Lecture 19. Magne&c materials (cont d)
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1 Lctu 19 Magn&c atials (cnt d)
2 Classifid atials accding t thi spns t an xtnal fild Lina agn&za&n Nga&v spns: diaagn&s Vy wak, indpndnt f tp Psi&v spns: paaagnts Spins an&- align altnatly: An&fagn&s; N fild Nn lina spns Spins align and an&- align but nt ains: Fiagn&s; stng, annt pat All spins align and satuat: Fagn&s Stngst by fa, annt pat
3 Matials classifid by thi agn&c pp&s. Class χ dpndnt n B? Dpndnt n tpatu? Hystsis? Exapl χ Diaagn&c N N N wat Paaagn&c N Ys N Aluiniu Fagn&c Ys Ys Ys In 3000 An&fagn&c Ys Ys Ys Tbiu 9.51E- 0 Fiagn&c Ys Ys Ys MnZn(F O 4 ) 500 hap://inf..suy.ac.uk/wkshp/advic/cils/u/ hap:// wiss.php hap://
4 Physics: hap://lctns.wikidt.c/agn&s- in- xid- agn&t
5 In, Nickl, Cbalt Stng aaac&n annc
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8 Fagn&s X is psi&v and vy lag, but nt cnstant with th xtnal fild. Matials a stngly aaactd t xtnal filds Th atials tain s agn&za&n af th xtnal fild is vd. Th dipls f ach at lin up with th xtnal fild. But that is nly a sall pat. Magn&c dains dvlp t ats gup tgth in dains wh all nts a alignd. This dpnds n th icstuctu. Whn n xtnal fild is psnt, ths dains andly align within ach dain. Ovall th nt fild is s&ll z.
9 N fild With xtnal fild Tansi&n btwn dains. In th dain wall th dipls gadually tat.
10 Whn th tpatu is incasd th thal ngy f th ats wks against th agn&c fc f tying t align th dipls. Th satua&n agn&za&n Ms dcass with tpatu. Evntually it dps t z at th Cui tpatu. Th Cui tpatus a f Ni: 358 C; F: 770 C and C: 1131 C.
11 Hystsis: Whn an un- agn&zd sapl (all and dipls) is agn&zd and thn th xtnal fild is vsd, hystsis ccus. As th xtnal fild dps t z, a fac&n f th agn&za&n ains. This is th annt fild. Th vall fild t vc this annc is th cciv fc. Th aa insid th hystsis lp indicats hw had agn&cally th atial is. Sf in has a sall aa with sall annt agn&za&n (M ) and sall cciv fild H c. Had atials hav a lag aa, lag M and lag H c.
12 Pizagn&za&n: is whn th agn&za&n f th atial dpnds n th chanical stss that is applid t it at th sa &. It is a atial ppty. Nickl spnds stngly t applid stss. Cpssiv stss incass th agn&za&n and tnsil stss ducs it. Nickl- in allys (pally) hav th ppsit spns. In in th spns is wak and vais pats f th xtnal fild gin. Th ppsit ffct f th applid agn&c fild changing th dinsins f th atial is calld agntstic&n. (This is th caus f th huing f tansfs and th ballast in fluscnt lights). Tb- Dy- F allys shw agntstic&n 3 ds f agnitud lag than in nickl- in allys. hap://what- whn- hw.c/lctnic- pp&s- f- atials/agn&c- phnna- and- thi- intpta&nclassical- appach- agn&c- pp&s- f- atials- pat- 1/
13 An&fagn&s: Matials hav sall psi&v X. Blw a ci&cal tpatu (T n ) th atic dipls align spntanusly. Hwv, this ccus in altna&ng ppsit dic&ns f an vall vanishing agn&za&n. Macscpically th atial appas paaagn&c. Th ci&cal tpatu is calld Nl tpatu.
