Comment on Magnetization Process of Single Molecule Magnets at Low Temperatures

shorttimes,∆M(t)=|M(t)−M(0)|followstheusualtshort-timerelaxationisexpectedwhenthe

dipolarinteractiondominatesoverthehyperfinecou-pling,ie.,whenthespreadofdipolarfieldbiasWDwhereξoistherangeofenergiesoverwhichthenuclear≫ξo,biasfluctuates[2](inacompletelydemagnetizedsam-pleWDisseveraltimeslargerthanthestrengthEDofnearest-neighbourdipolarinteractions).Itshouldpersistatleastuntilt∼(WD/ξo)τo,whereτoisamicroscopicsinglemoleculetunnelingrelaxationtime.Intheveryshorttimelimittherelaxationislinearint.Sincethesepredictionsalldependedonthelong-rangepartofthedipolarinteraction,theyshouldnotdependonlatticestructure.

Toshowthis,weperformMCsimulationsforBCC,FCCandtricliniclatticeswithandwithoutperiodicboundaryconditions(P.B.C.).Att=0allspinsori-entationswererandomanduncorrelated,withM0andS󰀗(0)=

i=±zˆ(|zˆ|=1).Thedipolarinteraction

VD(󰀗rij)=ED[S

󰀗iS󰀗j−3(S󰀗i󰀗rij)(S󰀗j󰀗rij)/r23fieldsandspinconfigurationswereupdatedij]/rij,anddipoleattimein-tervalsδtbyflippingindividualspinswithprobability

1−exp{−δtτcoherentrelaxationN−1(ξ)exp(−ξ/T)}.Hereτrateτ−1−1N−1

(ξ)isanin-−|ξ|/ξo

(see[2]);putτN(ξ)=τ0e

weo=1andassumecontactwithabathattem-peratureT.Thetotalbiasenergyξ=ξdip−geµBSHz,includingtheinternaldipolarcontributionξdip.

InthecaseofBCCandFCCclusterswithP.B.C.,withdimensions16×16×16forED=10ξowe,asin[1],foundM(t)∼t∼0.7.However,wealsofoundthatintheFCCcluster(forexample)thenumberofspinsinresonance(|ξ|<∼ξo)isverysmall,muchsmallerthanforthecorrespondingSCcluster.ThismeansthatinsmallFCCclusters,theMCproceduremaynotaccumulateproperstatistics.

Tosolvethisproblemonecan(i)increasetheclustersize,or(ii)increasethefractionofspinsinresonance,byreducingED/ξo.ForaBCClattice(2moleculesperunitcell)weappliedthefirstscenario.ForaFCClattice(4moleculesperunitcell)weappliedboth,takingED=

1

2.5ξo.SinceinacompletelydemagnetizedFCCsample

WDThe∼10ED,thenWD/ξo∼25,ie.,forstilllarger>>samples1.

√results(Fig.1)areclear-onefinds

taresensitivetothecrystal

structure.

M(t)0.16(a) - cubic bccM(t)(b) - cubic fccED=10ξ0, Hz=50ξ00.25ED=2.5ξ0, Hz=25ξ00.12 T=10ξ0, ξ0=10.2 T=5ξ0, ξ0=10.080.150.10.040.050t is in units of τ0 0t is in units of τ0 0204060801000102030405060sqrt(t)sqrt(t)M(t)(c) - triclinic (Fe-8)0.05Hz=0.4 K, T=50 mK0.04 ξ0=6 mK0.030.020.01t is in units of τ00 020406080sqrt(t)FIG.1:M(t)vs

√

tslopeofthecurve;(b)FCClattice,ofsize32×32×32,

andP.B.C.(solidline),andofsize48×48×48,noP.B.C.(diamonds);and(c)Tricliniclatticeof603Fe−8molecules,with√

noP.B.C.(Diamonds-theMCresult;solidline-the