Chapter 11. Magnetism

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1 ptr. nts Dnts. ntston of nt trl s oppost to t totl nt fl n ppl fl H, n t nt susptblty χ s nt. nt susptblty s fn s χ.. Dnts s rtrst of tos wt los sll. Eltrons wll rspons to trnl fl by Fry s w. urrnts wll rrn tsls to oppos t n of nrsn fl, n n s n t oppost rton of H.. lssl tory of nts: onsr n ltron n rulr orbt of rus r n nulr frquny. R ntrptl for F R If nt fl δ s turn on, n ssu t fft only. δ R R R q δ R q δ R R R δ R q δ R R δ R q δ R n only frst orr tr, R qδ q δ Rδ δ δ δ δ

2 lsslly, t fl wll t r q rol fstr f q s post. If t prtl s n ltron, t wll rol slowr. urrnt for by t loop I r roluton son q I q f q δi δ δ For n ltron n n to, δi δ t nt sn s rs to nts 4 Z nt ont of t to I r of t orbtl loop Z Ir Z I < R y ppln nt fl δ, Z Z δ δ δi < R > < R 4 R s t rus of t ltron loops. If r rus of If < < R < r >< >< y >< t tr nsonl ltron sll, > < y >< > < y > < < R > < r > Z δ Z δ δ r r < > 4 < > 6 If ubr of tos pr unt olu, n ntton of t spl, Z δ δ δ < r 6 δ Z χ < r > δ 6 > > > > > Z δ > < R 4 nn quton for nts >

3 Prnts. Wn tos possss tr own nt ont, prnts wll our.. Intrns nt ont f rlt to t totl nulr ontu nlun orbtl n spn of t ltrons n n to. γ s t yront rto, s t ftor, n s t or nton.. For t spn of fr ltron,. For t orbtl ontu of n ltron,. For fr to, s n by t n ftor: γ ss ss ss ts nto t prous quton, ubsttut lrly,, On t otr n, n In oupln, s s l l l l l l

4 4. Ornl quntu nubr:,,,. Quntu nubr ftr oupln:,,,. to notton:, P, D, F, G, H,. for l,,,, 4,. ssptly. 5. Quntu nubr for t totl nulr ontu s trn by Hun s rul: t tr b ltrons n t outr sll. E sll n ol y ltrons. s sll n ol y ltrons. p sll n ol y6 ltrons. sll n ol y ltrons. f sll n ol y4 ltrons. Drw y bos. Epl, for sll: 5 bos Unr bos, lbl orn to t of t sll fro u to nu. Epl, for sll: Hun s rul # ow to fll up t bos: lwys fll up bos on by on fro lft to rt. Do not oubl oupy t bos untl t sll s lf full. trt to oubl oupy t bos ftr t sll s lf full, strt fro lft to rt n. Hun s rul # ow to lult,, n : Σ, Σ, f sll s lss tn lf full or lf full, n f sll s or tn ll full or lf full. Espl : : 7 ltrons n sll : Σ or F Σ Groun ll of t to: 4 F 9 6. r r sublls wt,,,,,,,,. If w fn t nry for s, tn t nry of of ts stt s n by E

5 rlt populton n ll n b lult s: E E, t α α > < α > < α α α α ot ot n n n,,, n n n l l l

6 Dfn rlloun funton : ot ot Inrsn Drsn W < > α < > V V For sll fl, << ot O ot ot 4 4 V for sll. K for for sll fl

7 χ V V [ ] p p fft or ntron nubr for sll fl usptblty of prnts follows ur w: χ χ s t ur onstnt, p V 7., n n b stt fro Hun s rul. ftr s stt, n b lult wt t n quton n t p fft or ntron nubr s nown. stt lu n b opr wt prntl lu. ots: Hun s rul wors wll for ost rr rt 4f ltrons, n t lult p s ry los to t sur lu. In so ss l Er Europu n ru, nry btwn t ultplts s too sll n wll us probl n t n orr prturbton. Hun s rul os not wor fn for trnston tls ltrons. In s of rr rt, t 4f ltrons r p ns t on n wll or by t 5s n 5p slls. s s not t s for t trnston tls. ltrons r tully tn furtr out n pos to t fls fro t nbors rystl fl. s rystl fl wll fft t oupln n ofy Hun s rul n lultn. rystl fl wll not oupl wt, bus spn s no rl sp rbls n t. Howr, t rystl fl potntl wll oupl wt. It wll splt t ornl nrt lorbtls >>.

