Modeling of Toroidal Ordering in Ferroelectric Nanodots

Transcription

1 Modlng of Toodal Odng n Folctc Nanodots by Joshua C. Con and Pt W. Chung ARL-TR-465 Jun 007 Appovd fo publc las; dstbuton s unlmtd.

2 NOTICES Dsclams Th fndngs n ths pot a not to b constud as an offcal Dpatmnt of th Amy poston unlss so dsgnatd by oth authozd documnts. Ctaton of manufactu s o tad nams dos not consttut an offcal ndosmnt o appoval of th us thof. DESTRUCTION NOTICE Dstoy ths pot whn t s no long ndd. Do not tun t to th ognato.

3 Amy Rsach Laboatoy Abdn Povng Gound, MD ARL-TR-465 Jun 007 Modlng of Toodal Odng n Folctc Nanodots Joshua C. Con and Pt W. Chung Computatonal and Infomaton Scncs Dctoat, ARL Appovd fo publc las; dstbuton s unlmtd.

4 REPORT DOCUMENTATION PAGE Fom Appovd OMB No Publc potng budn fo ths collcton of nfomaton s stmatd to avag hou p spons, ncludng th tm fo vwng nstuctons, sachng xstng data soucs, gathng and mantanng th data ndd, and compltng and vwng th collcton nfomaton. Snd commnts gadng ths budn stmat o any oth aspct of ths collcton of nfomaton, ncludng suggstons fo ducng th budn, to Dpatmnt of Dfns, Washngton Haduats Svcs, Dctoat fo Infomaton Opatons and Rpots , 5 Jffson Davs Hghway, Sut 04, Alngton, A Rspondnts should b awa that notwthstandng any oth povson of law, no pson shall b subct to any pnalty fo falng to comply wth a collcton of nfomaton f t dos not dsplay a cuntly vald OMB contol numb. PLEASE DO NOT RETURN YOUR FORM TO THE ABOE ADDRESS.. REPORT DATE DD-MM-YYYY Jun TITLE AND SUBTITLE. REPORT TYPE Fnal 3. DATES COERED Fom - To July 006 to May 007 5a. CONTRACT NUMBER Modlng of Toodal Odng n Folctc Nanodots 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHORS Joshua C. Con and Pt W. Chung both of ARL 5d. PROJECT NUMBER 7UH7CL 5. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAMES AND ADDRESSES U.S. Amy Rsach Laboatoy Computatonal and Infomaton Scncs Dctoat Abdn Povng Gound, MD SPONSORING/MONITORING AGENCY NAMES AND ADDRESSES 8. PERFORMING ORGANIZATION REPORT NUMBER ARL-TR SPONSOR/MONITOR S ACRONYMS. SPONSOR/MONITOR S REPORT NUMBERS. DISTRIBUTION/AAILABILITY STATEMENT Appovd fo publc las; dstbuton s unlmtd. 3. SUPPLEMENTARY NOTES 4. ABSTRACT Ths pot dtals pogss and th compltd study of folctc popts n nanodots fo potntal applcaton to toodal odng concpts n nonvolatl mmoy matals. Th wo was pfomd und suppot though th Studnt Tmpoay Employmnt Pogam at th U.S. Amy Rsach Laboatoy. Bgnnng wth an ntoducton of basc concpts, th pot vws th cunt stat-of-th-at of folctc nanodot tchnology though a ltatu vw and dntfs aas of nd fo contnud study. As pat of th vw, Ewald s summaton fo Coulomb ntactons n podc cystals, a ctcal contbuton to th atomstc ngy that nabls th long-ang odng n folctc solds, was dvd and s psntd n th appndx. 5. SUBJECT TERMS band gap; cystals; modlng; photoncs 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT 8. NUMBER OF PAGES 9a. NAME OF RESPONSIBLE PERSON Joshua C. Con a. REPORT Unclassfd b. ABSTRACT Unclassfd c. THIS PAGE Unclassfd SAR 3 9b. TELEPHONE NUMBER Includ aa cod Standad Fom 98 Rv. 8/98 Pscbd by ANSI Std. Z39.8

