MagneticFerritesand Related Nanocomposites
AliGhasemi
Elsevier
Radarweg29,POBox211,1000AEAmsterdam,Netherlands
TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates
Copyright © 2022ElsevierLtd.Allrightsreserved.
Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans, electronicormechanical,includingphotocopying,recording,oranyinformationstorage andretrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowto seekpermission,furtherinformationaboutthePublisher’spermissionspoliciesandour arrangementswithorganizationssuchastheCopyrightClearanceCenterandthe CopyrightLicensingAgency,canbefoundatourwebsite: www.elsevier.com/permissions .
Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightby thePublisher(otherthanasmaybenotedherein).
Notices
Knowledgeandbestpracticeinthis fieldareconstantlychanging.Asnewresearchand experiencebroadenourunderstanding,changesinresearchmethods,professional practices,ormedicaltreatmentmaybecomenecessary.
Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledge inevaluatingandusinganyinformation,methods,compounds,orexperimentsdescribed herein.Inusingsuchinformationormethodstheyshouldbemindfuloftheirownsafety andthesafetyofothers,includingpartiesforwhomtheyhaveaprofessional responsibility.
Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,or editors,assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasa matterofproductsliability,negligenceorotherwise,orfromanyuseoroperationofany methods,products,instructions,orideascontainedinthematerialherein.
ISBN:978-0-12-824014-4
ForinformationonallElsevierpublicationsvisitourwebsite at https://www.elsevier.com/books-and-journals
Publisher: MatthewDeans
AcquisitionsEditor: EdwardPayne
EditorialProjectManager: JohnLeonard
ProductionProjectManager: NirmalaArumugam
CoverDesigner: GregHarris
TypesetbyTNQTechnologies
TomywifeAzadeh forhercontinuedlove,patience,andsupport AND mychildren
Reza,Ava,andNava, whoarethereasonforthemercyofGod
Thispageintentionallyleftblank
CHAPTER1Fundamentalsofferrites ..........................................1
1.1 Introduction. .....................................................................1
1.2 Briefhistoryofmagnets .....................................................1
1.3 Basicscienceofmagnetism ................................................3
1.3.1Originofmagnetism ..................................................3
1.3.2CoulombandLorentzforces .......................................3
1.3.3Definitionoffundamentalmagneticparameters ..............4
1.3.4Ampe ` re’slaw...........................................................5
1.3.5Faraday’slaw ...........................................................6
1.3.6Lenz’slaw.. .............................................................6
1.3.7Maxwell’sequations ..................................................6
1.4 Classesofmagneticmaterials.. ............................................7
1.4.1Diamagnetism...........................................................7
1.4.2Paramagnetism... .......................................................7
1.4.3Ferromagnetism. .....................................................10
1.4.4Antiferromagnetism. ................................................11
1.4.5Ferrimagnetism.. .....................................................13
1.5 Importanceofferrites... .....................................................15
1.6 Fundamentalsofferritecrystalstructures... ...........................15
1.6.1Spinelferrites .........................................................16
1.6.2Hexagonalferrites... ................................................16
1.6.3Garnetstructure. .....................................................22
1.6.4Orthoferritestructure ...............................................23
1.7 Superexchangeinteraction. ................................................23
1.8 Applicationsofferrites. .....................................................26
1.8.1Applicationsofferritesinmicrowave-absorbing media....................................................................27
1.8.2Applicationsofferritesinharddiskdrives. ..................30
1.8.3Applicationsofferritesinbiosciences.. .......................32
1.8.4Applicationsofferritesintheenvironment ..................35
1.8.5Applicationsofferritesaspermanentmagnets.. ............35
1.8.6Applicationsofferritesinmodernelectronics... ............36
1.8.7Applicationsofferritesinmicrowavedevices... ............41 References.. ....................................................................45
CHAPTER2Ferritecharacterizationtechniques
2.1 Introduction .....................................................................49
2.2 X-raydiffraction... ...........................................................49
2.2.1FundamentalprinciplesofX-raydiffraction. .................50
2.2.2X-raydiffractioncomponentsandperformance.. ...........51
2.2.3Applications.. ..........................................................53
2.2.4Strengthsandlimitations. ..........................................53
2.3 Scanningelectronmicroscopy. ............................................54
2.3.1Thebasicprinciplesofscanningelectronmicroscopy .....54
2.3.2Scanningelectronmicroscopycomponentsand performance.. ..........................................................55
2.3.3Energy-andwavelength-dispersivespectroscopy ...........57
2.3.4Applications.. ..........................................................58
2.3.5Strengthsandlimitations. ..........................................58
2.4 Transmissionelectronmicroscopy .......................................59
