磁性材料：原理、工藝與應用

MagneticMaterials:Basictheory,ProcessingandApplicationsLecture1磁學根本概念與磁性物理根底1OutlineIntroductiontothiscourseOriginofMagnetismVarioustypesofmagnetismVariousmagneticmaterialsSummary2Beforestart,somequestions…Whatmetalsaremagnetic?SinceFearemagneticmetal,whydoesitnotattractasmallpieceofiron?Pureironismagneticandsomesteelisnot,Why?Fe,W,Mo,V,Nbareallstructuredandhaveunpairedelectrons,whyisonlyFemagnetic?WhydoNdFeBmagnetspackedwithFefoilwhenposted?3ASurveyHaveyoueverstudied-Ferromagnetism《鐵磁學》?Magnetism《磁學》?Electromagnetism《電磁學》?SolidPhysics《固體物理》?MaterialsPhysics《材料物理》?GeneralPhysics《普通物理》〔《大學物理》〕?4AboutThisCourseItisnot-Electromagnetism《電磁學》!Magnetism《磁學》!MagneticPhysics《磁性物理》！Itis–MagneticMaterials！Weemphasizetheory,processingandapplication!5CourseStructure共32學時，含：論文報告4學時學術報告4學時討論2學時講授24學時內容：磁性根底、軟磁材料、硬磁材料、磁記錄、磁致伸縮材料、磁性-物性相互作用、巨磁阻材料、吸波材料、磁性薄膜、磁性納米結構、磁性材料最新進展6Whatisyouropinionaboutthiscourse?Whatdoyouwanttolearn?Howtoteach?Letmeknowbyemail!7AllAboutExam論文報告，70%；平時，30%。Topicsforyourreport:Recentprogressinadvanced-1.NanocompositeRare-earthpermanentmagneticmaterials;2.Nanocompositesoftmagneticmaterials;3.perpendicularmagneticrecording;4.Magnetoelectricmaterials;5.Magneticthinfilmsformicrowaveabsorber;6.GMRmaterials;7.One-dimensionmagneticnanostructures;8.Spintronics;9.Magnetocaloricmaterials;10.Magnetostrictionmaterials.YoucanwriteyourreportinChinesethoughuseofEnglishisencouraged!NoteInformaljournalpaperstyle;Recentprogress;Noplagiarismallowed.8TermMagnetcomesfromtheancientGreekcityofMagnesia,atwhichmanynaturalmagnetswerefound.PlinytheElder(23-79ADRoman)wroteofahillneartheriverIndusthatwasmadeentirelyofastonethatattractediron.KnowninChinaandEurope-800BCLodestoneLet’sgetstart:Astory9LODESTONENow,werefertothesenaturalmagnetsaslodestones(alsospelledloadstone;lodemeanstoleadortoattract)whichcontainmagnetite,anaturalmagneticmaterialFe3O4.Whenlightningstrikestheearthitcouldcreateamagneticfieldlargeenoughtosaturatethemagnetizationoflodestone.Typicalcurrent~1,000,000Amp.Oncein1–10millionyears10HistoryChineseasearlyas121ADknewthatanironrodwhichhadbeenbroughtnearoneofthesenaturalmagnetswouldacquireandretainthemagneticproperty…andthatsucharodwhensuspendedfromastringwouldalignitselfinanorth-southdirection.Useofmagnetstoaidinnavigationcanbetracedbacktoatleastthe11thcentury.Basically,weknewthephenomenonexistedandwelearnedusefulapplicationsforit.Wedidnotunderstandit.司南11

ElectrifiedAmberattractssmallobjectsLodestoneattractsironAConnection?HansChristian?rsted(1777–1851)

Finally,theScience-

Oersted’sExperimentDanishscientistHansChristianOerstedobservedthatacompassneedleinthevicinityofawirecarryingelectricalcurrentwasdeflected!aconnectionbetweenelectricalandmagneticphenomenashown.Oersted’sexperiment(1820)12AquantitativerelationshipbetweenachangingmagneticfieldandtheelectricfieldcreatedbythechangeMichaelFaraday

(1791-1867)Faraday:

EffectofachangingmagneticfieldIn1831,Faradaydiscoveredthatamomentarycurrentexistedinacircuit,whenthecurrentinanearbycircuitwasstartedorstopped.Shortlythereafter,hediscoveredthatmotionofamagnettowardorawayfromacircuitcouldproducethesameeffect.13Henry’swork:alesson!JosephHenry(1797-1878)JosephHenryfailedtopublishwhathehaddiscovered6-12monthsbeforeFaradayHenrywasalwaysslowinpublishinghisresults,andhewasunawareofFaraday'swork.TodayFaradayisrecognizedasthediscovererofmutualinductance(thebasisoftransformers),whileHenryiscreditedwiththediscoveryofself-inductance.14TheconnectionismadeSUMMARY:Oerstedshowedthatmagneticeffectscouldbeproducedbymovingelectricalcharges;FaradayandHenryshowedthatelectriccurrentscouldbeproducedbymovingmagnetsSo....Allmagneticphenomenaresultfromforcesbetweenelectricchargesinmotion.15Ampere:MolecularCurrents