14 Th tpatu bhavi f th suscp&bility X f an&fagn&cs is chaactisitc. Abv a ci&cal tpatu, calld th Nél tpatu (T N ) th suscp&bility bys th Cui- Wiss law f paaagnts but with a nga&v intcpt indica&ng nga&v xchang intac&ns. Exapl atials a: C FMn Ha&t (F O 3 ) NiO Insulats and sicnducts hap://
15 Fiagn&s: Matials hav lag psi&v X and bhav vy uch lik fagnts. Spntanus agn&za&n ccus. Thy hav a Cui tpatu, hystsis and annc. It ccus nly in cpunds with cplx cystal stuctu. Th stuctu is cpsd f tw agn&c sublalcs, spaatd by xygn anins. Th dipls a alignd within ach sublalc but ppsit f th th sublalc and f diffnt agnitud du t a diffnt nub f ats. Th vall agn&c nt is pa&ally (but nt cpltly) canclld. Fiagnts a p lctic cnducts (caics). Hnc, n ddy cunts dvlp. Ths a a aj suc f ngy lss in tallic agnts. Fiagnts a suitabl f high fquncy applica&ns. Applica&ns: ludspaks, ts, dflc&n yks, intfnc suppsss, pxiity snss, cding hads, tansfs and inducts. Exapls a: agn&t (F 3 O 4 ), Yaiu- in- gant (YIG), and fits cpsd f in xid with aluinu, cbalt, angans and zinc.
16 Oigin f agn&za&n: In classical thy th bital &n f lctns sults in a agn&c nt. This can b cpad with a cunt lp. Th cunt I flws aund an aa A: Cunt is chag Q f n lctns p & t: H, n1 f a singl lctn. Th & cs f th spd f lctns v and th cicufnc f th aa (cicl). Th xtnal agn&c fild inducs an lctic fild n th chag (chag ving aund a agn&c fild). This fc is Th inducd lctic fild can b xpssd as an inducd bias U v an bital lngth L. H, th inducd bias is latd t th flux by Lnz s law Th agn&c flux is and cbining bth t S π A π A I A t n A t Q v v 1 π π a E E Q F E E t v a φ t L V L E t v a H t A t A H A B φ φ
17 Rsults in with S Intga&ng sults in a chang in vlcity du t a chang in agn&c fild f 0 t H. Cbin this with th agn&c nt f th pvius pag and nw us a singl lctn n1 and Rsult: Rind: In d t ign ding this with vcts, th agn&c fild is ppndicula t th cicula lctn &n. Avaging v all bital plans with spct t th fild th sult is with bing th an adius. This is th classical Langvin thy which xplains diaagn&s. Δv L A H t A L t L t v π π φ H t H t t v π π H t v v v v Δ 1 v 1 H v Δ H Δ 4 H Δ 6
18 Th ag&za&n M is th su f all agn&c nts f all lctns Z in ach at f all ats N M N Z Δ N Z 6 H And X is Χ M H N Z 6 f th diaagn&c suscp&bility Paaagn&s: Can b divd f bital &n f lctns as wll. Bifly, ach at als has a agn&c nt. In th psnc f an xtnal agn&c fild B th is th ptn&al ngy f th dt- pduct f th tw vcts P B a Which is iniu whn bth a paalll. Cnsva&n f angula ntu fbids alignnt. Pcssin sults. Hwv, viba&ns (du t tpatu) allw f nn cnsving fcs t chang th dic&n. Nw thal ngy want t andiz th inta&n and th agn&c fild wants t align th nts. Bth cpt k T B B a
19 T btain th ttal agn&za&n, n has t intgat v all ats with thi spc&v thal ngy distibu&n and thi inta&n in th agn&c fild. With dn ats in th ngy windw f E t E+dE th Bltzann distibu&n says Th intgal v all ngis sults in th ttal nub N f ats, which dfins c A lial cplx ath fllws and th nd sult is f th paaagn&c suscp&bility. de c dn T k E B / de c dn N T k E B / T k N H M B a 3 Χ B k N Cnst T Cnst a 3 Χ
20 Oigin f agn&za&n; Quantu chanical thy vsin: Th agn&c nts f th spinning lctns a th dinant cntibu&ns. Each atic lvl ay b ccupid by tw lctns. Whn a agn&c fild is applid, lctns ty t chang thi spinning dic&n. Hwv, stats a quan&zd. Th sallst tansi&n wuld b a stp. Futh, at abslut z, th ngy ust b high than E F. Givn th agn&c nt f th lctn du t its spin Δ E H s th chang in ngy is Th dnsity f stat distibu&n (f ali lctus) is z(e) Th agn&za&n (p vlu) is Δ N z( E) ΔE M V Δ N V ΔE z( E ) F at th Fi lvl.