5 Contnts Lst of Fgus Acnowldgmnts v v. Intoducton. Bacgound on Folctcs 3. Bacgound on Toodal Odng of Nanodots 3 4. Ltatu Rvw 4 5. Advantags of Folctc Nanodots 6 6. Futu Wo 7 7. Rfncs 8 8. Bblogaphy 9 Appndx A. Dvaton of Ewald Sum Euaton Dstbuton Lst 5

6 Lst of Fgus Fgu. Schmatc of th polazaton phnomnon n a povst cystal cll 3... Fgu. Polazaton domans and doman walls n an nhomognously polazd matal 3... Fgu 3. Hystss loop common to folctc matals Fgu 4. a Fly standng nanodot b FEN und tnsl stan c FEN und compssv stan...6 v

7 Acnowldgmnts Th authos gatfully acnowldg patal suppot fom th U.S. Amy Rsach Laboatoy s Mao Shad Rsouc Cnt at th Computatonal & Infomatonal Scncs Dctoat, Hgh Pfomanc Computng Dvson, Computatonal Scncs & Engnng Banch though th Studnt Tmpoay Employmnt Pogam. Patal suppot s also gatfully acnowldgd though th Jont Scnc and Tchnology Offc of th Dfns That Rducton Agncy. v

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9 . Intoducton Th unu popts of folctc matals hav ld to numous studs amd at ncopoatng folctcs nto mmoy dvcs. On patcula applcaton s th caton of non-volatl folctc andom accss mmoy NFRAM. A folctc matal can mantan an nducd polazaton wthout an xtnally appld voltag, thus movng th nd fo a bac-up ds and mang th mmoy non-volatl. Th v-ncasng dmand fo small mmoy dvcs has ld to ncasd sach n th fld of folctc nanostuctus. Folctc nanodots off a potntal ncas n th stoag dnsty of NFRAM fom 0. ggabt p sua nch Gbt/n. to 60 tabts p sua nch, whch s also fou ods of magntud gat than th -Gbt/n. capacty of cunt magntc codng dvcs. Th mpovd capacts fo mmoy hav nspd much ntst n th popts and bhavo of folctc nanostuctus. On aa of ntst s th toodal odng of dpols n folctc nanodots. Ths s a latvly unxplod fld that appas pomsng yt us xtnsv sach bfo commcalzaton can b sously consdd.. Bacgound on Folctcs Folctc matals a n a unu catgoy of matals dfnd by th appaanc of spontanous polazaton. Folctc cystals a a class of dlctc matals, whch mans thy a smconductos that hav nsulatng and conductv popts. Thy may sustan ntnal lctc dpol momnts wthout an xtnally appld lctc fld. By contast, dlctcs gnally u an lctc fld to sustan a polazaton. Folctc popts also ma thm attactv fo numous applcatons n multfunctonal lctonc dvcs. Such popts nclud hgh dlctc constants, th pyolctc ffct, th lcto-optcal ffct, and th pzolctc ffct. Folctc cystals bcom polazd whn th postvly chagd cntal atom shfts n th oppost dcton of th ngatvly chagd oxygn atoms. Fgu llustats how a nonpolazd folctc cystal bcoms polazd. Ths phas tanston only occus blow a ctcal tmpatu fd to as th Cu tmpatu o Cu pont. Th valu of th Cu tmpatu vas fo ach matal. Abov ths tmpatu, all folctc cystals a nonpola, o n a paalctc stat. Folctcs und th Cu tmpatu xhbt multstabl gound stats. Thfo, thy can chang polazaton dctons though th applcaton of an xtnal lctc fld.

