiaio o ΝΑ ↑(↓) iay e si oaiaio e aice is oe a e ia eessio o Sz is comeey ieee o C e ukow cosa o ooioaiy us is eeime aows o e eemiaio o e asoue si oaiaio ee o ay iig aamees e cosa o o- oioaiy C sysemaicay accous o a umeasue eeimea couigs — oica coecio eIciecy eeco eiciecy ec — wic oewise wou e eee o eae e measue iegae iesiy o e aaiae esiy o saes uemoe e sum ue wic eemies e ooioaiy ewee e measue asoio a e esiy o ia saes ca e mae igoous we a u iegaio oe eegy is use e eegy iegae asoio is ie- ee o ecioic o may-oy ieacios a ca e uesoo simy as couig e oa ume o aaiae k-saes i e sysem [13] e uceaiy is i eemiig e cu-o eegy o e iegaio Sice e oica asi- ios ae we seaae i eegy i suices o use e asiios wic ae as ia saes e spin-up a si-ow saes o e owes aau ee igue os e si oaiaio esus iig aco eemie om e aa i ig 1 a comaes i wi o sige-aice a skymio-ase moes eious cacuaios ae sow a a sige-aice moe ase o e ecage eace g-aco [1] a mouaes e oea o e wo eeco si ees ais o caue e eaio o Sz eseciay o < 1 [9] O e oe a e aa coom we o e skymio-ase moe I is sceme e ume o eese sis is quaie [15] so a e comoe o oa si aog e iecio o e eema ie is gie y o φ , wee N is e ume o eecos i e sysem φ is e ume o saes aaiae a - Νφ is e ume o skymios ese o Ν φ , S,z is gie y A is a iege quaum ume wic ees o e eaie seg o e eema a Couom ieacio ems I is e eea measue o e skymio sie [15] aee-ock cacuaios [] eic a o quaum Ηa eomages wi ou maeia aamees A sou e cose o 3 iicaig eac eciaio iuces 3 si is Ou aa ae i ecee ageeme wi is eicio oe 626 M Mnfr t l a e measue si oaiaio oes iee aoac uiy eacy a v = 1 as Τ — iicaig a e gou sae a = 1 is uy si oaie iay e cosa o ooioay C is aso isaye i ig e comee ack o sucue osee i C oe a ie age i wic e si oaiaio cages om eay eo o uiy is goo iicaio a ou sime sum ue is oeye 2.1.
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