First Principles Calculation of Fe L 2;3 -edge X-ray Absorption Near Edge Structures of Iron Oxides

Transcription

1 Mtrls Trnstons, Vol. 45, No. 5 (2004) pp to 1418 Spl Issu on Avns n Computtonl Mtrls Sn n Ennrn III #2004 Th Jpn Insttut o Mtls Frst Prnpls Clulton o F L 2;3 - X-ry Asorpton Nr E Struturs o Iron Oxs Hzu Ino 1; * 1, Iso Tn 1, Toru Mym 1; * 1, Thro Mshm 1; * 2, Hroho Ah 1 n Kzuyosh Oswr 2 1 Dprtmnt o Mtrls Sn n Ennrn, Kyoto Unvrsty, Kyoto , Jpn 2 Shool o Sn n Thnoloy, Kwns Gun Unvrsty, Sn , Jpn X-ry sorpton nr strutur (XANES) t L 2;3 - o 3 trnston lmnts s omnt y stron orrlton ts mon 2p or hol n 3 ltrons. In th prsnt stuy, w hv prorm systmt onurton ntrton (CI) lultons n orr to rprou n ntrprt F-L 2;3 XANES o FO, LFO 3 n SrFO 3. Rltvst our omponnts wv untons wr otn y solvn Dr qutons wth nsty untonl thory. CI lultons wr m usn th rltvst molulr ortls nst o tom ortls, whh nls nluson o th O-2p ortl ontrutons throuh ovlny. Th oslltor strnth o th ltr pol trnston ws thn omput. Exprmntl XANES sptr o thr ompouns wr ststorly rprou y th thortl sptr otn or (FO 6 ) m lustrs n othrl symmtry. Chml shts twn ompouns wr quntttvly rprou s wll. Componnt nlyss o CI ws systmtlly m n orr to nlyz th orn o rns n sptrl shps. (Rv Novmr 25, 2003; Apt Jnury 6, 2004) Kywors: X-ry sorpton, ltron nry-loss nr struturs (ELNES), rltvst ts, onurton ntrtons, ron oxs 1. Introuton Mny oxs o 3 trnston lmnts hv n wly us n morn thnoloy. Sn 3 ltrons ply ntrl rols n thm, xprmntl hrtrzton o th 3 ltrons s vry mportnt. X-ry sorpton nr struturs (XANES) s wll s ltron nry loss nr struturs (ELNES) provs tl normton on ltron stts nr th Frm nry. It montors ltron trnstons rom or ortl to unoup stts tht r llow y ltr pol trnston rul. Th 3 stts n thror nlyz rtly usn thr L 2;3 - or M 2;3 XANES n ELNES. 3 lmnts hs L 2;3 - n w 100 V ron, whh s srl or sot X-ry xprmnts s wll s or ELNES. As mttr o ts, thr hv n numr o xprmntl L 2;3 XANES r vll or mjor 3-mtl ompouns. Thr hml shts, sptrl shp s wll s th rto twn L 2 n L 3 sptr,.., rnhn rto hv n systmtlly nvstt. Th most prmtv wy to nlyz th sptr s so-ll nr prntn thnqu. A msur sptrum s nt y omprson wth rrn sptr otn or stnr mtrls. Howvr, th nr prntn thnqu s ovously not usul or nw systms n whh tom/ltron struturs r not nloous to prxstn ompouns. A oo thortl tool to nlyz th xprmntl sptr s thror mntory. I on n otn rll thortl sptrum or vn tom rrnmnts n ltron stts, th thortl sptrum n us s nw nr prnt. A populr mtho to omput thortl L 2;3 - XANES s th rystl l multplt lulton 1 4) n whh rystl l ts r norport nto n tom multplt prorm usn roup thortl ormlsm. Crystl l * 1 Grut