10 Fgu. Schmatc of th polazaton phnomnon n a povst cystal cll 3. Not all cystals n a stuctu sha th sam polazaton dctons. Rgons of unfom dpol momnts a fd to as domans, wth th aas btwn thm bng doman walls. A wall spaatng two ant-paalll domans s a 80-dg wall, whl a wall spaatng ppndculaly ontatd dpols s a 90-dg wall both shown n fgu. Th total polazaton of a folctc stuctu s dtmnd whn th volum of th domans s summd n ach dcton. Folctc domans a fomd to mnmz th lctostatc ngy of dpolazng flds causd by sufac chags 4. Th swtchng of polazaton s conductd though nuclaton and domanwall moton. Th swtchng tm s an mpotant popty fo many applcatons and s lmtd by ths two factos. 90 Wall 80 Wall Fgu. Polazaton domans and doman walls n an nhomognously polazd matal 3. Fgu 3 shows that th nt polazaton vsus appld lctc fld poducs a hystss loop. As an lctc fld s appld to a nonpola folctc, domans bgn to swtch untl all domans pont n th sam dcton A. Aft th maxmum polazaton s achd, th lctc fld dcass and som of th domans swtch bac. At a zo lctc fld, mo domans stll hav a postv polazaton B. Th valu at ths pont s th mnant polazaton. As a ngatv fld s appld, mo domans bcom ngatv untl th folctc s compltly nonpola C. Th fld ud to ach a zo polazaton s th cocv fld. Fnally, th fld bcoms mo

11 ngatv untl a maxmum ngatv polazaton s achd D. Th pocss s thn vsd whn w swtch bac to a postv lctc fld. Fgu 3. Hystss loop common to folctc matals 3. As a folctc swtchs bac and foth btwn th two polazd stats, th maxmum and mnant polazatons bgn to dcas. Ths loss n swtchabl pmannt polazaton s folctc fatgu. Bsds swtchng tm and folctc fatgu, a thd facto affctng th us of folctcs s dlctc badown. Ths occus whn an nsulatng matal, such as a folctc, s focd to conduct lctcty n lag lctc flds. Dlctc stngth masus th maxmum lctc fld that a matal can xpnc bfo dlctc badown occus. Th stngth s masud n volts p unt lngth of thcnss. 3. Bacgound on Toodal Odng of Nanodots Th concpt of toodal odng of folctc nanodots bgan n 946 wth th wo of Chals Kttl wth fomagntc domans n small patcls 5. Hs thoy was basd on th obsvaton that th dmagntzd stat s th stabl stat n lag fomagntc cystals n th absnc of an appld magntc fld. To achv a dmagntzd stat, a complx odng of th domans s ud. Th gound stat can b dtmnd f th f ngy uaton s optmzd n tms of th doman odng. Th f ngy of th stuctu s gvn by th uaton F F + F + F Th fst tm, F W, psnts th sufac ngy btwn domans and s calculatd by F W W σ M W S a 3

12 wh σ W s th sufac ngy p unt aa and dpnds on th ontaton of th bounday plan and th dffnc n spn dcton acoss th bounday. Th tm, S, s th total aa of th doman boundas. Th scond tm n th f ngy uaton, F M, s th magntc fld ngy of th confguaton o th wo ud to dstbut th ffctv magntc pols. Th ngy s calculatd by F M d H M wh M s th magntc momnt p unt volum magntzaton and H s th sultant magntc fld. Th ntgal s tan ov th volum of th spcmn. Th fnal tm n th f ngy uaton, F a, psnts th ansotopy ngy of spn ontaton. Ths fs to th ngy assocatd wth a pfd axs of magntzaton. It s calculatd by F ρ a wh ρ a s th ansotopy ngy dnsty of domans ontd n dctons oth than th dcton of th asst magntzaton and a s th volum of thos domans. Two cass fo small fomagntc nanodots w xamnd wth th f ngy uaton. Ths cass w fo a patcl wth on doman and fo a patcl wth toodally odd domans. Th fst cas had only magntc ngy snc th doman was n th dcton of pfd magntzaton and th w no doman wall sufacs. Thfo, th ngy could b dscbd as a F M 3 Th ngy fo cas two nvolvd ansotopy ngy and doman wall sufac ngy but had no nt magntzaton. Thfo, th ngy could b dscbd as a s L ρ F σ + a 3 W L L Though ths pocss, t was dscovd that th toodal odng sults n th mnmum ngy fo L 5 nm usng mpcal stmatons fo th oth vaabls Ltatu Rvw Th fld mand latvly unxplod ov th nxt 30 yas untl Zhludv t al. 6 fst potd such stuctus. Howv, th wo could nv b poducd and thfo, th study of toodal odng was agan abandond. A collcton of paps btwn 984 and 985 xtndd 4

