Ferromagnetism， Kittel.pdf

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1、PH575Spring2009Lecture#23Ferromagnetism:KittelCh.12Diamagnetism:tendencyofchargestoscreenappliedfieldfrominterior.Smallresponsefromallsystems,dominantonlywhenpermanentdipolesabsent.22nµ0Ze2nµ0Ze2χ=−ρ=−rdia4m6mParamagnetism:Permanentatomic-likedipolemomentsali

2、gninpresenceoffield.2222n(J+1)gµµnpµµC0B0Bχ===para3kT3kTTBBPauliParamagnetism:Small,temperatureindependentparamagneticresponseofconductionelectrons.2nµµ0Bχ=condkTBFFerromagnetism:BelowtheCurietemperature,dipolemomentsalignspontaneously,evenintheabsenceofanapp

3、liedfield.Cannotbeexplainedwithouttheconceptofspin.Cχ=FMT−TCAntiferromagnetism:BelowtheNeéltemperature,dipolemomentsanti-alignspontaneously,evenintheabsenceofanappliedfield.Cχ=AFMT+θFerrimagnetism:Antiferromagneticorder,buttwosublatticesdonotproducecompletecan

4、cellationofmagnetisation.Magneticdomainshttp://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/text_images/CH22/FG22_07.JPGHysteresisinferromagnets:SaturationVirginstate(noalignment)DomainsreversingDomainsaligningDomainsreversingCoerciv

5、efield(fieldreq’dtoreverse)Workdonetoreversealignment(irreversible)RemanentfieldSaturationinoppositedirection(internalfieldw/noextappliedfield)ElementalferromagnetsatroomtemperatureareFe,Co,Ni-Bandmodelofferromagnetismworkswellforthese.LargeDOSatEElementalCuisnon

6、-magnetic.F.Ferromagnetism&Antiferromagentism:Somematerialsarestronglyparamagneticaboveacertaintemperature.Belowthistemperature,themagneticmomentsspontaneouslyorder,andthematerialiseitherferromagnetic(momentsaligned)orantiferromagnetic(momentsanti-aligned)ev

7、enintheabsenceofanappliedfield.AFM1/χFMTTCurieTNeelFerromagnetshaveaparamagneticresponseabovethe“CurieTemperature”,andbelowthis,thesusceptibilityisinfinite.Thereisaphasetransition.Themagnetizationisshownbelow.Thewayinwhichthetransitionisapproachedfromaboveandb

8、elowcanbecalculated,andthese“criticalexponents”giveinformationaboutthemodel.1/χCχ∝T−TCTc(˚C)Rel.µFe7704,000Co354600Ni1115250Weissmodel:Large“effectivefield”intheferromagneticstatestabilizesthespo