2.4.1Selectedareadiffractionpatterns. ................................60
2.4.2Kikuchidiffractionlines.. ..........................................64
2.4.3Electronenergy-lossspectroscopy ...............................64
2.5 Atomicforcemicroscopy.. .................................................67
2.6 Magneticforcemicroscopy ................................................68
2.7 Fouriertransforminfraredspectroscopy................................68
2.7.1FundamentalprinciplesofFouriertransforminfrared spectroscopy.. ..........................................................68
2.7.2TypicalapplicationsofFouriertransforminfrared analysisofferritenanoparticles... ................................70
2.8 Thermalanalysismethods. .................................................73
2.8.1Thermalgravimetricanalysis. .....................................74
2.8.2Differentialthermalanalysis.. .....................................75
2.8.3Simultaneousthermalanalysis ....................................77
2.8.4Differentialscanningcalorimetry ................................77
2.9 Mo ¨ ssbauerspectroscopyofferrites ......................................77
2.10 Magneticanisotropy..........................................................82
2.10.1Magnetocrystallineanisotropy... ................................82
2.10.2Shapeanisotropy ....................................................84
2.10.3Inducedmagneticanisotropy ....................................85
2.10.4Magnetostrictionanisotropy. .....................................85
2.10.5Magneticsurfaceandinterfaceanisotropies ................86
2.11 Magneticdomains. ...........................................................86
2.12 Vibratingsamplemagnetometer... .......................................89
2.12.1Low-temperaturevibratingsamplemagnetometer... ......89
2.12.2High-temperaturevibratingsamplemagnetometer.. ......90
2.13 B H tracer.. ....................................................................91
2.14 Interpretationofthe M H loop. ..........................................92
2.15 Henkelplot. ....................................................................97
2.16 Alternatingcurrentmagneticsusceptibility ...........................97
2.17 First-orderreversalcurvemeasurement ..............................100
2.17.1First-orderreversalcurveanalysisbackground... ........100
2.17.2First-orderreversalcurveanalysismeasurements .......102
2.17.3First-orderreversalcurveanalysisapplications.. ........105
2.18 MeasurementofpermeabilityandCurietemperature... .........109
2.19 Measurementofpermittivity.............................................111
2.20 Definitionofintrinsicimpedance.......................................112
2.21 Microwavereflectionloss(R)measurements .......................113 References.. ..................................................................119
CHAPTER3Magneticferrites
3.1 Introduction. ..................................................................125
3.2 Importantdefinitions .......................................................125
3.2.1Particleswithsingle-domainstructure.. ......................125
3.2.2Timevariationofmagnetization................................127
3.2.3Superparamagneticstate ..........................................127
3.2.4Snoek’slaw. ..........................................................128
3.3 Hexagonalferrites.. ........................................................129
3.3.1M-typehexagonalferrites... .....................................131
3.3.2W-typehexagonalferrites... .....................................151
3.3.3Y-typehexagonalferrites .........................................162
3.3.4Z-typehexagonalferrites .........................................180
3.3.5X-typehexagonalferrites.... .....................................186
3.3.6U-typehexagonalferrites.... .....................................191
3.4 Spinelferrites... .............................................................201
3.4.1Simplespinelferrites ..............................................201
3.4.2Mixedspinelferrites ...............................................205
3.4.3Cobaltferrites ........................................................222
3.5 Biomedicalaspectsofmagnetite... ....................................242
3.6 Garnets. ........................................................................257
3.6.1Yttriumirongarnet.. ...............................................257
3.6.2Substitutedyttriumirongarnetnanoparticles.... ...........260
3.6.3Rare-earth-substitutedyttriumirongarnet nanoparticles .........................................................270
3.6.4Othertypesofgarnetnanoparticles ...........................279 References.. ..................................................................286
CHAPTER4Magnetoelectricferritenanocomposites
4.1 Introduction....
4.2 Magnetoelectriceffect .....................................................301
4.3 Boomgaard’srequirements ...............................................303
4.4 Ferroelectricsinmagnetoelectriccomponents......................304
4.5 Ferritesinmagnetoelectriccomponents...
4.6 Heterostructuralconfigurationofferrite/ferroelectric materialsinmagnetoelectriccomponents. ...........................306
4.7 Applicationsofmagnetoelectriccomponents.
4.8 Theoreticalaspectsofmagnetoelectriceffect
4.8.1Maxwell Wagnereffect...
4.8.2Koop’stheory..
4.8.3Jahn Tellerdistortions............................................309
4.9 Ferrite/ferroelectricnanocompositesformagnetoelectric components ...................................................................309
4.9.1Nickel-basedferrite/ferroelectriccomponents.
