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1、Chapter8MagneticResonance9.1Electronparamagneticresonance9.2Ferromagneticresonance9.3Nuclearmagneticresonance9.4OtherresonancemethodsTCDMarch20071Aresonanceexperimentinvolvesaspecimenplacedinauniformmagnetic?eldB0B0andapplyinganACmagnetic2b1cos!t?eldintheperpendiculardi
2、rection2b1cos!tB02b1cos!tAmagneticresonanceexperimentTCDMarch20072LarmorfrequencyBm="lmμ!=mxB0!=dl/dtdm/dt=-"mxB0!=!m=xμ"BB0NB.Theelectronprecessescounterclockwisebecauseofthenegativecharge,"isSolutionism(t)=m(sin#cos!Lt,sin#sin!Lt,cos#)where!L="B0negative.eBTorque!caus
3、eμtoprecessaboutBwiththeLarmorfrequency#=meMagneticmomentprecessesattheLarmorprecessionfrequencyfL="B0/2"TheLarmorprecessionishalfthecyclotronfrequencyfororbitalmoment,but"=-e/2meequaltoitforspinmoment."=-e/meTCDMarch20073Analternating?eldalongthex-axiscanbedecomposedin
4、totwocounter-rotating?elds.b=2b1cos!tyb=b1[exp!t+exp-!t]-!tx!tTCDMarch20074m="hSHZ=-"!B0SzEi=-"!B0MSMS=S,S-1,…S=1/2MS10-1Zeeman-splitenegylevelsforanelectronicsystemwithS=1Splittingis"!B0;!="B0TCDMarch20075WhydoestheAC?eldhavetobeappliedperpendiculartoB0?H=-"!(B0Sz+2b1S
5、x)Ifthe?eldisappliedinthez-direction,theHamiltonianisdiagonalsothereisnomixingofdifferentMsstatesHowever,Sxhasnonzerooff-diagonalelements(n,n±1).Thesecondtermmixesstateswith$MS=±1.Electronicenergylevels;ElectronicParamagneticResonance(EPR)GHzrangeNuclearenergylevels;Nuc
6、learMagneticLevels(NMR)MHzrangeFerromagneticmomentprecessionFerromagneticResonance(FMR)GHzrangeTCDMarch20076TCDMarch200779.1Electronparamagneticresonance(EPR)Larmorprecessionfrequencyforelectronspinis2%fL=!L=(ge/2m)B0f=28.02GHzT-1.LTCDMarch20078Microwavecavitydeliversb1
7、inaTM100mode.X-bandradiation,!9GHz,B0!300mT.Energysplittingof±1/2levelsis0.2K.PolarizationofthespinsystemisP=(n&-n')/(n&+n')=[1-exp(-gμBB0/kT)]/[1+exp(-gμBB0/kT])]!gμBB0/2kTAtRTin300mTthisisonly710-4.TCDMarch20079EPRlineshape.Fixfrequency!andamplitudeb1,scanmagnetic?eld
8、ataconstantrate.Absorptionlineismeasuredbymodulatingthe?eldB0withasmallac?eldandusinglockindetectionIntegrated
