Comment on Magnetic Relaxations of Antiferromagnetic Nanoparticles in Magnetic Fields

We have carried out in ferritin the Field-Cooling method and data analysis proposed by Mamiya et al. (Phys. Rev. Lett. 88, 67202 (2002) at T = 5 K in order to check the time magnetic relaxation of these antiferromagnetic nanoparticles as a function of the

Commenton”MagneticRelaxationsofAntiferromagnetic

NanoparticlesinMagneticFields”

arXiv:cond-mat/0203088v1 [cond-mat.mes-hall] 5 Mar 2002E.delBarco,M.Duran,J.M.Hernandez,andJ.TejadaDepartamentodeF´ sicaFundamental,UniversidaddeBarcelona.Diagonal647,Barcelona,08028,SpainInarecentLetterMamiyaetal.presentedanewandelegantexperimentalproceduretocontroltheinitialField-CooledMagnetization,MFC,ofthemagneticrelaxationsofferritinunderstudy.Theyuseastep-by-stepcoolingfromT=35Ktotherelaxationexperimentaltemperature,T0=8-9K,whileamagnetic eld,H=H0T/T0,isappliedateachsteptoeliminatetime-andcoolingrate-dependencesofMFC.Fromthetemperaturebehaviorofthetimemagneticrelaxationcurves,recordedattemperaturesbetween8Kand9K,theyconcludedthatrelaxationinferritinisessentiallydominatedbyclassicalactivatedprocess.Moreover,theyanalyzedthe elddependenceofthemagneticviscosityextractedfromtheslopesoftherelaxationcurvesrecordedatdi erent nal elds,Hf=0,-H0.TheyfoundthatmagneticviscosityatT=8Kwasindependentof eld.Theauthors nallyconcludedthatmagneticrelaxationsofferritininmagnetic eldsaredominatedbyclassicalsuperparamagnetic uctuationsinthetemperatureregimewherethermallyassistedResonantSpinTunneling(RST)hasbeendiscussedinrecentyears.Letus rsttopointoutthatweagreewiththeinterpretationtheauthorsdooftheirresultsinthetemperaturerange8-9Kintermsofthermalactivatedrelaxation.However,itisofgreatimportancetoclarifythatthereisnotanypaper(fromthosecitedbyMamiyaetal.)inwhichactivatedquantumtunnelinghasbeenusedtoexplainrelaxationphenomenaof

ferritininthishightemperaturerange,T～8-9K.Frommagneticviscositymeasurements,Tejadaetal.reportedresonantquantumtunnelingatzero eldattemperaturesaround4-5K.Theseresultswerecon rmedbyLuisetal.bya.c.susceptibilitymeasurementsatlowtemperature.Itisclearthatadecreaseoftheviscositywithsmall eldsaroundtheblocking

We have carried out in ferritin the Field-Cooling method and data analysis proposed by Mamiya et al. (Phys. Rev. Lett. 88, 67202 (2002) at T = 5 K in order to check the time magnetic relaxation of these antiferromagnetic nanoparticles as a function of the

temperature,TB=8K,isduetothelargevariationofthenumberofunblockedmagneticmoments.Thesamephenomenawasobservedatlowertemperatureswithhigher elds[2],whereS(H)showsamaximumatagiven eldwhichdecreaseswhenthetemperatureincreases.Recently,newexperimentalresultsonmagneticrelaxationofferritincon rmbothpurequantumtunnelingbehaviorbetween0.1Kand～2Kandthermallyactivatedquantumtunnelingupto～5K[4],throughmagneticviscositymeasurementsintheabsenceofmagnetic eldsintherelaxationprocesses.

WehavealsousedboththeField-CoolingmethodanddataanalysisofMamiyaetal.

[1]tostudytimerelaxationinferritinatT=5K,whereRSTwasreported[2].WehaveusedFLUKAcommercialdilutedferritin.Wehavemeasuredtimemagneticrelaxationfromdi erentinitial elds,H0,totwo nal elds,Hf=0,-H0,fromH0=5OeuptoH0=800Oe.In gure1weshowthe elddependenceoftheratiobetweentheslopesoftherelaxationcurvesforHf=-H0andHf=0,normalizedwith1/2totakeintoaccountthedi erencebetweentheequilibriummagnetizations.Figure1isdividedintwozones:ForSHf= H0

SHf=0<1(whitezone),therelaxation

isfasteratzero eld,inagreementwithRSTinterpretation.Asonecanobservein gure1,atT=5K,zero eldrelaxationinferritinisbiggerthan eldrelaxationfor eldsbelow500Oe.Thebiggestdi erence(～80%)isobservedatH=5Oe,wheretheratiobetweenviscositiesisminimum,ingoodagreementwiththezero eldresonantwidth, Heff～5Oe,foundthroughLandau-ZenerrelaxationexperimentsbyDuranetal.[4].

We have carried out in ferritin the Field-Cooling method and data analysis proposed by Mamiya et al. (Phys. Rev. Lett. 88, 67202 (2002) at T = 5 K in order to check the time magnetic relaxation of these antiferromagnetic nanoparticles as a function of the

FIGURECAPTIONS

Figure1:Ratiobetweennon-zero- eldandzero- eldviscositiesasafunctionofthemagnetic eld,H0,recordedatT=5Kinferritin.

We have carried out in ferritin the Field-Cooling method and data analysis proposed by Mamiya et al. (Phys. Rev. Lett. 88, 67202 (2002) at T = 5 K in order to check the time magnetic relaxation of these antiferromagnetic nanoparticles as a function of the

REFERENCES

[1]H.Mamiya,I.Nakatani,andT.Furubayashi,Phys.Rev.Lett.88,67202(2002).

[2]J.Tejada,X.X.Zhang,E.delBarco,J.M.Hernandez,andE.M.Chudnovsky,Phys.Rev.Lett.79,1754(1997).

[3]F.Luis,E.delBarco,J.M.Hernandez,E.Remiro,J.Bartolom´e,andJ.Tejada,Phys.Rev.B59,11837(1997).

[4]M.Duran,E.delBarco,J.M.Hernandez,andJ.Tejada,Phys.Rev.B(inpress)(2002).

We have carried out in ferritin the Field-Cooling method and data analysis proposed by Mamiya et al. (Phys. Rev. Lett. 88, 67202 (2002) at T = 5 K in order to check the time magnetic relaxation of these antiferromagnetic nanoparticles as a function of the

Figure 1: del Barco et al.

1.2 1.1 1.0 1.0

Thermal relaxation

S(H=-H )/ S(H=0)

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 100 200 300 400 500 600 700 800

f

Resonant tunneling

f

0

T= 5K H0 (Oe)

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