8 Epl of rystl fl splttn porbtls: p p p, p y E p, p y, p, p y p Unr t rystl fl slttn, s not oo quntu nubr ny or. On r or t, < >. rfor, for trnston tl, p wt ltrons n sll soul b lult s [ss] [ss] nst of [], sn os not ontrbut to nt proprts. For splttn of ll nrt orbtls, t rystl fl nnot b sytr, Vry oftn, f t rystl s sytr.. ub, t ons wll spl tsls to prou nonsytr rystl potntl to qun t nulr ontu. s s ll nllr fft, Pul prnts. Eltron s spn, so fr ltrons onstrt prnt proprty, s s nown s Pul prnts.. fft of Pul prnts s ry sll, bys ltrons ns t Fr spr nnot flp tr spns sly wn nrly ll stts r oup. Only ltrons nr t Fr surf n ontrbut to Pul prnts. orn to ur w: χ for sll fl Prnt of ltrons tt t fro to flp spn F. χ for tl F F Pul prnts s npnnt of tprtur.

9 . or qunttt trtnt: Wn tr s no fl: E E F on of n ltrons r t s. DE Wn n trnl fl s ppl, sy, n t rton, t wll lowr t nry of t ltrons by n rs t nry of t ltrons by E rnsfr of ltrons Unbln nt onts E F DE Pul E E F F E DE E DE E E F F DE EDE DE EDE F E F DE F F F

10 s trtnt s nor t sptl fft of nt fl. In ft, t nt fl n ofy t ltron w funton n prous nts. s nts s bout of t bo stt prnts n ntu: frltron Pul otl nts χ F F Pul F on rn nt orrn. on rn nt orrn s u to n fl E fro nbors. In otr wors, w ssu n n fl btwn nbors tt s rs to lon rn orrn.. nt orr stts s r sytry n t ours only t low tprturs wn <. s t rtl tprtur of t nt trnston.. r oon typs of nt orrn: Frront orrn ntfrront orrn Frrnt orrn 4. It s lr fro bo st rwns tt frronts n frrnts wll rs to spontnous ntston tn orrn ours t <. ntfrronts wll not prou ny nston bus of t two opposn spn oponnts. Wn > tr wll b no orrn n t trl s to b prnt.. t ons soul tr own spn t t bnnn. Epl: for ron F s 4K. Iron s tully frront possssn orrn n spontnous ntston t roo tprtur. It s not nt bus of on forton. otl nt ont

11 Frronts. n fl E s pprot by t r ntton fl wtn t spl: E wr s tprtur npnnt onstnt. s s nown s t n fl pproton. ot tt now t n fl wll bo stronr s tprtur s lowr, bus tt s wt os orn to ur w.. Wn > ur Wss w n rltonsp btwn n : If ppl fl n χ P prnt susptblty. χ P E E χ P n fl pproton χ s, χ s to so tt s fnt spon tn ous ntstonwn.. or urt rnorlton roup toury s χ For χ n n p p, V ur Wss w for V. > V.. Wn > lulton of spontnous ntston: E s so stron tt n b nor..., E ~ E. For splty, lwt us onsr lls, n. α ot ot ot ot ot ot

12 t, or, tr s no soluton bus spontnous ntton s to st. t sll, s ur y ~ t wll no soluton wt y pt t wn ~ tn tn tn t tn V V t V n t V t y t.4 t.7 t ytn t y V t t ~ t tn V V t t

13 s s onsstnt wt t rsult w r fro t s >. 4. pontnous ntton nt : s, s sll. Epnson of tn for sll : ot tt t bor of s slr to tt of n t s of syupronutty t ~ or urt rnorlton toy s V t t t t t tn O!!! 5!! 4!! 5!! tn ~

14 5. ow tprtur ttons nons: onsr spns oupl to tr nbors: U s nu wn ll spns r prlll roun stt t : If w onsr t t spn n ntprlll to t otrs, s wll rs t syst nry by n ount of 8. s tton nry wll b sllr f w llow ts ntprlll spn to b sr by ll brs of t syst forton of nons. onsr t t spn n t syst: s rlt to ts nt ont s Hsnbr ntrton U. Groun stt U [ ] 8 U 8 U [ ] [ ] U [ ] [ ] t t t t spn orqu tn on t t spn s tn n fl tn on t tr n {}n b ntf s U E E E E