5.5
6.4 Typesofcarbonmaterials... .............................................438
6.5 Polymersassupportingmediaforabsorption.......................441
6.6 Permittivityandpermeabilityofabsorbingmedia.. ..............442
6.7 Hardferrite/carbonnanotubenanocomposites... ...................444
6.8 Hardferrite/single-walledcarbonnanotube nanocomposites.. ............................................................459
6.9 Spinelferrite/carbonnanotubenanocomposites. ...................463
6.10 Ferrite/graphenenanocomposites.... ...................................481
6.11 Ferrite/grapheneoxidenanocomposites ..............................491
6.12 Ferrite/carbonblacknanocomposites..................................494
6.13 Ferrite/carbonfibernanocomposites ...................................498
6.14 Softferrite/amorphouscarbonnanocomposites. ...................500
6.15 Ferrite/porouscarbonnanocomposites.. ..............................503
6.16 Ferrite/graphitenanosheetnanocomposites. .........................505
6.17 Ferrite-MoS2@nitrogen-dopedcarbonhybridstructure. .........507 References.. ..................................................................509 Furtherreading. .............................................................517
CHAPTER7Nanoferritephotocatalysts....................................521
7.1 Introduction. ..................................................................521
7.2 Basicdefinitionofphotocatalysts... ...................................521
7.3 NanocrystallineCo-ferritephotocatalyst .............................525
7.4 NanocrystallineZn-ferritephotocatalyst .............................534
7.5 NanocrystallineNi Zn-ferritephotocatalyst .......................542
7.6 NanocrystallineCo Zn ferritephotocatalyst... ...................543
7.7 NanocrystallineMn-richferritephotocatalyst... ...................548
7.8 NanocrystallineLi-ferriteandMg-ferritephotocatalysts ........558
7.9 NanocrystallineBi-ferritephotocatalyst ..............................562
7.10 Ferritenanocompositesphotocatalysts.. ..............................564
7.10.1PhotocatalyticpropertiesofNi1 xCoxFe2O4/ multiwalledcarbonnanotubenanocomposites............564
7.10.2PhotocatalyticpropertiesofCu1 xCoxFe2O4/ multiwalledcarbonnanotubenanocomposites............567
7.10.3Photocatalyticpropertiesofreduced-graphene oxide-Ni0.65Zn0.35Fe2O4 ferritenanohybrids. .............571
7.10.4PhotocatalyticpropertiesofMnFe2O4 ferrite-graphenenanocomposites. ............................573
7.10.5PhotocatalyticpropertiesofTiO2/ferrite nanocomposites... .................................................579 References.. ..................................................................580
CHAPTER8Ferritesynthesismethods
8.1 Introduction.... ...............................................................587
8.2 Synthesistechniquesforferritenanoparticles ......................587
8.2.1Sol geltechnique. .................................................587
8.2.2Coprecipitationtechnique. .......................................589
8.2.3Microemulsiontechnique.. .......................................590
8.2.4Hydrothermalandsolvothermaltechniques .................591
8.2.5Mechanicalmillingtechnique. ..................................598
8.2.6Thermaldecompositiontechnique .............................598
8.2.7Otherferritenanoparticlesynthesistechniques ............601
8.2.8Comparisonofferritesynthesistechniques .................602
8.3 Bulkferritesynthesistechniques. ......................................604
8.3.1Sparkplasmasinteringtechnique. .............................604
8.3.2Hotpressingandhotisostaticpressingtechniques........608
8.3.3Coldisostaticpressingtechnique.. .............................610
8.4 Synthesistechniquesofferritethinfilms. ...........................612
8.4.1Physicalvapordepositiontechnique.. ........................612
8.4.2Pulsedlaserdeposition ............................................617
8.4.3Molecularbeamepitaxy... .......................................618
8.5 Synthesistechniquesforferritenanofibers ..........................621 References ....................................................................622
Preface
WhenIdecidedtowritethisbook,theworldwasreactingtotheunwanted COVID-19pandemic.Nowthatthefinalpagesarefinished,thefourthpeakof thispandemicisspreadingallovertheworldandaffectingmanypeople.Ithas beenacauseofgreatsorrowwitnessinginnocentpeopleperishingunexpectedly becauseofthisvirus.Iwishthosewhohavelosttheirlivesabeatifyingandblessed soul.Isincerelybelievethat,withtheaidofscience,humankindwillcompletely eliminatethispandemicfromthefaceoftheEarth.
Inmodernsocietiestoday,considerableattentionhasbeenpaidtothedevelopmentandanalysisofmagneticmaterials.Magneticferritesareamongthemost importantmaterialsandplayimportantrolesinmanyapplications,including microwave-absorbingmedia,high-densityrecordingmagnets,bioscience,telecommunicationdevices,magnetoelectricsensors,electromagneticnoisesuppressors, exchange-springmagnets,permanentmagnets,photocatalysts,andmanycomponentsofmicrowavedevices.
Despitetherebeingmanypublishedbooksonthissubject,nodetailedbookhas beenintroducedthatdealsexclusivelywiththemagneticpropertiesofferritenanocomposites.Thosewhobecomeinterestedinthescienceofmagnetismusuallyhave quitedifferentprofessionalbackgrounds.Theymaybemetallurgists,physicists, electricalengineers,chemists,geologists,orceramists.Consequently,although eachnewindividualtothefieldhasadifferentviewofsuchfundamentalsasatomic theory,crystallography,electriccircuits,andcrystalchemistry,thisbookcoversall ofthesetopics.Furthermore,recentdevelopmentsinferritenanocompositesare reviewed.Themainhighlightsincludenewexperimentalapproachesandfindings relatedtothemechanismsofmagneticfeatureswithinferritenanocomposites.
