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1、REVIEWSOFMODERNPHYSICS,VOLUME82,APRIL–JUNE2010AnomalousHalleffectNaotoNagaosaDepartmentofAppliedPhysics,UniversityofTokyo,Tokyo113-8656,JapanandCross-CorrelatedMaterialsResearchGroup(CMRG),andCorrelatedElectronResearchGroup(CERG),ASI,RIKEN,Wako,351-0198Saitama,JapanJairoSinovaD
2、epartmentofPhysics,TexasA&MUniversity,CollegeStation,Texas77843-4242,USAandInstituteofPhysicsASCR,Cukrovarnická10,16253Praha6,CzechRepublicShigekiOnodaCondensedMatterTheoryLaboratory,ASI,RIKEN,Wako,351-0198Saitama,JapanA.H.MacDonaldDepartmentofPhysics,UniversityofTexasatAustin,
3、Austin,Texas78712-1081,USAN.P.OngDepartmentofPhysics,PrincetonUniversity,Princeton,NewJersey08544,USAPublished13May2010TheanomalousHalleffectAHEoccursinsolidswithbrokentime-reversalsymmetry,typicallyinaferromagneticphase,asaconsequenceofspin-orbitcoupling.Experimentalandthe
4、oreticalstudiesoftheAHEarereviewed,focusingonrecentdevelopmentsthathaveprovidedamorecompleteframeworkforunderstandingthissubtlephenomenonandhave,inmanyinstances,replacedcontroversybyclarity.Synergybetweenexperimentalandtheoreticalworks,bothplayingacrucialrole,hasbeenatthehearto
5、ftheseadvances.Onthetheoreticalfront,theadoptionoftheBerry-phaseconceptshasestablishedalinkbetweentheAHEandthetopologicalnatureoftheHallcurrents.Ontheexperimentalfront,newexperimentalstudiesoftheAHEintransitionmetals,transition-metaloxides,spinels,pyrochlores,andmetallicdilutem
6、agneticsemiconductorshaveestablishedsystematictrends.Thesetwodevelopments,inconcertwithÞrst-principleselectronicstructurecalculations,stronglyfavorthedominanceofanintrinsicBerry-phase-relatedAHEmechanisminmetallicferromagnetswithmoderateconductivity.TheintrinsicAHEcanbeexpresse
7、dintermsoftheBerry-phasecurvaturesanditisthereforeanintrinsicquantum-mechanicalpropertyofaperfectcrystal.Anextrinsicmechanism,skewscatteringfromdisorder,tendstodominatetheAHEinhighlyconductiveferromagnets.ThefullmodernsemiclassicaltreatmentoftheAHEisreviewedwhichincorporatesana
8、nomalouscontributiontowave-packetgroupvelocityduetomom
