高等固体物理su11

Chapter11:MagnetismDiamagnetismParamagnetismFerromagnetismAntiferromagnetismFerrimagnetismMagneticmomentSources:(1)spinmomentofelectron(2)orbitalmomentofelectron(3)nuclearmagneticmoment(verysmall)MagnetizationM

themagneticmomentperunitvolumeMagneticsusceptibility

Diamagnetism:small,negativeParamagnetism:small,positiveFerromagnetism:large,positiveAntiferromagnetism:small,positiveFerrimagnetism:large,positive,usuallysmallerthanthatofferromagnetismDiamagnetismLenz’slaw:whenthefluxthroughanelectricalcircuitischanged,aninducedcurrentissetupinsuchadirectionastoopposethefluxchange来源于电子的轨道运动任何物质在外磁场作用下均应有抗磁性效应。但只有原子的电子壳层完全填满了电子的物质，抗磁性才表现出来，否则抗磁性被别的磁性掩盖。如：惰性气体；离子型固体；共价键的碳、硅、锗、硫、磷等；大部分有机物质；部分金属：铋、铅、铜、银等。(1)theLamorprecession(拉莫尔进动）(2)diamagnetismfromconductionelectronsofmetals金属中自由电子在磁场方向的运动保持不变，而在垂直磁场的平面内电子作圆周运动。此圆周运动产生的磁矩与外磁场方向相反，具有抗磁性。Paramagnetism1.Atoms,molecules,andlatticedefectspossessinganoddnumberofelectrons.Examples:freesodiumatoms;NO;Fcentersinalkalihalides2.FreeatomsandionswithapartlyfilledinnershellMn2+,Gd3+,…3.Afewcompoundswithanevennumberofelectrons4.MetalsVanVleckTemperature-IndependentParamagnetismanatomicormolecularsystemwhichhasnomagneticmomentinthegroundstateParamagnetismofConductionElectrons

FerromagneticOrderSpontaneousmagneticmoment:Amagneticmomenteveninzeroappliedmagneticfield.Theelectronspinsandmagneticmomentsarearrangedinaregularmanner.CuriepointandtheexchangeintegralExchangefield:aninternalinteractiontendingtolineupthemagneticmomentsparalleltoeachother.CurietemperatureTc:T<Tc,ferromagneticT>Tc,paramagneticMeanFieldApproximation:exchangefield:BE=Mparamagneticphase:Curielaw:Curie-Weisslaw:Meanfieldconstant

:Foriron,Tcabout1000K,gabout2,andSabout1;about5000.

Ms

1700,BE

103TTemperaturedependenceofthesaturationmagnetizationMeanfieldapproximationMAGNONSMagnon:aquantizedspinwaveMagnondispersionrelationforversuskQuantizationofspinwaveThequantizationofspinwavesproceedsexactlyasforphotonsandphonons.Theenergyofamodeoffrequencykwithnkmagnonsisgiveby:

Theexcitationofamagnoncorrespondstothereversalofonespin½.ThermalexcitationofmagnonsInthermalequilibriumtheaveragevalueofthenumberofmagnonsexcitedinthemodekisgivenbythePlankdistribution:ThetotalnumberofmagnonsexcitedatTistheBlochT3/2lawexperimentallyconfirmedNEUTRONMAGNETICSCATTERINGAnx-rayphotonseesthespatialdistributionofelectroniccharge,whetherthechargedensityismagnetizedorunmagnetized.Aneutronseestwoaspectsofacrystal:thedistributionofnucleiandthedistributionofelectronicmagnetization.Diffractionofneutronsbyamagneticcrystalallowsthedeterminationofthedistribution,directionandorderofthemagneticmoments.FERRIMAGNETICORDERBA=-MA-MB;BB=-MA-MB

CuriepointandthesusceptibilityofferrimagnetsInthemeanfieldapproximationMAT=CA(Ba-MB);MBT=CB(Ba-MA)T>Tc,ANTIFERROMAGNETICORDERNeeltemperatureTNinthemeanfieldapproximation,TN=

CT>TN,Experimentalresult:

SusceptibilitybelowtheNeeltemperatureTwosituations:withtheappliedfieldperpendiculartotheaxisofspins;withthefieldparalleltotheaxisofthespinsAntiferromagneticmagnonsThedispersionrelationformagnonsinanantiferromagnetisquitedifferentfrommagnonsinaferromagnet.FERROMAGNETICDOMAINSActualspecimensarecomposedofsmallregionscalleddomains,withineachofwhichthelocalmagnetizationissaturated.alsoseeninantiferromagnetics,ferroelectrics,antiferroelectrics,ferroelastics,superconductors,metals.Inweakfieldsthevolumeofdomainsfavorablyorientedwithrespecttothefieldincreasesattheexpenseofunfavorablyorienteddomains;Instrongfieldsthedomainmagnetizationrotatestowardthedirectionofthefield.

coercivity:HcBr:theremanenceinductionBs:thesaturationinductionB---HorM----HB=

0(H+M)AnisotropyenergyMagnetocrystallineoranisotropyenergyTransitionregionbetweendomainsExchangeenergyWallenergy(anisotropyenergy)OriginofdomainslowerenergyExchangeenergyAnisotropyenergyMagne