21 Th agn&za&n (p vlu) is and f X: 1 M ΔE z( EF ) H z( E s V V M X H V 1 z( E F s ) F ) Th iptant cpnnt h is, that nly lctns cls t th Fi lvl can jup t a high stat. Only thy a capabl f aligning with th xtnal fild. X f this qua&n ags vy wll with xpintal sults. Lt s ty a fw lnts: B(1s s ) a th ccupid stats. Th fist shll 1s is full, and th scnd shll has a full s lvl. Hwv, in th cystallin f th ngy stats f th s and th p bands vlap. Elctns ppulat th lw pats f th cbind band. Th dnsity f stats at E F (i.. z(e F )) is sall.
22 In th cas f Lithiu: Th s lvl has n lctn. Adding and ats tgth. Th s lvl sults in bnding and an&- bnding stats. p s nd s- lctn in at nd s- lctn f at nw in p- bital Li: n singl lctn unpaid: asy t align and gt paaagn&c.
23 Ovlap in B Hnc, a tal Lw dnsity f stats Þ Paaagn&c lw Þ X lw B: lctns, paid: diaagn&c. B: Magn&c Typ Diaagn&c Mass Magn&c Suscp&bility Mla Magn&c Suscp&bility Vlu Magn&c Suscp&bility
24 Cu: Th Fi lvl is cls t th dg f th cnduc&n band. Nt any f stats, i.. had t chang ngy and adapt t an xtnal fild. X paa is sall Th sul&ng spns is th diaag&c n. Intinsic sicnducts: Z dnsity f stats at th tp f th valnc band. Again, X paa is sall Hnc, sicnducts a diaagn&c. Highly dpd xtinsic sicnducts: X paa is nt vanishing, sall cntibu&ns xist X dia Z 6V s z( E V Th tpatu dpndnc is hiddn in z(e F ) and ngligibl. Tuns ut, st paaagn&c atials d nt fllw th Cui- Wiss 1/T dpndnc. X paa F )
25 F agn&c atials F, C, Ni (and swhat Gd) Th lnts hav gd d- bands and vlap with th nxt high s- band. Th ppula&n dnsity is nw dpndnt n th spin f th lctns. With agn&za&n lctns ccupy n spin dic&n band stuctu than th th. Th dnsity f stats is vy high at th Fi lvl.
26 Th dnsity f stats is vy high at th Fi lvl. A sall aunt f ngy is sufficint t shif th ppula&n dnsity f n spin stat t th th. In paaagn&c atials an xtnal applid agn&c fild is quid t pvid th ngy f spin alignnts. In Fagn&c atials ( fiagn&c) th xchang ngy in th atial suffics t unbalanc th dnsi&s f spins.
27 In Fagn&c atials ( fiagn&c) th xchang ngy in th atial suffics t unbalanc th dnsi&s f spins. Th Pauli- Pincipl quis that lctns hav ppsit spins, whn in th sa stat (bital). Hwv, that is ffst by an incas in ngy du t Culbic pulsin. S th altna&v is t ccupy tw siila stats futh apat but with th sa alignd spin dic&n. Th sult is a atial with lw ttal ngy. Nt all lnts aang t hav stats with unpaid lctns. Th is a balanc f ccupying lw stats (paid) unpaid na stats in th cystal stuctu. Th aining lnts a F, Ni, and C (and Gd) S why nt align all f th atial int th sa dic&n: 1) Th vall agn&c ngy f th atial: A big fild (and ngy builds up). Aanging dains In cicls iniizs th siz f th fild.
28 S why nt align all f th atial int th sa dic&n: 1) Th vall agn&c ngy f th atial: A big fild (and ngy builds up). Aanging dains In cicls iniizs th siz f th fild. ) Magn&za&n in diffnt cystal inta&ns is diffnt. Th a had and sf axs. Ovall th ngy ust b iniizd. Hnc, tw lng pats and n sall pat. 3) Magntstic&n causs sall dinsinal changs. Th cpssiv and tnsil ngis ust b accdatd. Th sult a spntanus dains f t 0.1 in siz. In th gin btwn th dains, th Blch walls, th spins tat f n dic&n t th nxt.
29 Blch wall spin ta&ns
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