Thebookcompriseseightchapters.Theirsequenceischosentogivereadersan insightintothebehaviorofmagneticferritenanocomposites. Chapter1 providesa quickreviewofmagnetismandrelatedphenomena.Theoriginofmagnetism,thedefinitionofmagneticparameters,andimportantequationsareintroduced.Theimportanceofdifferenttypesofferritessuchashexagonalferrites,spinelferrites,garnets, andorthoferriteswithindustriallyrelatedapplicationsisemphasized. Chapter2 discussesthesubjectoftechniquesforcharacterizingferrites.Thechapterprovides insightsintophaseidentificationandstructuralandthermalanalysisofferrites.Measurementapproachesforstaticanddynamicmagneticfeaturesandhigh-frequency permeability,permittivity,andreflectionlossarealsoreviewed. Chapter3 develops generalinformationaboutsubstitutedferrites.Structuralandmagneticfeaturesof differenttypesofhexagonalferrites,includingM,W,Y,U,X,andZtypes,spinel ferrite,ironoxides,andgarnetsarestudied.Theroleofsubstitutingcationson themagneticpropertiesofferritenanoparticles,bulks,andthinfilmsisevaluated. Chapter4 coversthemagnetoelectric(ME)componentsofferrite ferroelectric nanocompositesusedinfabricatingspintronicdevices,nanoscaleelectronics,sensors, informationstorage,andmagneticMRAMs.Also,differentferroelectricandmagnetic
ferriteswithvariousheterostructuralconfigurationsthataremostlyemployedtoprepareMEcomponentsareintroduced. Chapter5 dealswithexchange-springferrite nanocomposites.Nanostructureferritesdesignedwithspecificratiosofhard-to-soft magneticphaseareintroducedforenhancingmaximum-energyproducts.Therole ofeffectiveprocessingparameters,thenanocompositeconfigurationofsoftand hardphases,and(BH)max variationarealsostudied. Chapter6 isdevotedtoferrite carbonnanocompositeswithdifferentcompositionalandmorphologicalcharacteristicsusedinmicrowaveabsorptionmedia.Theroleofcarbonmaterialadditionsin balancingpermeabilityandpermittivityisinvestigatedinawidefrequencyrangeto reachthehighestreflectionlossvalues. Chapter7 startswiththebasicdefinitionof photocatalysts.Thephotocatalyticactivationoftypicalferritesisinvestigated,and theeffectofadsorbentdoseonthephotodegradationperformanceofdyesusingferrite isevaluated.Therolesofshapefactorsandeffectiveparametersinthecatalyticactivityofferritesarealsoevaluated. Chapter8 presentsvarioustechniquesforfabricating magneticferrites,suchasparticles,bulks,coatings,andfibers.
Thereferencesemployedcompriserelevantbooks,classicalpapers,reviewarticles,andconferenceproceedingsandareprovidedattheendofeachchapter.
Thisbookisanticipatedtobeusefulformaterialsscientists,physicists,electronicengineers,andchemistsinvolvedindevelopingandresearchinghighqualitymagneticferrites.Astheauthorofthisbook,Iamprivilegedtoacquaint readerswiththescientificaspectsofthesubjectwhilealsointroducingtheoutcome ofmymanyexperimentalandresearchendeavorspresentedinthisbook.Isincerely hopethecontributionwillassistreadersinproliferatingtheirknowledgeofferrites andrelatednanocomposites.
AcknowledgmentismadeofthesupportofProf.Q.Taghizadeh,presidentofthe MUT,forprovidinglaboratoryfacilitiesandfinancialsupport.Iwouldliketo expressmygratitudetoEng.MohammadRezaNasrIsfahaniandEng.Behnoush Alirezaeiforspendingconsiderabletimeprocuringtherequiredpermissionsand revisingthephotographsanddiagrams.Theirthoughtfuleffortssignificantly reducedtheburdenofpreparingthefinalversionofthisbook.IhavebenefitedenormouslyfromtheassistanceofDr.TahminehSodaeeinprovidingusefulinformation aboutthephotocatalyticperformanceandsynthesizingtechniquesofferrites. Dr.SamiraSamanifarprovidedliteratureaboutFORC,andDr.AliRostamnejadi helpedtointerpretmagneticsusceptibility.IalsowouldliketothankDr.AmirHosseinMontazerforhiscriticalcommentsandconstructivesuggestionsonpartsofthe book.Further,Iowemycolleaguesadeepdebtofgratitude;inparticular,Dr.EbrahimPaimozdandDr.GholamrezaGordaniforprovidingafriendlylaboratoryenvironmentandassistanceinpurchasingtherawmaterialsneededoverthecourseofthe experiment.IthankDr.ArkomKaewrawang,Prof.VladimirSepelak,andProf. AndreaPaesanoJr.fortheircontributionsinoriginalresearchworksthatbecame thebasesofmyexperimentalsetups.IacknowledgeSimonHolt,JohnLeonard, andNirmalaArumugamfortheirpatienceduringthecourseofwritingthisbook. IamverygratefultothelateProf.ArdeshirHosseinpour,whoinitiallyencouraged metopursuemyinterestinthefieldofmagneticferrites.Itisapleasuretoexpress
mydeepappreciationtoallindividualswhohelpedmepromotemyknowledgeof magneticferrites,especiallyProf.AkimitsuMorisakoandProf.XiaoxiLiu.Iam alsoobligedtothemanypublishersandindividualswhohavegivenmepermission toreproducetheirfiguresandtables.Lastbutbynomeansleast,Iwouldliketo thankElsevierfortheirencouragementandsteadycollaboration.