Stunt, Kyoto Unvrsty * 2 Unrrut Stunt, Kyoto Unvrsty ts r nlu wth prmtrs n thy r trmn so s to st t to xprmntl sptr. A numr o ompouns hv n nvstt throuh ths pproh, n th prmtrs hv n trmn or mny ons wth rnt vln stts n oornton nvronmnt. Althouh ths mtho hs n sussul or rproun mny xprmntl sptr, th mjor rw n oun n th mtho tht uss mprl prmtrs. Wth th rs o th symmtry o ln l, th numr o mprl prmtrs nrss, thry vn rs to th muty o th omputtonl rsults. Entrly rst prnpls mtho s thror stronly rqur. In 2001, novl mtho to prorm suh non-mprl lulton hs n rport y th prsnt uthors roup. 5) Totlly rltvst rst prnpls molulr ortl lultons wr m. Eltron orrltons mon 2p 1=2, 2p 3=2 n 3 ltrons wr rorously lult y tn Sltr trmnnts o ll ltron onurtons m y ths molulr ortls. In othr wors, onurton ntrtons (CI) mon ths molulr ortls wr omput. Thy hv su n rproun xprmntl sptr rom thr ompouns hvn rnt -ltron numrs n oornton numrs,.., SrTO 3, NO n CF 2. In th prsnt stuy, w hv xtn ths mtho to thr ns o ron oxs wth rnt orml hrs,.., FO (F(II)), LFO 3 (F(III)), n SrFO 3 (F(IV)). Th usulnss o th mtho or th ron ompouns wth rnt orml -ltron numrs s onrm. Componnts nlyss o CI hs n m to nlyz th orn o ps tht ppr n th sptr. 2. Computtonl Prour For th lulton o thortl F L 2;3 - XANES, mol lustrs o (FO 6 ) m tht r ompos o n F on n sx nrst nhor O ons wr us. Th totl numr o ltrons n th lustr ws otn rom orml hrs,

2 Frst Prnpls Clulton o F L 2;3 - X-ry Asorpton Nr E Struturs o Iron Oxs 1415 thus m ¼ 10, 9, 8 or FO (F(II)), LFO 3 (F(III)), n SrFO 3 (F(IV)) rsptvly. All lustr mols wr m to show othrl (O h ) symmtry or smplty vn whn rl rystls xht slht storton rom th u symmtry. Th F-O on lnths wr 216.0, n pm or FO, LFO 3, n SrFO 3, rsptvly. In orr to t ount tv Mlun potntl, pont hrs wr put t th xtrnl tom sts. Fully rltvst molulr ortl (MO) lultons wr rr out y solvn Dr qutons wth nsty untonl thory usn rltvst SCAT o. 8) In ths o, our-omponnt rltvst molulr ortls r xprss s lnr omnton o tom ortls (LCAO). Th numrlly nrt our-omponnt rltvst tom ortls (1s to 4p or F n 1s to 2p or O) wr us s ss untons. Atr on ltron lultons o rltvst MO, onurton ntrton (CI) lultons wr prorm. In prsnt lulton, only F 2p ortls n MO mnly ompos o F 3 ortls wr onsr xpltly, sn th CI lulton or ll N ltrons n th lustr rqurs prohtv omputtonl tm n rsours. An tv mny-ltron Hmltonn s xprss s, H ¼ Xn hðr Þþ Xn X n j< 1 jr r j j ; ð2:1þ whr n s th numr o ltrons n th slt MO. Th on-ltron oprtor hðr Þ s sr s, hðr Þ¼p þ 2 X Z v v jr R v j þ V 0ðr Þ; ð2:2þ whr, r Dr mtrs, s th vloty o lht, p s th momntum oprtor, Z v s th hr o vth nulus, n V 0 ðrþ s th potntl rom othr N-n ltrons. In ths pproh, th Coulom ntrton n xhn-orrlton ntrton mon th slt n ltrons r onsr xpltly, whl thos ntrtons twn th slt n ltrons n othr N-n ltrons r nlu n V 0 ðrþ. Th xplt orm o V 0 ðrþ ws rv y Wtn n Kmmur. 