13 Kttl s wo. Ths paps nclud Gnzbug t al. 7, Sannov 8, and Sannov and Zhludv 9. All ths paps confm th xstnc of toodal momnts n magntsm. A dcad lat, Gobatsvch and Kopav 0 and Sannov futh xtndd th wo. Howv, th wo stll mand latvly unnotcd untl Naumov t al. pfomd ab nto smulatons on fly standng nano-patcls of lad zconat ttanat. Th smulatons showd that phas tansfomatons do occu n zo-dmnsonal patcls nanodots and that th phas tansfomatons lad to spontanous toodal momnts und a ctcal tmpatu of appoxmatly 600K. Ths toodal momnts occu to mnmz th dpolazng fld. Naumov t al. found that two stabl gound stats xst fo nanodots wth a damt lag than 3. nm and th stats can b swtchd va a magntc fld ath than a statc lctc fld as usd fo bul folctcs. Th wo was contnud by paps such as Ponomava t al., and Posandv t al. 3. Ponomava t al. publshd two paps n 005 poposng modls to xamn th dpolazng flds 4 and ffcts of lctcal and mchancal bounday condtons on folctc nanopatcls. Th atomstc modls xamn th dpolazng fld and ngy fo folctc nanostuctus. Thy found th dpolazng fld and ngy by calculatng th dffnc btwn dpol-dpol ntactons fo folctc nanostuctus dung pfct opn-ccut and shotccut lctcal bounday condtons. An opn-ccut condton xhbts a maxmum dpolazng fld, whl a shot-ccut condton compltly scns th ffct of th dpolazng fld. Th ngs calculatd va th modl w ndpndnt of dot sz and agd xactly wth th stablshd contnuum appoach. Though th smulatons, Ponomava t al. found that toodal momnts occu whn th scnng of th dpolazng fld s lss than 88% fo a fly standng lad zconat ttanat nanostuctu. Aft applyng tnsl and compssv stans of.65%, thy dscovd that toodal momnts occu und tnsl stan wth a scnng of lss than 88% but not und compssv stan. Ths sults a llustatd n fgu 4. Posandv t al. 3 poposd a swtchng mchansm that uss nhomognous statc lctc flds to alt th toodal momnt of th nanodots wthout affctng th suoundng nanodots. Thy dd ths by placng two oppost dpola soucs at ach nd of th dot. Ths stup pvnts any nt polazaton that could affct naby nanodots. By otatng th souc, thy could swtch th toodal momnt. Th ablty to swtch th dcton of th toodal momnt s vtal fo th ntgaton of folctc nanodots FENs nto mmoy dvcs and oth applcatons. 5

14 a b c Fgu 4. a Fly standng nanodot b FEN und tnsl stan c FEN und compssv stan. 5. Advantags of Folctc Nanodots An obstacl fo mplmntng FENs nto NFRAM s th undstandng of th phas tansfomatons on th nanoscal. In ctan condtons, th polazaton of nanodots s ontd toodally ath than ctlnaly. Th local dpols a dctd n a sutabl dcton to ulbat th dpolazng fld. Th sultant ontaton poducs a toodal momnt. aous popts of th toodally odd nanodots a conducv fo us n NFRAM. Th phas s bstabl, manng that two mnmum ngy stats xst. Ths stats can b asly tanslatd to 0 o n Boolan logc. Gound stats can b swtchd wth th us of a magntc fld that dos not u contact wth lctods, whch s challngng to cat on th nanoscal. Th local dpol ontaton dos not sult n a nt polazaton; thfo, nghbong nanodots wll not b affctd whn on nanodot swtchs polazaton. All ths popts ma toodally odd FENs appalng to NFRAM. 6