AliGhasemi ShahinShahr,Isfahan
May2021
Thispageintentionallyleftblank
Fundamentalsofferrites 1
1.1 Introduction
Thischapterexplainstheprinciplesofmagneticphenomenaandrelatedtheoriesto provideabackgroundforthosewithlimitedfamiliaritywithmagnetismandrelated effects.Magneticmaterialsofvariousnatures,includingmetallic,ceramic,andcomposite,encompassmanycategoriesandapplications.Metallicspecimenssuchas SmCo,NdFeB,FePt,andTbFeCohaveanimportantroleindevelopinghardmagneticfeatures.Softmetallicmagnetssuchasironcobalt,mu-metal,permalloy,and superalloyhaveapplicationsinshieldingenvironmentsandrecordingheads.The mostimportantmagneticceramicsaretheferritesusedincommunicationandelectronicengineeringfields.Ferritesareusuallyknownasferrimagneticoxides.Ferritesareelectricallyinsulatingandexhibitlowlosswithinhigh-frequencyfields, makingthemappropriatecandidatesforcommunicationandmicrowavedevices. Thecrystalstructureofferritecontainsaninterlockingnetworkofpositively chargedcationsandnegativelychargeddivalentoxygenanions.Thesiteoccupancy ofionsandthecrystalstructureofferriteplayanimportantroleindeterminingmagneticfeatures.Largevarietiesofferritesindifferentconfigurationsarefabricatedto beemployedinmanynewtechnologieswithvariousrequirements.Thefrequency applicationsofferritesatwhichanyelectronicdevicecanfunctionrangefrom DCtomicrowave.
1.2 Briefhistoryofmagnets
LodestonerocksrichinFe3O4 ferritesaspermanentmagnetswereknownbypriests andpeoplein“Sumer,China,pre-ColumbianAmerica,andancientGreece.”The Chineseusedmagneticcompassessometimebefore2500BCE.Thefirstdevice basedonalodestonewasdevelopedbytheChineseandnameda“Southpointer” (Coey,2010).Inthe6thcenturyBCE,TheGreekphilosopherThalescarriedout theearliestobservationofmagnetismforwhichalodestoneormagnetiteattracted iron.Thefirstmanufacturedmagnetswerefabricatedbyrubbingironneedleson magnetitetoformtheessentialpartsofacompass(Goldman,2006).In1064,Zheng Gongliangcarriedoutthermoremanentmagnetizationthroughspecialheat
MagneticFerritesandRelatedNanocomposites. https://doi.org/10.1016/B978-0-12-824014-4.00009-3 Copyright © 2022ElsevierLtd.Allrightsreserved.
treatmentofiron.ShenKuainventedthenavigationcompassin1088.TheperpetuummobilewasdescribedbyPetrusPeregrinusinthefirstEuropeantextonmagnetism(Coey,2010).WilliamGilbertfoundthatmeltedandforgedsteelbarscooled underthemagneticfieldoftheearthcontainmagneticfeatures.Hepublishedthe firstsystematicexperimentalstudyonmagnetismin1600.HefoundthattheEarth isthegreatestmagnetintheworldandidentifieditasthesourceofthemagneticfield thataffectsthecompassneedleanddeterminesthedirectionofnavigationsystems (O ¨ zguretal.,2009a).
ThehorseshoemagnetwasinventedbyDanielBernoulliin1743.In1819, Oerstedfoundthatawirecarryingcurrentcoulddeflectacompassneedle,representingakindofcorrelationbetweenmagnetismandelectricity.Then,inParis, Andre-MarieAmpereandDominique-FrancoisAragowoundwireintoacoiland demonstratedthatamagneticfieldcouldbegeneratedbyapplyingcurrenttothe coil(Coey,2010).
WilliamSturgeonintroducedtheiron-coreelectromagnetin1824,which wasmoreeffectivethanaweakpermanentmagnetinelectricmotorsand generators.MichaelFaradaydiscoveredelectromagneticinductionin1821and themagneto-opticeffectin1845.Thepreviousexperimentalinvestigationinspired JamesClerkMaxwelltoformulatethetheoryofelectricityandmagnetismin1864 (Coey,2010).
ThefirsthysteresisloopwasplottedbyWarburgforanironmagnetin1880.
Curiefoundthetransitiontemperaturefromferromagnetismtoparamagnetism (Curielaw)in1895.Thetheoryofdiamagnetismandparamagnetismwasdiscussed byLangevinin1905(Ozguretal.,2009a).
ThetheoryofferromagnetismwasproposedbyPierre-ErnestWeissin1907to describethetransitiontemperature(Curietemperature)(Ozguretal.,2009a).