9) As ss untons to onlz th mny-ltron Hmltonns sr n q. (2.1), ll th possl Sltr trmnnts orrsponn to th roun stt (GS) onurton n th xt stt (ES) onurton nlun or hol wr onstrut. Th mny-ltron wv untons r thn xprss s lnr omnton o thos Sltr trmnnts ¼ XM p¼1 C p p ; ð2:3þ whr M s th numr o Sltr trmnnts. In th s o FO (F(II)), th GS onurton s ð2pþ 6 ð 3 Þ 6, n th ES onurton s ð2pþ 5 ð 3 Þ 7 whr 3 nots th MO mnly ompos o F 3 ortls. Th possl ltron onurtons or GS r 210 (= 6 C 6 10C 6 ) n thos o ES r 720 (= 6 C 5 10 C 7 ). Thus 930 o Sltr trmnnts wr us s ss untons. For LFO (F(III)), th GS onurton s ð2pþ 6 ð 3 Þ 5, n th ES onurton s ð2pþ 5 ð 3 Þ 6. Th possl ltron onurtons or GS r 252 (= 6 C 6 10 C 5 ) n thos o ES r 1260 (= 6 C 5 10 C 6 ) o Sltr trmnnts wr thror us s ss untons. Rrn SrFO (F(VI)), th GS onurton s ð2pþ 6 ð 3 Þ 4, n th ES onurton s ð2pþ 5 ð 3 Þ 5. Th possl ltron onurtons or GS r 210 (= 6 C 6 10 C 4 ) n thos o ES r 1512 (= 6 C 5 10C 5 ). Th numr o Sltr trmnnts us s ss untons ws Th mtrx lmnts o H twn two Sltr trmnnts, p n q, n nrlly xprss s, H pq ¼h p jhj q ¼ XL þ XL j¼1 A pq j hjhjj j¼1 ¼1 l¼1 B pq jl hjjjl; whr L s th numr o slt MO n, hjhjj ¼ X4 X 4 Z ðrþh ðrþ j ðrþr; hjjjl ¼ X4 ¼1 ¼1 X 4 ¼1 ¼1 ZZ ðr 1Þ j ðr 2Þ ð2:4þ ð2:5þ 1 jr 1 r 2 j ðr 1 Þ l ðr 2 Þr 1 r 2 : ð2:6þ Hr ( ¼ 1, 2, 3, 4) s th th omponnt o th th rltvst MO n h ðrþ s lmnt o hðrþ. Th onts A pq j n B pq jl n otn y xpnn th Sltr trmnnts. Th oslltor strnth o th ltr pol trnston vr ovr ll rtons s vn y I ¼ 2 * + 3 ðe X n 2 E Þ r ; ð2:7þ whr n r mny-ltron wv untons or th ntl stt n th nl stt, whl E n E r thr nrs. Usn q. (2.3), q. (2.7) n xpn s * + * + X n r ¼ XM X M C p C X n q p r q whr ¼1 p¼1 q¼1 ¼ XM hjrjl ¼ X4 X M p¼1 q¼1 ¼1 3. Rsults n Dsusson Z C p C q ¼1 ¼1 ¼1 l¼1 ðrþr lðrþr: A pq j hjrjl; ð2:8þ ð2:9þ Clultons wr m or FO (F(II)), LFO 3 (F(III)), n SrFO 3 (F(IV)). Wth th nrs o th orml hr o trnston lmnts, th ovlnt onn twn F-3 n O-2p s nown to nrs n nrl. Fur 1 shows ontour mps o t 2 molulr ortls n thr lustrs otn y non-spn polrz n nonrltvst lultons. Th O-2p omponnt n t 2 s oun

