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)(1−1GuozhuWeiCollegeofSciences,NortheasternUniversityShenyang,China110004InternationalCenterforMaterialPhysics,AcademiaSinicaShenyang,China110015guozhuwei02@sina.comQiZhangCollegeofSciences,NortheasternUniversityShenyang,China110004zhangqi0446@sina.comZihuaXinCollegeofSciences,NortheasternUniversityShenyang,China110004YaqiuLiangCollegeofSciences,NortheasternUniversityShenyang,China110004AbstractThemagneticpropertiesofthemixedferro-ferrimagneticcompoundswithCBAyxx)(1−,whereA,BandCarethreedifferentmagneticionsandformthreesublattices,arestudiedbyusingthestandardmean-fieldtheory.Thephasediagramisobtained,themagnetizationcurves,internalenergyandspecificheatarealsoinvestigated.Thisworkisrelatedtoexperimentalworkofmolecule-basedferro-ferrimagnetOzHCNCrMnNixx265.11])([)(⋅ΙΙΙΙΙ−ΙΙ.1.IntroductionInrecentyears,molecule-basedmagnetsarecurrentlyofconsiderableinterestbecauseoftheirspecialcharacteristicfeatures,suchaselectricalinsulate,lowdensity,transparency,highcriticaltemperature,andlow-temperaturefabrication.Importantadvanceshavebeenmadeinthesynthesisofnewmagnetsbasedonmoleculesasbuildingblocks.Molecule-basedmagnetspresentseveralattributesunavailableinconventionalmetal/intermetallicsandmetal-oxidemagnets.Severalfamiliesofmolecule-basedmagnetsaremadebymeansoforganicsyntheticmethodologiesthatarefrequentlyassociatedwiththedevelopmentofpharmaceuticals,ratherthanbymeansofthehigh-temperaturemetallurgicalmethodstypicallyusedtomakemagnets.Prussianblueanalogscompriseoneofthemoreattractiveclassesofmolecule-basedmagnets[1-4].Theircommonf.c.cstructureallowsustoeasilyunderstandthesuperexchangeinteractionsbetweentheneighboringmetalionsthroughthecyanidebridgingligands.Dependingonthetypesofmetalionsincorporated,Prussianblueanalogsshoweitherferromagnetism1ProjectsupportedbytheDoctorateFoundationoftheMinistryofEducation,China(GrantNo.20030145019).])([6CNCrCsNibecomesferromagnetbelow90K[5],])([6CNCrVisferrimagnetbelow315K[6].InPrussianblueanalogs,onlythesuperexchangeinteractionsbetweenthenearestneighboringmetalionshavetobeconsidered,thecontributionsfromthesecondnearestneighborsitescanbeneglectedduetotherelativelylongdistancesbetweenmetalions.Thusthetheoreticaltreatmentoftheirmagneticpropertiesismuchsimpler.Shin-ichiOhkoshiet.al.havesucceededindesignandpreparationofmolecule-basedferro-ferrimagnet])([)(65.11CNCrMnNixxΙΙΙΙΙ−ΙΙbasedonphenomenologicalmolecularfieldtheory[7]andforx=0.38acompensationtemperature,whichisapproximately39K,isfound.However,inRef.[7],therearesomemistakesinthecalculationbasedmolecularfieldtheory.Fromthetheoreticalpointofview,itisnecessitytorecalculate.Ontheotherhand,theIsingmodelhasbeenfrequentlyandsuccessfullyadoptedforthedescriptionandunderstandingofmanycharacteristicfeaturesofferrimagnets.InRef.[8-11],thestandardmeanfieldtheoryisusedtoinvestigatethemagneticproperties,inparticularthecompensationpoint,ofbinary-alloyIsingferrimagnets.Theseworksonlydealwithtwo-sublatticesystem.Theworksdealwiththree-sublatticesystemhavenotbeenreported.Inpresentwork,thestandardmeanfieldtheoryisusedtoinvestigatethemagneticpropertiesofmixedferro-ferrimagneticcompoundswithCBAyxx)(1−,whichdealwiththree-sublatticeIsingsystem.Theoutlineofthispaperisasfollows.Insection2,wepresenttheeffectivemodelHamiltonianandreviewtheformulationinthestandardmeanfieldofIsingsystemwithCBAyxx)(1−.Insection3,wepresentthenumericalresultsanddiscussions.Then,section4containstheconclusion.2.FormulationInIsingmixedferro-ferrimagneticcompoundswithCBAyxx)(1−,theydenotesthemolarratioof(A+B)toC,xisthemolefractionofAin(A+B),andmagneticionsAandBarerandomlyincorporatedinthef.c.c.lattice.Theinteraction(0ACJ)betweennearestneighboringmagneticionsAandCisferromagnetic,theinteraction(0BCJ)betweennearestneighboringmagneticionsBandCisantiferromagnetic,whiletheinteractionbetweenmagneticionsAandBisneglectedduetoCandeitherAorBarelinkedinanalternatingfashion[7].TheeffectivemodelHamiltonianofthesystemis∑∑++++−−=δδδδξξiizCiziBiBBCiizCiziAiAACSSJSSJH,,22,(1)wherethesummationisoverallnearest-neighborpairs,ziBziASS,andziCStake(12+AS),(12+BS)and(12+CS)valuesthatallowedforA,BandCions,respectively.Theoccupationnumbers1,0=αξi(BA,=α)dependingwhethertheithsiteisoccupiedbyanionoftypeαornot,andtheysatisfytherelations1=+iBiAξξ,xciA=ξandxciB−=1ξ,(2)wherecLdenotestherandomconfigurationaverage.Whenweusethestandardmean-fieldapproximation,themeaneffectivefieldsAE,BEandCEactingonthethreesublatticesitesaregivenby=zCACCAASJZE2,(3)=zCBCCBBSJZE2,(4)−+=zBBCBCzAACACCSJZxSJxZE)1(22,(5)whereKLZarethenumbersofthenearest-neighborK-siteionssurroundingaL-siteion.ThezAS,zBSandzCSarethethermallyaveragedvaluesofthespinoperatorofthreesublattices,andtheyaregivenby)(AAAAzASEFSSβ=,(6))(BBBBzBSEFSSβ=,(7))(CCCCzCSEFSSβ=,(8)where)/(1TkB=β,KSisthespinquantumnumberofionK,and)(xFKdenotestheBrillouinfunctionwhichistheoddfunctionofx,)21coth(21)212c