Regardingmagneticmaterials,itiswellknownthatcarbonsteelwasthefirst importantpermanentmagnetduring1820 1900.The1920swasthebeginningof quantummechanicsandthephysicsofmagnetism,whichwereusedforadeeper explanationofmagneticphenomena.Atthebeginningofthe20thcentury,thedevelopmentofpermanentmagnetsrapidlygrewbyaddingothermagneticornonmagneticelementssuchasMn,Co,W,Al,andNiintothecompositionwhile controllingprocessingconditions,especiallythequenchingstepsoftheheattreatmentprocess.During1900 1935,theAlnicowasdeveloped.Ferritepermanent magnetswereintroducedinthe1930sandusedinloudspeakersandlaterformotors inportableappliances.Substitutingvariouscationsinferritesandmakingnewnanocompositesarestillrapidlyexpandingareas.Thefirstrareearthcobaltpermanent magnetwasfabricatedinthe1960s,andtheNdFeBhardmagnetwasdeveloped inthe1980s(Goldman,2006; Ozgu ¨ retal.,2009a).Novelachievementsinpermanentmagnets,magneticrecording,andhigh-frequencymaterialshavemadeprogressintelecommunications,computerscience,andmicrowavesystems.Inrecent decades,theimpactofnanomagnetismandspinelectronicsinmodernelectronics hasbeenconsiderable.
1.3 Basicscienceofmagnetism
Inthissection,someimportantmagneticparametersandwell-knownlaws describingmagneticphenomenaareexplained.
1.3.1
Originofmagnetism
Accordingtothebasicscienceofatomicconfiguration,atomicmagneticmoment originatesfromtheorbitalmotionoftheelectronaroundthenucleusandthespin motionoftheelectronarounditsownaxis.Considerasimplemodelofanatom inwhichtheelectronmovesinacircularloopwithradius r andangularvelocity of u.Thetotalmagneticmomentproducedbycircularandspinmotionsis
where m and e arethemassandelectricchargeofasingleelectron,respectively (e/m ¼ 1.76 1011 C/kg), m0 isthemagneticpermeabilityoffreespace (m0 ¼ 4p 10 7 H/m),and P denotestheangularmomentumofthecircularmotion. Thefactorof g iscalled“gyromagneticratio”orsimply g factor,whichis1and2for orbitalandspinmotions,respectively.Theunitoforbitalmagneticmomentandspin magneticmomentistheBohrmagneton(Chikazumi & Graham,2009).
Notethatinmagneticceramicssuchasferrites,thecrystallinefield(electric field)resultingfromthesurroundingionswouldcausethequenchingoforbital moments,inwhichcasetheorbitalmomentofelectronsisfarsmallerthanspin moments(Smit,1959,pp.278 280).
1.3.2 CoulombandLorentzforces
Considertwomagneticpoleswithdistance r inmeter,aswellasstrengthsof m1 (weber)and m2 (weber).Theforceexertedinnewtonsfromonepoletotheother, knownastheCoulombforce,isgivenby
Theforceonthemagneticpolecanalsobeimposedbyemployinganelectric current.Forexample,byconsideringaninfinitelylongcoilorsolenoidcarryinga currentof I,theuniformmagneticfieldisgeneratedanddefinedby
where N denotesthenumberofturnsperunitlength(alongtheaxis)ofthesolenoid (Chikazumi & Graham,2009; Morrish,2001).
Ontheotherhand,byconsideringaparticlewithchargeqmovingwithavelocity of v andsubjectedtomagneticandelectricfieldsof B and E,theLorentzforceof f ¼ q(E þ v B)canbedefined.Cyclotronsandotherparticleaccelerators,cathode raytubetelevisions,andgeneratorsarebasedontheLorentzforceequation.
1.3.3 Definitionoffundamentalmagneticparameters
Whenamagneticfield(H)isappliedtoamaterial,theresponseofmaterialsiscalled magneticinduction(B),whichheavilydependsonthenatureofthespecimen.The relationof B and H definesthepropertiesandstatementsofmagneticmaterialtypes. Infreespaceandsomelimitedmaterials,therelationislinear,whileinmanycases, itisverycomplicatedandnotevensingle-valuedinsomemagnets.Animportant parameterthatcanbeextractedfromtherelationofmagneticinductionwithamagneticfieldispermeability,whichcanberepresentedasfollows:
Permeabilityindicateshowpermeablethematerialistothemagneticfield.The relationofmagneticinductionwithmagneticfieldisexpressedinthefollowing:
where m0 isthe B/H ratiomeasuredinavacuum,and M isthemagnetizationofthe material.Incgsunits,thepermeabilityoffreespaceisunityandsodoesnotappear intheequation(Cullity & Graham,2011; Spaldin,2010).
Magnetizationisaveryimportantparameterofmagneticmaterials.Magnetizationstronglydependsonboththeindividualmagneticmomentsoftheconstituent ions,atoms,ormoleculesandthetypeandstrengthofinteractionofmagneticmomentswitheachotherinamedium.Ingeneral,magnetizationisdefinedasthemagneticmoment(m)pervolumeunit(V):
Magneticpolarization(J)indicatestheintensityofmagnetizationandisgivenby
Thepolestrengthfortheareaunitperpendicularto M isfoundbythefollowing:
where n istheunitvectornormaltothesurfaceand s isthepolestrengthperunitof area.
Themagnetization-to-magneticfieldratioiscalledmagneticsusceptibilityand reflectshowresponsiveamaterialistoanappliedmagneticfield.Thesusceptibility equationinbothunitsisexpressedby
TherelationsbetweenpermeabilityandsusceptibilityinSIandcgssystemsare givenby(Cullity & Graham,2011; Morrish,2001)
Themagneticflux F isdefinedasthefluxofmagneticinductionthroughasurfacearea A;thatis,
where n istheunitnormal.Alargeamountoffluxdensityinmaterialsreflectsthe highpermeabilityvalueofthemedium(Morrish,2001).