3 1416 H. Ino t l. FO LFO 3 SrFO 3 F. 1 Contour mp o t 2 molulr ortl n (FO 6 ) m lustr otn y non-rltvst n non-spn polrz lulton. Sol n ott urv r or postv n ntv vlus, rsptvly. () h () FO LFO 3 h () SrFO 3 xp. Rn t l., (2002) xp. At t l., (1992) xp. At t l., (1992) h F. 2 Thortl F L 2;3 - XANES n () FO, () LFO 3 n () SrFO 3 (uppr pnl), n orrsponn xprmntl XANES sptr tn rom Rs. 10) n 11) (lowr pnl). Brs n th uppr pnl show oslltor strnth wth mny-ltron nvlus or th Gussn ronn. to nrs wth th nrs o th orml hr o F. As mttr o t, tom ortl populton o O-2p s 2%, 7% n 18% n t 2 or FO, LFO 3, n SrFO 3, rsptvly. Th tom ortl populton o O-2p s rtr or ortl. Thy r 9%, 16% n 23% or FO, LFO 3, n SrFO 3, rsptvly. CI lultons usn th molulr ortls nst o tom ortls nl nluson o th O- 2p ortl ontrutons throuh th ovlny. Usn rltvst molulr ortls, CI lultons wr thorouhly m. Comput oslltor strnths vn y q. (2.7) wr shown wth rs n F. 2. Thy wr ron y Gussn untons o FWHM = 1.0 V to m thortl L 2;3 - XANES. Thy r ompr wth xprmntl sptr n F. 2. Bst ttn wth xprmntl sptr n oun whn solut trnston nry o th thortl sptr s sht y 6:4 V. Th rror my sr to unrstmton o orrlton ts n th prsnt thortl mtho s suss y Oswr t l. 6,7) Whn ll thortl sptr r sht or th sm mount, thy n rprou thr xprmntl sptr to th tls. Chml shts o h ompoun s n y th rltv poston o th most promnnt p r lso wll rprou. As ompr wth FO, t s +2.2 V or oth LFO 3 n SrFO 3. Fur 3 shows ontrutons o our onurtons to mny ltron nvlus. Althouh only prt o ths omponnts snntly ontrut or th oslltor strnth, th rm s qut usul. Th L 3 sorpton n v nto two prts wth rnt numr o ltrons n t 2 n ortls. Thror, th wth o th L 3

4 Frst Prnpls Clulton o F L 2;3 - X-ry Asorpton Nr E Struturs o Iron Oxs 1417 () (2p 1/2 ) 1 (2p 3/2 ) 4 (t 2 ) 5 ( ) 2 (2p 1/2 ) 1 (2p 3/2 ) 4 (t 2 ) 4 ( ) 3 () () FO LFO 3 (t 2 ) 5 ( ) 2 (t 2 ) 4 ( ) 3 (2p 1/2 ) 1 (2p 3/2 ) 4 (t 2 ) 4 ( ) 2 (2p 1/2 ) 1 (2p 3/2 ) 4 (t 2 ) 3 ( ) 3 (t 2 ) 4 ( ) 2 (t 2 ) 3 ( ) 3 (2p 1/2 ) 1 (2p 3/2 ) 4 (t 2 ) 4 ( ) 1 (2p 1/2 ) 1 (2p 3/2 ) 4 (t 2 ) 3 ( ) 2 SrFO 3 (t 2 ) 4 ( ) 1 (t 2 ) 3 ( ) 2 F. 3 Conurton nlyss o mny-ltron wv untons t th nl stts o th F L 2;3 - XANES. sorpton s prmrly trmn y th rn n th vr nry o two onurtons, whh s vn y th xtton nry rom t 2 to. Th nry s ll 10Dq or o whn mtl on s othrlly oornt. Thortl o or thr lustrs s stmt y th rn n onltron nvlus ws 1.1, 1.8 n 1.8 V or FO, LFO 3, n SrFO 3, rsptvly. Th lrr o y 39% xplns why th L 3 o LFO 3, n SrFO 3 show tl towr hh nry n th ron t roun 714 V. FO os not show suh tl. No ovrlp twn L 3 n L 2 n oun or FO. A smll ovrlp n oun or oth LFO 3 n SrFO 3. Th mntu o th ovrlp n prmrly trmn y th mntu o th splttn twn 2p 1=2 n 2p 3=2. Howvr, th mntu o splttn s not pnnt on vln stt o ons. As mttr o t, th splttn or F-2p lvls n thr lustrs s th sm s 12.5 V y th prsnt rltvst lulton. Th orn o th ovrlp twn L 3 n L 2 n LFO 3 n SrFO 3 nnot xpln y th rn n th splttn o F-2p lvls. Th ovrlp n xpln y th rn n o, whh s th sm orn s th tl n th L 3 sptrum towr hh nry n LFO 3 n SrFO 3. Msurmnt n ntrprtton o F-L 2;3 sptr o LFO 3 n SrFO 3 hv n m y At, Groot n oworrs n ) Thy hv onlu tht th prsn o ln hol s not y L ply mjor rol n trmnn th sptrum o SrFO 3. Usn th rystl l multplt mtho, thy lm tht th lulton tn 3 4 s roun stt nnot rprou th xprmntl sptrum. Thy hv propos tht th us o 3 5 L s roun stt onurton o SrFO 3 s ssntl. In th prsnt lulton, howvr, th xprmntl sptrum n ststorly rprou y th lulton y tn 3 4 s roun stt, whr 3 s th molulr ortl mnly ompos o F-3. It s tru tht snnt mxtur o O- 2p n F-3 ts pl splly or F(IV). Thr shoul non-nll ontruton o th ln hol to th F- L 2;3 sptrum. Howvr, th mjor prt o th ontruton n nlu y th CI lultons usn th molulr ortls nst o tom ortls. Usn th omputtonl mtho n ths stuy, th mjor prt o th ln hol t on th L 2;3 sptrum n nlu wthout normton on th ovlny pror. Thus th prsnt mtho shoul mor usul or nlyss o nw n o mtrls n whh lttl normton s vll. 4. Summry Frst prnpls lulton o F-L 2;3 XANES o FO, LFO 3 n SrFO 3 hv n m y CI lultons usn ully rltvst our omponnts wv untons. Rltvst MO lultons wr rr out y solvn Dr qutons wth nsty untonl thory. CI lultons wr m usn th molulr ortls nst o tom ortls, whh nls nluson o th O-2p ortl ontrutons throuh ovlny. Thn th oslltor strnth o th ltr pol trnston ws omput. Exprmntl XANES sptr o thr ompouns wr ststorly rprou y th thortl sptr otn or (FO 6 ) m lustrs n othrl symmtry. Chml shts twn ompouns wr quntttvly rprou s wll. Componnt nlyss o CI ws systmtlly m n orr to nlyz th orn o rns n sptrl shps.

5 1418 H. Ino t l. Anowlmnts Ths wor ws support y thr prorms rom Mnstry o Euton, Sn, Sports n Cultur o Jpn,.., 1) Grnt-n- or Snt Rsrh on Prorty Ars (No. 751), 2) Computtonl mtrls sn unt n Kyoto Unvrsty, n 3) 21st ntury COE prorm. REFERENCES 1) F. M. F. Groot, J. C. Ful, B. T. Thol n G. A. Swtzy: Phys. Rv. B41 (1990) ) F. M. F. Groot, J. C. Ful, B. T. Thol n G. A. Swtzy: Phys. Rv. B42 (1990) ) F. M. F. Groot: J. Eltron Sptros. Rlt. Phnom. 67 (1994) ) B. T. Thol n G. vn r Ln: Phys. Rv. B38 (1988) ) K. Oswr, T. Iwt, Y. Koym, T. Ish, I. Tn n H. Ah: Phys. Rv. B64 (2001) ) K. Oswr, T. Mym, I. Tn n H. Ah: Mtr. Trns. 43 (2002) ) K. Oswr, T. Ish, I. Tn, n H. Ah: Phys. Rv. B61 (2000) ) A. Rosén, D. E. Ells, H. Ah n F. W. Avrll: J. Chm. Phys. 65 (1976) ) S. Wtn n H. Kmmur: Mtr. S. En. B3 (1989) ) M. At, F. M. F. Groot, J. C. Ful, A. Fujmor, O. Strl, F. Lopz, M. Dom, G. Knl, G. A. Swtzy, M. Tno, Y. T, H. Es n S. Uh: Phys. Rv. B46 (1992) ) T. J. Rn, H. Ohl, C. Stmm, F. Noltn, J. Lünn, n J. Stöhr n R. L. Wht: Phys. Rv. B64 (2001)