Amperefirstsuggestedin1820thatmagneticpropertiesofmatterwereduetotinyatomiccurrents: ExistenceofsmallmolecularcurrentsEachatom/moleculewouldbehaveasasmallpermanentmagnetWouldaligninthepresenceofamagneticfieldAndreMarieAmpere

(1775-1836)16Themagneticfieldinspacearoundanelectriccurrentisproportionaltotheelectriccurrentwhichservesasitssource.Ampere'sLawForanyclosedlooppath,thesumofthelengthelementstimesthemagneticfieldinthedirectionofthelengthelementisequaltothepermeabilitytimestheelectriccurrentenclosedintheloop.17Donotforgetthem?rstedshowedthatmagneticeffectscouldbeproducedbymovingelectricalcharges;FaradayandHenryshowedthatelectriccurrentscouldbeproducedbymovingmagnets.Allmagneticphenomenaresultfromforcesbetweenelectricchargesinmotion.Amperefirstsuggestedin1820thatmagneticpropertiesofmatterwereduetotinyatomiccurrents.18Toptenlist:whatweshouldhaveknownaboutmagnetism？1.ThereareNorthPolesandSouthPoles.2.Likepolesrepel,unlikepolesattract.3.Magneticforcesattractonlymagneticmaterials.4.Magneticforcesactatadistance.5.Whilemagnetized,temporarymagnetsactlikepermanentmagnets.6.Acoilofwirewithanelectriccurrentflowingthroughitbecomesamagnet.7.Puttingironinsideacurrent-carryingcoilincreasesthestrengthoftheelectromagnet.8.Achangingmagneticfieldinducesanelectriccurrentinaconductor.9.Achargedparticleexperiencesnomagneticforcewhenmovingparalleltoamagneticfield,butwhenitismovingperpendiculartothefielditexperiencesaforceperpendiculartoboththefieldandthedirectionofmotion.10.Acurrent-carryingwireinaperpendicularmagneticfieldexperiencesaforceinadirectionperpendiculartoboththewireandthefield.19OriginofMagnetismofMatterAmpere:molecularcurrentsModernphysics:magneticmomentsinatoms〔“磁矩學說”或“磁偶極矩學說”〕1)unpairedelectronspinsmainly2)theorbitalmotionofelectronswithinthematerialtoalesserextent20物理學原理：任何帶電體的運動都必然在周圍的空間產生磁場。電動力學定律：一個環形電流具有一定的磁矩，它在磁場中行為像個磁性偶極子。設環形電流的強度為I〔A〕，它所包圍的面積為A〔m2〕,那么該環流的磁矩為：m=I*A〔Am2〕玻爾〔Bohr〕原子模型：原子內的電子在固定的軌道上繞原子核作旋轉運動，同時還繞自身的軸線作自旋運動。前一種運動產生“軌道磁矩”，后一種運動產生“自旋磁矩”。物質磁性來源的同一性：盡管宏觀物質的磁性是多種多樣的，但這些磁性都來源于電子的運動。OriginofMagnetismofMatter21原子磁矩Macroscopicpropertiesaretheresultofelectronmagneticmoments。Momentscomefrom2sources:Orbitalmotionaroundanucleus〔軌道磁矩〕與Spinningaroundanaxis〔自旋磁矩〕。原子核磁矩比電子磁矩小3個數量級，一般情況下忽略不計。因此，原子磁矩主要來源于原子核外電子的。原子中的電子成對地存在。這些成對電子的自旋磁矩和軌道磁矩方向相反而互相抵消，使原子中的電子總磁矩為零。——非磁原子。原子中的電子磁矩沒有完全抵消使原子中電子的總磁矩〔有時叫凈磁矩，剩余磁矩〕不為零。——磁性原子。22原子的總磁矩應是按照原子結構和量子力學規律將原子中各個電子的軌道磁矩和自旋磁矩相加起來的合磁矩。原子磁矩ThenetmagneticmomentforanatomisthesumofthemagneticmomentsofconstituentelectronsAtomswithcompletelyfilledelectronshellsareincapablepermanentmagnetizationAllmaterialsexhibitsomeformofmagnetization.Threetypesofresponse;ferro,diaandparamagnetic.23原子的磁矩電子和原子核均有磁矩，但原子核的磁矩僅有電子磁矩的1/1836.5。電子軌道磁矩：

l：軌道角量子數，0,1,2,3,4…n-1(s,p,d,f,…電子態)；n:主量子數；波爾磁子

B=9.273210-24A/m2軌道磁矩在外磁場方向的投影:

l,H=ml

B

ml:角動量方向量子數或磁量子數=0,1,2,…l電子自旋磁矩：

s：自旋量子數，s=1/2自旋磁矩在外磁場方向的投影:

s,H=2ms

B

ms:自旋角動量方向量子數=1/224原子的磁矩原子磁矩=電子軌道磁矩+自旋磁矩對于3d過渡族和4f稀土金屬及合金，原子磁矩：

式中:

稱為郎德因子。J：原子總角量子數；L：原子總軌道角量子數；S：原子總自旋量子數；波爾磁子

B=9.273210-24A/m2量子力學證明，原子磁矩在外磁場方向的投影也是量子化的

J,H=gJmJ

B

mJ:原子角動量方向量子數或原子磁量子數=0,1,2,…JIfJ,LandSareknown,JandJ,Hcanbecalculated.25在一個填滿的電子殼層中，電子的軌道磁矩和自旋磁矩為零。對于次電子層〔等〕未填滿電子的原子，在基態下，其總角量子數J、總軌道量子數L和總自旋量子數S存在如下關系：〔1〕在未填滿電子的那些次電子層內，在Pauli原理允許的條件下S和L均取最大值；〔2〕次電子層未填滿一半時，J=L-S；〔3〕次電子層填滿一半或一半以上時，J=L+SHund規那么

J,H=gJmJ

BmJ=0,1,2,…J26原子磁矩盡管上述計算方法有其深奧的量子力學來源，但與實驗值之間的符合并不十分好。對鐵磁和反鐵磁材料，有時也使用更簡化的方程：μ=gs

或者干脆將g作為可調參數以與實驗結果吻合。27眾所周知，電子軌道運動是量子化的，因而只有分立的軌道存在，換言之、角動量是量子化的，并由下式給出普郎克(Planck)常數：玻爾磁子(Bohrmagneton)電子的軌道磁矩電子的角動量是：電子的軌道磁矩：°●PMLeiv電子的軌道磁矩28與自旋相聯系的角動量的大小是?/2，因而自旋角動量可寫為：S是自旋角動量量子數自旋磁矩通常磁矩

和P之間的關系由下式給出：這里g因子(g-factor)對自旋運動是2，而對軌道運動是1。不管是自旋磁矩，還是軌道磁矩，都是玻爾磁子B的整數倍。P

se電子的自旋磁矩29TheUniversality:MagnetismAllmatteraremagnetic物質磁性無處不在〔1〕物質的各種形態，無論是固態、液態、氣態、等離子態、超高密度態和反物質態都具有磁性；〔2〕物質的各個層次，無論是原子、原子核、根本粒子和根底粒子等都會具有磁性。〔3〕無限廣袤的宇宙，無論是天體，還是星際空間都存在著或強或弱的磁場。地球磁場強度：~240A/m，太陽的磁場強度~80A/m，中子星磁場強度高達~1013-1014A/m。物質的磁性與其他屬性之間存在著廣泛的聯系，并構成多種多樣的耦合效應和雙重〔多重〕效應〔如磁電效應、磁光效應、和磁熱效應等〕。這些效應是了解物質結構和性能關系的重要途徑，又是開展各種應用技術和功能器件〔如磁光存儲技術、磁記錄技術和霍爾器件等〕的根底。30MagneticPoles(磁極)theexternalmagneticfieldisstrongestatthepolesThetwotypesofmagneticpolescannotexistseparately–alwayscoupledtogetherasadipole.Isolatedmagneticmonopoleshavenotyetbeendetected.表示磁極強弱的物理量稱為“磁極強度”。兩個強弱相同的磁極，在真空中相距1厘米時，如果它們之間相互作用力為1達因，那么每個磁極的強度就規定為一個電磁系單位制的磁極強度單位。磁極強度〔Wboremu〕為m1、m2的磁極間相互作用力：F=km1m2/r2k=1/4μ0,0=410-7H/m31Amagneticdipole〔磁偶極子〕AloopofelectriccurrentgeneratesamagneticdipolefieldFieldlinesrunfromtheNorthpoletotheSouthpoleFieldlinesindicatethedirectionofforcethatwouldbeexperiencedbyaNorthmagneticmonopole32MagneticMoment〔磁矩〕電流在其四周產生環繞的磁場。如果把通電導線圈成一個半徑為r的圓環，其周圍的鐵屑那么展示了其產生的磁場的形態。這個磁場等效于一個磁矩為M的磁鐵產生的磁場。由電流i產生的磁場，其強度和圓環的面積相關〔圓環越大，磁矩就越大〕，即M=iπr2。由n個圓環產生的總磁矩是由這些單一圓環產生的磁矩的迭加，即：M=niπr2因此，磁矩M的單位為Am2。環電流磁矩：M=IA棒狀磁鐵磁矩：M=mllmAI33MagneticField〔磁場〕,HAmagneticfieldHisgeneratedwheneverthereiselectricchargeinmotion(electriccurrents).Thiscanbeduetomacroscopiccurrentsinaconductor,ormicroscopiccurrentsassociatedwithelectronsinatomicorbits,orbeproducedbyapermanentmagnet.HismeasuredinA/morOe(SIsystemorcgssystem).1A/m=0.01257OeForasolenoid:H=NI/L34MagneticField〔磁場〕,H電流能夠產生磁場，因此可以借助于電場來定義由其產生的磁場。當導線通以電流時，根據右手法那么，右手的大拇指指向電流方向〔即正方向，與電子流動方向相反〕，其它成環狀的四指那么指示了相應的磁場方向。磁場H同時垂直于電流方向和徑向單位矢量r，其強度與電流強度成正比。磁場強度H可以由安培定律給出：因此，磁場強度H的單位為A/m。35MagneticField,HAforcefieldsimilartothegravitationalandelectricalfield,detectedbyaprobe.Amagneticfieldexertsatorquewhichorientsdipoleswiththefield.Directionofmagneticfieldatanypointisdefinedasthedirectionofmotionofachargedparticleonwhichthemagneticfieldwouldnotexertaforce.Magneticfieldlinesdescribethestructureofmagneticfieldsinthreedimensions.Foramagnet:H=F/m1=k