Theunitsofmagneticinduction,magneticfield,magnetization,magneticpolarization,permeability,susceptibility,andmagneticflux,alongwiththeconversion factors,aresummarizedin Table1.1
1.3.4 Ampe ` re’slaw
Andre-MarieAmpe ` rediscoveredanimportantlawin1826whichrelatesthemagneticfieldalongaclosedloopinwhichcurrent I carriedthroughtheloop.The lawisasfollows:
where j representsthecurrentdensity.Ampe ` re’slawcanbeemployedforcalculatingthemagneticfieldofcurrentdistributionswithahighdegreeofsymmetry. Ingeneral,usingthislaw,themagneticfieldgeneratedbythecurrentcanbecalculatedfordifferentgeometries,suchasstraightlinesandcoaxialcable.Notethatthe currentshouldbesteadyandnotchangewithtime,andonlycurrentscarryingacross thepathsectionareconsideredforfindingthemagneticfield(Morrish,2001; O’handley,2000).
Table1.1 TherelationshipbetweensomemagneticparametersincgsandSI units.
Magneticinduction(B)GT10 4
Appliedfield(H)OeA/m103 4p
Magnetization(M)emu/cm3 A/m103
Magnetization(4pM)GA/m103 4p
Magneticpolarization(J)emu/cm3 T4p 10 4
Permeability(m)DimensionlessH/m4p 10 7
Susceptibility(c)emu/cm3 Dimensionless4p
Magneticflux(F)maxwell(Mx), G.cm2 weber(Wb),volt. second(V.s) 10 8
where, A,Ampere; emu,electromagneticunit; G,Gauss; H,Henry; J,Joule; Oe,Oersted; T,Tesla; Wb, Weber.
1.3.5 Faraday’slaw
In1831,MichaelFaradaydiscoveredthattime-varyingmagneticfieldscould generateanelectricfield.Thefollowingequationwasobtainedexperimentally:
where A isasurfacewhichhasthecircuitasitsboundary, n denotesthenormalvector,and E representstheelectrostaticfield.Thephenomenonisknownaselectromagneticinduction.Hedemonstratedthattheelectromagneticforce(emf) ε inducedinacoilisproportionaltothenegativerateofchangesinthemagneticflux:
Foracoilconsistingof N loops,theemfisgivenby(Morrish,2001; O’handley, 2000)
1.3.6 Lenz’slaw
Lenz’slawdeterminesthedirectionofaninducedcurrent.Theinducedcurrentgeneratesmagneticfieldsthattendtoopposevariationsinmagneticfluxwiththefields imposingsuchcurrents.Consideraconductingloopplacedinauniformmagnetic field,withthepositivedirectionofthenormalvectordefined.Then,byfinding therateoffluxchange d F=dt throughdifferentiation,threepossibilitiescanbedetermined.If d F=dt ispositive,then ε < 0;ifitisnegative,theinducedemfispositive; finally,considering d F=dt ¼ 0, ε ¼ 0.Theright-handruleisusedtodeterminethe directionoftheinducedcurrent.Bypointingthethumbinthedirectionofthearea vectorandcurlingthefingersaroundtheclosedloop,theinducedcurrentflowsinthe samedirectionasthedirectionoffingerscurlbyconsideringpositiveinducedemf, whileitistheoppositedirectionif ε < 0(Cullity & Graham,2011; Morrish,2001).
1.3.7 Maxwell’sequations
InresponsetotheexperimentscarriedoutbyAmpereandFaraday,Maxwelldevelopedthefollowingequations:
where V$ and V arevectoroperatorsofdivergenceandcurl,respectively. E isthe electricalfield, D showsthedisplacementvector, j denotesthecurrentdensity, r representstheelectricchargevolumedensity,and t istime.Thedisplacementvectoris relatedtotheelectricalfieldbythefollowingequation:
where ε0 isthepermittivityoffreespace(ε0 ¼ 8.85 10 12 Fm 1), P denotesthe polarizationofelectricdipoleperunitvolume,and ε isthedielectricconstant (Morrish,2001).
1.4 Classesofmagneticmaterials
Allmaterialscanbeclassifiedintermsoftheirmagneticsusceptibilityintofivemajorgroups(O’handley,2000):
1. diamagnetism
2. paramagnetism
3. ferromagnetism
4. antiferromagnetism
5. ferrimagnetism
1.4.1 Diamagnetism
MichaelFaradaydiscoveredthediamagneticnatureinSeptember1845.Diamagnetismistheweakestformofmagnetism.Thismagnetismisrelatedtotheorbitalrotationofelectronsaroundthenucleiinducedelectromagneticallywithinanexternal magneticfield.Indiamagneticsubstances,applyinganexternalmagneticfieldinducesamagneticmomentthatopposestheexternalmagneticfieldcausingit; thus,anegativemagnetizationisproducedwherethesusceptibilityofadiamagnetic materialisnegativeandveryweak(Chikazumi & Graham,2009).Thesusceptibility indiamagneticmaterialsistemperatureindependent.Superconductorsareanideal typeofdiamagnetsthathavegreatapplicationsinmodernindustries.Byapplyingan externalmagneticfield,dependingonfieldstrengthandworkingtemperature,superconductorsexpelthefieldlinesfromtheirinteriors.Allnoblegases,bismuth,and pyrolyticgraphitearediamagnets.