15 y y y [ ] t ssu s not off ln wt t otr spns so tt, y <<. W n nor son orr trs l y n pprot s. qutons of t t spn n t b wrttn s: y [ t y [ t t rl soluton : t u 4s [ os ] ty y 4s [ os ] u u u n y r 9o out of ps wt qul pltu... spn s prssn rulrly bout t s: y u, r onstnts, pltu tt sur t u ton of t spn. ubsttut ts trl solutons nto t ffrntl qutons: t s t [ t] [ t] u [ ] s u [ ] 4s u [ os ] y lrly, fro t quton for : t 4s u[ os ] u, non trl soluton only f{ 4s [ os ] 4s os If ts onton s stsfy, soln for u n : ] ]

16 op w: orl o of spn yns pn yns s qunt nto nons, of nry. ny spn onfurton n b prss s obnton of ts nons. Dsprson rlton of nons: 4s os 8s sn For sll, ~ 8s E s for sll. E E for sll. 6. rl ttons of nons: W n r t trl proprts of nons fro t sprson rltonsp. lr to t s of ponons, nons r bosons:

17 s 4 V n, n t p s 4 V p s 4 V n s 4 V D s s V D s V D V V 4 D V 4 D s s 4s 4s s : sll of pprot t wol bn by tt p D n D n s n ] s n [ ] s nons ubr of [ s. tospn flp out of non orrspons s. E non s spn of p n > < > <

18 n V s n s ~.587V s s t low tprtur. ns s n V ~ ~ Frrnt orr. Epl: ntt FO F O 4 t low tprturs: F O 44 { F F s u sllr tn tt by onsrn F O 4 s frront. In ntl:

19 En fl on st : En fl on st : For frront orr to our, >>, ν: t t ur onstnts of subltt n b n rsptly. n fl tory, wn > : Frrnt orrn to subltt Du to subltt Du 44 to subltt Du to subltt Du ν to subltt Du to subltt Du { { ppl fl ppl fl : n soluton of trl for non, norn, t

20 ntfrronts. χ Frront orrn ntfrront orrn En fl: > En fl: < χ χ rtl tprtur: ur tprtur rtl tprtur: l tprtur

21 . ntfrronts s spl s of frrnts wt,.. Eprntlly,. Wn < : s. If s of spn t χ χ nrst nbor ntrton nt bus of not tly s θ θ χ 4 U U : n o ] [ sn os 9 os 8 os fls r n n U o o

22 s. If s of spn r s no n n U. χ sn 4 U U : n o ] [ sn os 9 os 8 os fls r n n U o o χ χ θ χ χ

23 4. ntfrront nons: s u [ ] 4s u [ os ] y lrly, fro t quton for : t 4s u[ os ] u, non trl soluton only f{ u u u Fro s of frronts: ow, f ltt orrspons to n ns n ltt to o ns, tn soul oppost sn wt n. Rwrtn t quton for frronts: y y y [ t y y [ rwrttn t y y y [ ] t n slrly, t t u 4s [ os ] If ts onton s stsfy, soln for u n : t y [ y t [ s [ 4s [ os ] 4s os 4s [ os ] t [ t] ] ] [ t] ] y front ] ntfrront

24 orrsponn qutons for ltt : t t t [ t rl soluton : u bo ffrntl qutons bo u [u 4 u [u os ] u [ u u [ u os ] For non trl soluton : 4 4 os [ y [ y [ t] [t] n y 4 os 4 y u y ] ] ] ] ] os 4 4 os 4 os 4 sn 4 sn

25 E E E for sll. ntfrronts E for sll. Frronts Dons. pn n trl wt lon rn nt orrn frront, ntfrront t. for ons.. Rson for on forton: Hr nry owr nry. For sll fl: on s wll n n orn to t rton of t nt fl. n n on s n b rrsbl or rrrsbl.

26 4. For lr fl: on ntton wll rln wt t trnl fl. 5. sturton ntton rotton Irrrsbl bounry splnt Rrsbl bounry splnt 6. Irrrsbl bounry splnt n ntton rotton r t uss of ystrss:

27 turton s Rnn r H orty H fl n to ru b to

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