15 6. Futu Wo Th futu of toodally odd folctc nanodots n mmoy dvcs s bght. In pncpl, combnng th popts shad by all folctcs wth thos unu to toodal odng can lad to small, fast, and mo labl mmoy matals. Howv, mo sach must b pfomd on all aspcts of th popts and bhavos bfo folctc nanodots can b mplmntd. Among many mchansms that man unstudd, th ntactng latonshps among atomc stuctu, lctomagntc flds, and mchancal stans a not nown. Fo xampl, th ol of mchancal stans and thmal xpanson on th stablty of th toods s unnown. Most mpotantly, t s stll uncla f toodal odng has v occud xpmntally snc concpts hav bn postd manly though thotcal modls and calculatons. Thfo, xpmntaton must accompany th thotcal calculatons bfo folctc nanodots a sously consdd fo NFRAM. 7

16 7. Rfncs. Aucllo, O.; Scott, J.F.; Ramsh, R. Th Physcs of Folctc Mmos. Physcs Today July 998, 5 7, -7.. Naumov, I.; Bllach, L.; Fu, H. Unusual Phas Tanstons In Folctc Nanodss and Nanoods. Natu 004, 43, Dagosts, Klaus. Stuctual Popts of Povsts. Modlng and Smulaton of Folctc Dvcs, 000. < 4. Ponomava, I.; Naumov, I.I.; Konv, I.; Fu, H.; Bllach, L. Atomstc Tatmnt of Dpolazng Engy and Fld n Folctc Nanostuctus. Physcal Rvw B 005, 7, Kttl, Chals. Thoy of th Stuctu of Fomagntc Domans n Flms and Small Patcls. Physcal Rvw 946, 70, Zhludv, I.S.; Palna, T.M.; Smnovsaya, E.M.; Fonton, S.S.; Yamuhamdov, Y.N. Magntc Popts of Ncl-Boact Iodd. Jounal of Expmntal and Thotcal Physcs Ltts 974, 0, Gnzbug,.L.; Gobatsvch, A.A.; Kopayv, Y..; olov, B.A. On th Poblm of Supdamagntsm. Sold Stat Communcatons 984, 50 4, Sannov, D.G. Anomals n th Dspson of th Dlctc Suscptblty of Intnsc Toocs. Jounal of Expmntal and Thotcal Physcs Ltts 985, 4, Sannov, D.G.; Zhludv, I.S. On th Possblty of Phas Tanstons Wth Spontanous Toodal Momnt Fomaton n Ncl Boacts. Sovt Physcs-Sold Stat 985, 7, Gobatsvch, A.A.; Kopav, Y.. Toodal Od n Cystals. Folctcs 994, 6, 3.. Sannov, D.G. Fotooc Phas Tanstons n Boacts. Folctcs 998, 9, 77.. Ponomava, I.; Naumov, I.I.; Bllach, L. Low-Dmnsonal Folctcs Und Dffnt Elctcal and Mchancal Bounday Condtons: Atomstc Smulatons. Physcal Rvw B 005, 7, Posandv, S.; Ponomava, I.; Konv, I.; Naumov, I.I.; Bllach, L. Contollng Toodal Momnt by Mans of an Inhomognous Statc Fld: An Ab Into Study. Physcal Rvw Ltts 006, 96,

17 8. Bblogaphy. Fnl, Daan; Smt, Bnd. Undstandng Molcula Smulatons, pp 9-300, Acadmc Pss: San Dgo, CA, 00.. Gbbon, Paul; Sutmann, Sodhad. Long-Rang Intactons n Many-Patcl Smulatons. NIC Ss 00, 0, Scott, J. F. Foltcs: Novl Gomtc Odng of Folctcty. Natu 005, 4, Scott, J. F. Nanofolctcs: Statcs and Dynamcs. Jounal of Physcs: Condnsd Matt 006, 8, R36-R Yoshoa, Dao. Intoducton to Statstcal Physcs. Spng-lag: Nw Yo, 6 Novmb