1.4.2 Paramagnetism
Inmanycases,paramagneticmaterialscontainmagneticatomsorionswithamagneticmomentduetounpairedelectronsinpartiallyfilledorbitals.Thespinsareisolatedfromtheirsurroundingenvironmentandcansomehowfreelyaligninthe directionoftheappliedfield.Theinteractionbetweenmagneticmomentsisvery weak,andtheorderofmagnitudeofmagneticsusceptibilityis10 3 to10 5 .
Inparamagneticmaterialsatfinitetemperatures,thespinsareagitated,andthermalenergycausesmisalignmentofspins.Withanelevationoftemperature,thethermalagitationwillincrease,causingvibrationinatomicmagneticmomentsthat reducessusceptibility.ThisbehaviorisdescribedbytheCurielaw,inwhichsusceptibilityhasanoppositetrendtotemperature.TheCurielawisgivenby(Cullity & Graham,2011)
where T istheabsolutetemperatureand C isamaterialconstantcalledtheCurie’s constant.Laterexperimentsdemonstratedthatthesusceptibilityofsomematerialsis fittedbyCurie Weisslaw:
where w isaconstant.Inthisequation, w canbepositive,negative,orzero.Clearly, when w ¼ 0,thentheCurie WeisslawequatestotheCurielaw.When w isnonzero, thenthereisaninteractionbetweenmagneticmomentsofneighboringatoms,and thematerialsareonlyparamagneticaboveacertaintransitiontemperature.If w is positive,thenthematerialisferromagneticbelowthetransitiontemperaturewhere thevalueof w correspondstothetransitiontemperature(Curietemperature, TC).If w isnegative,thenthematerialisantiferromagneticbelowthetransitiontemperature (Ne ´ eltemperature, TN),thoughthevalueof w doesnotrelateto TN.Notethatthis equationisonlyvalidwhenthematerialisinaparamagneticstate.Itisnotvalid formanymetalsastheelectronscontributingtothemagneticmomentarenotlocalized.However,thelawdoesapplytosomemetals,e.g.,rareearth,wherethe4felectronsthatcreatethemagneticmomentarecloselybound(Chikazumi & Graham, 2009).
Dependingonthestrengthanddirectionoftheexternalmagneticfield,partial alignmentoftheatomicmagneticmomentsoccurs,resultinginanetpositive magnetizationandpositivesusceptibility.Afterapplyingamagneticfieldtoaparamagneticsystemwithnointeractionbetweenatomicmagneticmoments,thepotentialenergy UH isgivenby
where q istheanglebetweenthedirectionofappliedfield H andatomicmagnetic moment m.Byconsideringcosq ¼ 1andmagneticfieldstrengthof106 A/m,the magnitudeofenergyisontheorderof10 23 J.Theorderofmagnitudeofthermal energykBT, wherekB isBoltzmannconstantatroomtemperature,is4.1 10 21 J. Whenthetwoenergiesarecompared,thethermalenergyislargerbyfactorsof102 to103 comparedwiththepotentialenergyofthemagneticfield(Chikazumi & Graham,2009).Thisindicatesthatatroomtemperatureforanoninteractingparamagneticsystem,thethermalenergycausesrandomfluctuationofmagneticmoments andprovidesveryweakmagnetization.Forreachingsaturationinpractice,thetemperaturemustbeverylowforfreezingthespins,whiletheintensityofthemagnetic fieldshouldbeveryhigh.
Paramagneticmaterialsobeyfromimportanttheories,includingLangevinand Paulimodels.TheLangevinmodel,whichistrueformaterialswithnoninteracting
c ¼ C =T (1.23)
c ¼ C =ðT wÞ (1.24)
UH ¼ mH cos q
(1.25)
localizedelectrons,statesthateveryatomhasamagneticmomentthatisrandomly orientedasaresultofthermalagitation.Byconsidering N atomicmomentsperunit volume,themagnetizationcanbecalculatedbasedontheLangevintheory.Inthis case,let nðqÞd q denotethenumberofatomicmomentsintheunitvolumeproviding ananglebetween q and q þ d q withthedirectionoftheappliedfield,whichisproportionaltothesolidangle2psinqd q andBoltzmannfactor expððmH cosqÞkB T Þ accordingtothefollowing:
where n0 isaproportionalityfactordeterminedbyconsideringthatthetotaldensity ofatomicmomentis N
Theintensityofmagnetizationisexpressedby
Bycombiningtheaboveequations,onecanreach
Bysetting mH =kB T ¼ a andcosq ¼ x,thefollowingexpressionisobtained:
ThefunctionintheparenthesesistheLangevinfunction, L(a).For a << 1,the Langevinfunctioncanbeexpandedas
Consideringthefirsttermintheaboveequation,theintensityofmagnetization canbesimplifiedto
Themagneticsusceptibilitycanalsobedeterminedbythefollowing:
