高等固體物理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來(lái)源于電子的軌道運(yùn)動(dòng)任何物質(zhì)在外磁場(chǎng)作用下均應(yīng)有抗磁性效應(yīng)。但只有原子的電子殼層完全填滿了電子的物質(zhì)，抗磁性才表現(xiàn)出來(lái)，否則抗磁性被別的磁性掩蓋。如：惰性氣體；離子型固體；共價(jià)鍵的碳、硅、鍺、硫、磷等；大部分有機(jī)物質(zhì)；部分金屬：鉍、鉛、銅、銀等。(1)theLamorprecession(拉莫爾進(jìn)動(dòng)）(2)diamagnetismfromconductionelectronsofmetals金屬中自由電子在磁場(chǎng)方向的運(yùn)動(dòng)保持不變，而在垂直磁場(chǎng)的平面內(nèi)電子作圓周運(yùn)動(dòng)。此圓周運(yùn)動(dòng)產(chǎn)生的磁矩與外磁場(chǎng)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:

Theexcitationofamagnoncorrespondstothereversalofonespin?.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