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19 Appndx A. Dvaton of Ewald Sum Euaton Th followng mathmatcal dvaton was an assgnmnt dung th ntnshp. Th dtals of th mthod w uncovd to hlp us undstand basc pdagogy of modlng folctc systms fom th atomstc lvl. Th Ewald sum s a mans to calculat th lctostatc ntactons of podc systms. Its contbuton to th total ngy nabls th fomaton of long ang od and s th physcal undpnnng of folctc polazaton. Th mthod nvolvs supmposng a sphcal Gaussan cloud on ach on n al spac. Ths sphcal clouds hav a chag oppost th on. A sphcal Gaussan cloud s also supmposd on ach on n cpocal spac. Ths clouds hav th sam chag as th on thy suound. Th Ewald sum calculaton nvolvs usng Posson s uaton and Fou tansfoms. Th Ewald sum uaton s compsd of a tm to calculat shot-ang ntactons n al spac, a tm to calculat long-ang ntactons n cpocal spac, and a cocton tm fo slf ngy. Gnal Euaton fo Elctostatc Engy: U n + nl wh / accounts fo doubl countng of atom ntactons and a th chags on atoms and and a th coodnats of atoms and n th unt cll nl s th dsplacmnt vcto fo th dffnt mag clls U φ wh φ Elctc Potntal at φ + nl Chag Dnsty: ρ n Pont Chag Gaussan Chag + Gaussan Chag Dnsty of Pont Chag: ρ δ wh δ s th Dac dlta functon

20 Dnsty of Gaussan Chag: 3 / ρ wh s a paamt affctng th Gaussan wdth and affcts computatonal ffcncy + 3 / 3 / δ ρ Elctc Potntal Shot Rang: shot φ Potntal fom Pont Chag Potntal fom Gaussan Chag Potntal fom Pont Chag: P shot, φ Potntal fom Gaussan Chag: Posson s Euaton: 4 ρ φ 3 / ρ 4 ρ φ φ d 4 ρ d 3 / d 3 / / d 0 / φ f φ wh f s th o functon and - nl f nl nl n shot φ Shot Rang Contbutons Long Rang Contbutons

21 nl φ shot fc + n + nl wh fc s th complmntay o functon Elctostatc Engy Shot Rang: fc + nl U shot + nl n Cocton Tm fo Slf Intacton: φ f φ 0 By tang th lmt as appoachs zo usng L Hoptal, / φslf U slf φ slf U slf Elctc Potntal Rcpocal Spac: Posson s E: φ 4ρ Posson s E aft Fou Tansfom: φ 4ρ 4 φ ρ φ φ ρ ρ d 3 n 3 + d all spac d 3

22 4 Sd not: Ψ Ψ 4 d Snc th bounds of th ntgal a,, + can b placd by f f 4 ρ 4 φ 4 4 φ φ φ 4 4 long U 4 Ewald Sum: slf long shot U U U U n nl fc nl U 4 In f s omttd bcaus of choc of unts. Ths tm dos not appa n any oth dvaton th and s attbutd to th choc btwn SI and CGS.

23 NO. OF COPIES ORGANIZATION NO. OF COPIES ORGANIZATION DEFENSE TECHNICAL PDF INFORMATION CTR ONLY DTIC OCA 875 JOHN J KINGMAN RD STE 0944 FORT BELOIR A DIRECTOR US ARMY RSCH LABORATORY ATTN AMSRD ARL CI HC J CLARKE P CHUNG 5 CYS BLDG 394 US ARMY RSRCH DE & ENGRG CMD SYSTEMS OF SYSTEMS INTEGRATION AMSRD SS T TH ST STE 00 FORT BELOIR A DIRECTOR US ARMY RESEARCH LAB IMNE ALC IMS 800 POWDER MILL RD ADELPHI MD DIRECTOR US ARMY RESEARCH LAB AMSRD ARL CI OK TL 800 POWDER MILL RD ADELPHI MD DIRECTOR US ARMY RESEARCH LAB AMSRD ARL CS OK T 800 POWDER MILL RD ADELPHI MD DIRECTOR US ARMY RESEARCH LAB AMSRD ARL CI J GOWENS R NAMBURU 800 POWDER MILL RD ADELPHI MD ABERDEEN PROING GROUND DIRECTOR US ARMY RSCH LABORATORY ATTN AMSRD ARL CI OK TECH LIB BLDG 4600 DIRECTOR US ARMY RSCH LABORATORY ATTN AMSRD ARL CI H C NIETUBICZ BLDG 38 5