m1/r2F=km1m2/r236Fluxdensity〔磁通密度〕,B磁通量〔Magneticflux，〕 磁場是一個矢量場，在任何一點它都由方向和強度共同定義。其方向由磁力線箭頭確定，而其強度那么由磁力線的密度確定。磁力線即為磁通量，其密度可用來衡量磁場的強度〔即磁感應強度B〕。Densityofflux(orfield)linesdeterminesforcesonmagneticpolesDirectionoffluxindicatesdirectionofforceonaNorthpoleHigherfluxdensityexertsmoreforceonmagneticpoles37FluxdensityBBdependsonGeometryandcurrentinsolenoidMagneticpropertiesofthematerialGeometryofmaterial38MagneticInduction〔磁感應強度〕,BThemagneticinductionB,alsoknownasthefluxdensity,measuredinTesla(SI)orGauss(cgs),istheresponseofamediumtothepresenceofamagneticfield.1T=10000GsHfieldcreatesmagneticinduction Bisthemagneticinduction;themagnitudeoftheinternalfieldwithinasubstance39MagneticPermeability〔磁導率〕,B=Histhepermeability〔磁導率〕ofthemedium(Henriespermeter)B0=0H0isthepermeabilityofavacuumr=/0ristherelativepermeability40Magnetization(磁化強度),MWedefinemagnetizationasthetotalmagneticdipolemoment(magneticmoment)perunitvolumewithinthematerialItismeasuredinA/m(SI)oremu/cm3(cgs).41Magnetizationdependson……..NumberdensityofmagneticdipolemomentswithinmaterialMagnitudeofthemagneticdipolemomentswithinthematerialThearrangementofthemagneticdipoleswithinthematerial42Polarization〔磁極化強度〕,JThemagneticpolarisationJ,measuredinTesla,isgivenbyJ=

oM,where

o(=1.23664

10-6H/m)isthepermeabilityoffreespace.Mincreasesasmoreelectronicmagneticmomentsarealigned.Whenallmagneticmomentsarealignedinthesamedirection,thesaturationmagnetisation(polarisation)Ms

(Js)isachieved.43HowdoesMrespondtoH?ThereisavarietyofwaysthatMrespondstoHResponsedependsontypeofmaterialResponsedependsontemperatureResponsecansometimesdependontheprevioushistoryofmagneticfieldstrengthsanddirectionsappliedtothematerial44Non-linearresponsesGenerally,theresponseofMtoHisnon-linearOnlyatsmallvaluesofHorhightemperaturesisresponsesometimeslinearMtendstosaturateathighfieldsandlowtemperatures45B,H,M,JRelationshipsB(inT)consistsoftwocontributions:onefrommagneticfieldH(A/m),theotherfrommagnetisationM(A/m).Thisleadstooneofthemostimportantrelationsinmagnetism:IfthereisnomagnetizationM…..46MagneticSusceptibility〔磁化率〕,B=

0(H

+M)ReplaceB=

H→

H=

0(H

+M) →r

0H=

0(H

+M) →0M=0(r-1)H →M=

(r

-1)H

MagneticSusceptibilityM=

H

=

r?1

,Susceptibility,measuresthematerialresponserelativetoavacuum(Dimensionless)47VariousMagnetismBasedon抗磁性〔Diamagnetism〕順磁性〔Paramagnetism〕鐵磁性〔Ferromagnetism〕亞鐵磁性〔Ferrimagnetism〕反鐵磁性〔Antiferromagnetism〕>0,typically10-3-10-5>>1,typically

50-104<0,typically

-10-7Magneticorderingmaterials48VariousMagnetismDiamagnetsarematerialswhichhavenonetmagneticmomentontheiratoms,becausetheelectronsareallpairedwithantiparallelspins.WhenamagneticfieldHisapplied,theorbitsoftheelectronschangeinaccordancewithLenz’slaw,andtheysetupanorbitalmagneticmomentwhichopposesthefield,andthereforegivesverysmallnegativesusceptibility.Paramagnetsarematerialswhichhaveanetmagneticmomentperatomduetounpairedelectronspins.Inzerofieldthesemagneticmomentsarerandomlyorientedbut,undertheactionofanexternalfieldH,theycanbealignedinthefielddirection.Asaresultofthisalignment,themagnetisationMisparalleltothefieldand,hence,thesusceptibilityispositive.Ingeneral,verylargefieldsareneededtoalignallthemomentsandthereforethesusceptibility,althoughpositive,isverysmall.Orderedmagneticmaterials(

>>1,typically

50-104)showlarge,intrinsicmagneticmoments,andcanbehaveasiftheywerespontaneouslymagnetised.Varioustypesofmagneticmomentorderinghavebeenobserved:(1)Ferromagnetic;(2)Ferrimagnetic;(3)Antiferromagnetic.49VariousMagnetism50Diamagnetism〔抗磁性〕Diamagnets

havenonetmagneticmomentontheiratoms,becausetheelectronsareallpairedwithantiparallelspins.拉莫爾進動

WhenamagneticfieldHisapplied,theorbitsoftheelectronschangeinaccordancewithLenz’slaw,andtheysetupanorbitalmagneticmomentwhichopposesthefield,andthereforegivesverysmallnegativesusceptibility(磁化率χ<0).M與H的方向相反，所以由此而產生的物質磁性稱作抗磁性。抗磁性存在于一切物質中，但只有在抗磁性物質中才能從宏觀上表現出來，在另外的物質中，這種磁性被其他磁性所掩蓋。51Thesusceptibility,isnegativeItdoesnotchangemuchwithtemperatureWhenadiamagneticmaterialisplacednearamagnet,itwillberepelledfromtheregionofgreatermagneticfield,justoppositetoaferromagneticmaterial.Examples:Peopleandfrogsarediamagnetic.

Metalssuchasbismuth,copper,gold,silverandlead,aswellasmanynonmetalssuchaswaterandmostorganiccompoundsarediamagnetic.water,inertgases

TDiamagnetism抗磁性52根據抗磁性物質χ值的大小及其與溫度的關系可將抗磁性物質分為三種類型：1、弱抗磁性例如惰性氣體、金屬銅、鋅、銀、金、汞等和大量的有機化合物，磁化率極低，約為-10-6，并根本與溫度無關；2、反常抗磁性例如金屬鉍、鎵、碲、石墨以及γ-銅鋅合金，其磁化率較前者約大10-100倍，Bi的磁化率χ比較反常，是場強H的周期函數，并與溫度強烈相關；3、超導體抗磁性許多金屬在其臨界溫度和臨界磁場以下時呈現超導性，具有超導體完全抗磁性，其χ=-1.Diamagnetism抗磁性53VeryhighfieldswouldsaturatemagnetizationHeatingthegaswouldtendtodisorderthemomentsandhencedecreasemagnetizationWhenaparamagneticmaterialisplacednearamagnet,itwillbeattractedtotheregionofgreatermagneticfield,likeaferromagneticmaterial.Thedifferenceisthattheattractionisweak.

Itisexhibitedbymaterialscontainingtransitionelements,rareearthelementsandactinideelements.

Liquidoxygenandaluminumareexamplesofparamagneticmaterials.

Paramagnetism(順磁性)54原子、分子或離子具有不等于零的磁矩，并在外磁場作用下沿軸向排列時便產生順磁性。順磁性物質的磁化率χ>0，數值很小，約為10-3-10-6。順磁性也可以分為三類：1、郎之萬〔Langevin〕順磁性包括O2和N2氣體、三價Pt和Pd、稀土元素，許多金屬鹽以及居里溫度以上的鐵磁性和亞鐵磁性物質。原子磁矩可自由地進行熱振動，χ值與溫度有關，服從居里〔Curie〕定律：χ=C/T或居里-外斯〔Curie-Weiss〕定律：χ=C/〔T+θ〕式中：C—居里常數〔K〕，T—絕對溫度〔K〕，θ—外斯常數〔K〕1/T(K)θΧ斜率C居里（Curie）定律居里-外斯（Curie-Weiss）Paramagnetism(順磁性)552、泡利〔Pauli〕順磁性典型代表物為堿金屬，它們的磁化率相對較前一種為低，并且其值幾乎不隨溫度變化。3、超順磁性在常態下為鐵磁性的物質，當呈現為極微細的粒子時那么表現為超順磁性。此時粒子的自發極化本身作熱運動，產生郎之萬磁性行為，初始磁化率隨溫度降低而升高。Paramagnetism(順磁性)56

MisproportionaltotheappliedfieldH=Lim

H→0M/H=C/TCURIE’SLAWPIERRECURIENormalparamagneticsubstancesobeytheCurieLawExamples:Aluminum,platinum,manganese,chromium

=C/T1/=T/C

1/T

inKParamagnetism(順磁性):Curie’sLaw57強磁性(Magneticorderingmaterials)在強磁性物質中，原子間的交換作用使得原子磁矩保持有秩序地排列，即產生所謂自發磁化。Magneticdomain:原子磁矩方向排列規律一致的自發磁化區域叫做磁疇。存在飽和磁化強度Ms。強磁性物質的磁化率χ值是很大的正值，并且易于在外磁場作用下到達飽和磁化。強磁性可以分為如下三種類型：鐵磁性、亞鐵磁性、弱鐵磁性。58whereqistheanglebetweenspinsandJexistheexchangeintegral.ForJex>0,ferromagneticorderresultsinanenergyminimum;forJex<0,anantiferromagneticalignmentisfavoured.Whenconsideringasolid,itisthennecessarytosumtheexchangeoveralltheelectronswhichcancontributetothisenergy,sothat:ExchangeinteractionExchangeinteractionisresponsibleforthephenomenonofmagneticmomentordering.Itsphysicaloriginisquantum-mechanical.Theexchangeinteractionreducestheenergyassociatedwithparallelalignmentofspins,evenintheabsenceofanexternalfield.Thisresultsinanetmagneticmoment.In1928,Heisenberg[2]showedthatexchangeenergy(Eex)canberepresentedby:59Exchangeinteraction對于磁性物質，由于近鄰原子共用電子〔交換電子〕所引起的磁矩之間的交換作用所產生能量，稱作交換能〔Jex〕，因其以積分形式出現，也稱交換積分。它取決于近鄰原子未填滿的電子殼層相互靠近的程度，并決定了原子磁矩的排列方式和物質的根本磁性。i〕Jex>0，交換作用使得相鄰原子磁矩平行排列，產生鐵磁性〔Ferromagnetism〕。ii〕Jex<0，交換作用使得相鄰原子磁矩反平行排列，產生反鐵磁性〔Antiferromagnetism〕。iii〕原子間距離足夠大時，Jex值很小時，交換作用缺乏于克服熱運動的干擾，原子磁矩隨機取向排列，于是產生順磁性〔Paramagnetism〕60鐵氧體材料具有亞鐵磁性〔Ferrimagnetism〕,其中金屬離子具有幾種不同的亞點陣晶格，因相鄰的亞點陣晶格相距太遠，因此在其格點的金屬離子之間不能直接發生交換作用，但可以通過位于它們之間的氧原子間接發生交換作用，或稱超交換作用〔Superexchange〕。反鐵磁性〔Antiferromagnetism〕材料中也存在超交換作用。Superexchangeinteraction超交換作用反鐵磁性NiO中的超交換作用61原子磁矩方向一致整齊排列，MaterialsthatretainamagnetizationinzerofieldQuantummechanicalexchangeinteractionsfavourparallelalignmentofmomentsExamples:iron,cobaltFerromagnetism〔鐵磁性〕62ThermalenergycanbeusedtoovercomeexchangeinteractionsCurietempisameasureofexchangeinteractionstrength原子磁矩的排列為方向一致的整齊排列，隨著溫度的升高，這種排列受熱擾動的影響而愈加紊亂，同時物質的自發磁化強度也愈來愈小。當溫度上升到某一定值TC(居里溫度)時，自發磁化消失，物質由鐵磁型轉變為順磁性。大局部強磁性金屬和合金屬于這種磁性。Ferromagnetism〔鐵磁性〕63MdecreasesrapidlywithHBeyondtheCurietemperatureitbehaveslikeaparamagneticsubstanceExamples:iron,cobalt,nickelBehaveslikeaparamagnetCurieTemperatureTCMdecreasesrapidlywithHFerromagnetism〔鐵磁性〕64Theinternalexchangeinteractiontriestokeepthemagneticmomentsaligned,butthisorientationcanbedestroyedbyincreasingtemperature.Whenasufficientlyhightemperatureisreachedthethermalenergyovercomestheexchangeenergyandthematerialundergoesanorderedferromagneticphasetoadisorderedparamagneticphase.ThetemperatureisknownastheCurietemperatureTc.TheCurielawstatesthatthesusceptibilityofaparamagnetisproportionaltothereciprocalofthetemperatureT,i.e.whereCisconstant.Toincludethosematerialswhichundergoanorder-disordertransitiontoferromagnetismorferrimagnetismatTc,theaboverelationshipbecomescalledCurie-Weisslaw,whichisageneralisationoftheCurielaw.Ferromagnetism:Curietemperature〔居里溫度〕，TC65Antiferromagnetism〔反鐵磁性〕Insomematerials,exchangeinteractionsfavourantiparallelalignmentofatomicmagneticmomentsMaterialsaremagneticallyorderedbuthavezeroremnantmagnetizationandverylowManymetaloxidesareantiferromagnetic反鐵磁性物質的原子磁矩具有完全相互抵消的有序排列，因而自發磁化強度為零。在外磁場作用下仍具有相當于強順磁性物質的磁化率〔χ為10-3-10-6〕，所以這類磁性為弱磁性。Example:CobaltOxides66likeparamagnetsaboveacriticaltemperatureTNcalledNeéltemperature(奈耳溫度).BelowTNissmall&T-dependenceisdifferentfromparamagnets.Thermalenergycanbeusedtoovercomeexchangeinteractions,MagneticorderisbrokendownattheNéeltemperature(c.f.Curietemp)隨著溫度升高，磁矩完全抵消的有序排列受到越來越大的破環，磁化率χ值也隨之上升。當溫度上升到TN時，χ值到達最大；超過TN，有序排列完全破環，而轉化為順磁性。HeatAntiferromagnetism〔反鐵磁性〕67根據原子磁矩排列方式的不同，分為：1〕正常反鐵磁性原子磁矩排列為互相平行而大小和數量相等的兩組。MnO、NiO及FeS等化合物2〕螺旋磁性在晶體的一個平面內，原子磁矩的排列方向一致，而在相鄰的另一平面內，原子磁矩較前一個平面內的原子磁矩一致性地旋轉了一定的角度，形成螺旋式的旋轉。重稀土金屬Tb、Dy、Ho、Er、Tm等具有這種磁性。3〕自旋密度波原子磁矩密度〔自旋密度〕本身具有正旋波調制結構。在Cr及其合金中存在這種結構。Antiferromagnetism〔反鐵磁性〕68Ferrimagnetism〔亞鐵磁性〕AntiferromagneticexchangeinteractionsDifferentsizedmomentsoneachsublatticeresultinnetmagnetization原子占據兩種或兩種以上的亞點陣。同一種亞點陣上的原子磁矩平行排列，但不同亞點陣間原子磁矩的反平行排列。原子磁矩相加的結果表現為不等于零的自發磁化強度MS。由于每種亞點陣的磁化強度隨溫度變化的規律不同，因而總的磁化強度隨溫度的變化曲線具有不同于鐵磁性的各種特殊形狀，可以分為Q型、P型、R型和N型。Example:magnetite,maghemiteTTcR型P型N型TCOM69Likeferromagnets,buttheeffecttendstobesmaller.The1/curveisveryclosetozerobelowacriticaltemperature,alsocalledNeéltemperature.Examples:magnetite(Fe3O4)andspinelferritesFerrimagnetism〔亞鐵磁性〕70BPARAmagneticDIAmagneticFERROmagneticFERRImagneticANTIFERROmagneticBComparison〔磁場作用〕71MagnetizationCurves(磁化曲線)抗磁順磁鐵磁亞鐵磁反鐵磁DIAmagneticFERROmagneticFERRImagneticPARAmagneticANTIFERROmagnetic72磁化率與磁行為類型磁性種類典型的χ值χ隨溫度的變化χ隨場強的變化抗磁性-1×10-6無變化無關順磁性10-4~10-5減小無關鐵磁性102~106減小無關反鐵磁性0~10-2增加有關Comparison磁化率與磁行為PARAmagnetic>0,r

>1DIAmagnetic<0,r

<1

r

=0(superconductors)(r

-1)=→

r

=

+1FERROmagnetic>0,r

>>173MagneticdomainsApplyingafieldchangesdomainstructure;Domainswithmagnetizationindirectionoffieldgrow;OtherdomainsshrinkApplyingverystrongfieldscansaturatemagnetizationbycreatingsingledomainFerromagneticmaterialstendtoformmagneticdomains;Eachdomainismagnetizedinadifferentdirection;Domainstructureminimizesenergyduetostrayfields74MagneticdomainsRemovingthefielddoesnotnecessarilyreturndomainstructuretooriginalstateHenceresultsinmagnetichysteresis75MagnetichysteresisMdependsonpreviousstateofmagnetizationRemanentmagnetizationMrremainswhenappliedfieldisremovedNeedtoapplyafield(coercivefield)inoppositedirectiontoreduceMtozero.76Heatingamagnetizedmaterialgenerallydecreasesitsmagnetization.RemnantmagnetizationisreducedtozeroaboveCurietemperatureTcHeatingasampleaboveitsCurietemperatureisawayofdemagnetizingitThermaldemagnetizationEffectoftemperatureonremanentmagnetization77GeneratingauniformmagneticfieldinthelaboratoryAnelectriccurrentrunthroughaconductingcoil(solenoid)generatesauniformfluxdensitywithinthecoil78InsertingaspecimenintothecoilGenerally,theorbitalandspinmagneticmomentswithinatomsrespondtoanappliedmagneticfieldFluxlinesareperturbedbyspecimen79SpecimeninmagneticfieldIfspecimenhasnomagneticresponse,fluxlinesarenotperturbed80“Magnetic”materials“magnetic”materialstendtoconcentratefluxlinesExamples:materialscontaininghighconcentrationsofmagneticatomssuchasiron,cobalt81DiamagneticmaterialsDiamagneticmaterialstendtorepelfluxlinesweaklyExamples:water,protein,fat82MagneticMaterialsROOMTEMPERATURE83對于磁學單位，考慮強度為p1,p2的磁極，其單位為靜電單位〔electrostaticunits，esu〕，那么上式變為:在cgs單位系統中，力的單位為達因〔dyn)〕，所以一個單位的磁極強度為1gm1/2cm3/2s-1。實際上，自然界沒有獨立的單磁極子。但是磁極強度的概念仍然是cgs磁學單位的核心。cgsUnits在cgs〔厘米-克-秒〕系統中推導磁學單位與在SI系統中完全不同。根據庫侖定律，兩個電荷〔q1，q2〕之間的力為：其中r為兩個電荷之間的距離。在cgs單位系統中，比例常數k為1。而在SI單位系統中，其值為1/(4π0)，其中0=107/4c2，c是真空中的光速。因此0=8.859*10-12AsV-1m-1。[可見為什么大多數學者偏愛cgs單位！]84cgsUnits一個磁極子或者一個獨立的電荷會在其周圍空間產生一個磁感應強度0H。一個單位的磁場強度定義為〔1oersted或者Oe〕相當于在每單位磁極強度上施加一達因的力。因此三者之間的關系為：所以，具有一單位磁極強度的磁極放在1Oe的磁場中會受到一達因的力。這個力也等效于在距離具有一個磁極強度的磁極1cm的地方所受到的力。因此，在距離一個單極子1cm的地方的磁場為1Oe，并且按著1/r2的規律遞減。現在我們可以定義1Oe是每平方cm上1line的力。假設一個半徑為r的球包圍一個磁單極子，球的外表積為4r2，這個球就為單位圓球〔aunitsphere〕〔r＝1〕，在球面上的磁場就為1Oe。那么一定有4lines的力穿過這個球。85cgsUnits至于磁矩，從cgs系統的觀點看，我們假設一個長為l的磁鐵，其兩端磁極的強度為p。把這個磁鐵放在

0H的磁場中，那么這個磁鐵所受的扭力矩為：其中pl是磁矩m，的單位是能量〔在cgs系統中，其單位是ergs〕，所以，磁矩的定位是ergs/Oe。我們因此定義一電磁單位〔emu〕為1erg/Oe。注意，以上推導中的系數0，在使用cgs單位的Cullity〔1972〕以及很多書籍和文章中并不存在。原因是，在應用cgs系統時，這個系數值為1，所以oersteds(H)和gauss(B)經常被互換使用。然而在SI系統中，二者并不相同，因為這個系數的值為4x10-7。86UnitsandConversions87UnitsandConversionsSymbolDefinitionCGSSIConversionCGStoSI

FluxMaxwellWeber(Wb)10-8MMagnetisation,Numberofpolesinagivencross-sectionOersted(Oe)A/m103/4

BFluxDensityorInductionB=m0H+JMaxwell/cm2orGauss(G)Wb/m2orTesla(T)10-4HMagneticFieldStrengthOersted(Oe)A/m103/4

m0PermeabilityoffreespaceUnit4px10-7Henry/metre-JIntensityofmagnetisationormagneticvolumeperunitvolumeGauss(G)Tesla(T)10-4HcCoercivity,magneticfieldrequiredtoreduceBtozeroaftersaturationO