Muonium avoided level crossing measurement of electron spin relaxation rate in a series of substituted anthradithiophene based molecules

Muonium

avoided

level

crossing

measurement

of

electron

spin

relaxation

rate

in

a

series

of

substituted

anthradithiophene

based

molecules

S.

Han

a,b

,

K.

Wang

a,b

,

M.

Willis

a

,

L.

Nuccio

c

,

F.L.

Pratt

d

,

J.S.

Lord

d

,

K.J.

Thorley

e

,

J.

Anthony

e

,

A.J.

Drew

a,b,d

,

S.

Zhang

a,b

,

L.

Schulz

a,

*

a

SichuanUniversity,SchoolofPhysicalScienceandTechnology,Chengdu,Sichuan610064,China

b_{QueenMaryUniversityofLondon,MileEndRoad,LondonE14NS,UK}

c_{DepartmentofPhysicsandFribourgCentreforNanomaterials-Frimat,UniversityofFribourg,CheminduMusée3,CH-1700Fribourg,Switzerland} d

ISISMuonFacility,RutherfordAppletonLaboratory,STFC,HarwellScienceCampus,Chilton,DidcotOX11,UK

e

DepartmentofChemistry,UniversityofKentucky,Lexington,Kentucky40506-0055,USA

Muonspinspectroscopyandinparticulartheavoidedlevelcrossingtechniqueisintroduced,withthe aimofshowingitasaverysensitivelocalprobeforelectronspinrelaxationinorganicsemiconductors. Avoidedlevelcrossingdataontert-butyl-ethynylanthradithiophene,tri-methyl-silyl-ethynyl anthra-dithiopheneandtri-ethygermyl-ethynylanthradithiopheneatdifferenttemperaturesarepresented.This seriesofmoleculeshaveanidenticalanthradithiophenebackbone,butwehaveperformedatargeted substitutiononthecentralatomofthetwosidegroups,ofC,SiandGe.Weextractedtheelectronspin relaxationforthethreemoleculesofthisseriesanddiscusstheminthecontextofpreviouslypublished results.

1.Introduction

Organicsemiconductorsareextremelypromisingmaterialsfor spintronicsthankstotheirlongspincoherencetimes.However, spinphenomenainthesematerialsarenotyetfullyunderstood, partlyduetothelackofsuitablecharacterisationtechniques,since thoseextensivelyusedtocharacteriseinorganicsemiconductors arenotalwaysapplicabletoorganicmaterials[1–3].Muonspin relaxation(

m

SR)hasbeenproventobeanapplicableprobeinthis field,asitissensitivetospindynamicsinorganicsemiconductors onamolecularlengthscale[4–7].Inorganicsemiconductorsthe implantedmuonsformahydrogen-likesystem,calledmuonium, bycapturinganelectron.Inmuoniumthemuonandelectronspins are coupled through hyperfine interaction. As a consequence relaxationontheelectronspincaninducechangesinthemuon spin, which can be detected. By performing targeted chemical

substitutions, it is then possible to identify the underlying mechanismofelectronspinrelaxationintheseriesofmolecules, whichhasbeenamatterofdebateforsometime[5].

2.Muonspinrelaxationandavoidedlevelcrossing

In

m

SRexperiments,100%spinpolarisedmuonsareimplanted in thesample, and as partof its thermalisation process in the material, it takes part in a series of electron capture and loss processes,thermalising asan interstitial positivemuon oras a hydrogen-like species called muonium (Mu) [8–10]. Thislatter species can then chemically bind to an unsaturated organic molecule,inasimilarwaytohydrogenation,andisanextremely sensitiveprobeofspindynamicsintrinsictothemolecule[5–10].If anexternalmagneticfieldisappliedinthedirectionoftheinitial muonspin,asitisinsocalledlongitudinalfieldexperiments,the Hamiltonianformuoniumcanbewrittenas

H¼

g

mhIBþ

g

ehSBþhSAI (1)

where

g

_mand

g

earethemuonandelectrongyromagneticratios,B is the applied longitudinal field, I and S are the muons and

*Correspondingauthor.Tel.+8618180519891.

E-mailaddresses:sijie.zhang@scu.edu.cn(S. Zhang),lschulz@scu.edu.cn

(L. Schulz).

1

Published in 6\QWKHWLF0HWDOV±

which should be cited to refer to this work.

electronsspinsandAisthehyperfinetensor[10].Theenergylevels asafunctionoftheappliedmagneticfieldthatoriginatesfromthis Hamiltonianforanisotropichyperfineinteractionareshowninthe Breit–RabidiagraminFig.1(a).

At high enough fields the electron and muon spins are decoupled and the state of the system can be described by productsofpureZeemanstatesfortheelectronandmuon.Ata highfieldwhichdependsonthevalueofthehyperfinecoupling constant, two of thelevelsshouldcross,as canbeobserved in

Fig.1(b)(dashedlines).ForaHamiltonianH=H0+HIwhereHIcan betreatedasaperturbation(forexample,frominteractionswith nucleiorcross-relaxationeffects),thecorrectiontotheenergiesup tosecondorderisgivenby

EnE0n¼

C

njHIj

C

n D E þ

S

_mj

C

njH I j

C

n D E j2 E0 nE0m (2) whereE0nand

C

narethen-thzeroorderenergyandeigenstateand

thedenominatorbecomestinywhenthetwounperturbedlevels approach[9,10].Theeffectofthiscorrectiontotheenergylevelsis toavoid thecrossing(see Fig.1(b)).Close tothis avoidedlevel

crossing(ALC),thestatesarenolongerpureZeemanstates,but they are instead mixtures of states corresponding to different valuesofthemuonmagneticquantumnumber.Asaconsequencea lossofpolarisationofthemuoncanbeobserved[8,9].ALCscanbe classified by the change in total quantum number M. If the hyperfineinteractionisisotropic,themostcommonlyobserved ALCistheonewith

D

M=0,thatcorrespondstoamuon–nuclear spin flip–flop. However in solids the most intense crossing is

D

M=1,correspondingtoa muonspin flipandisobserved only whenanisotropyintheinteractionispresent.

D

M=2transitions exist,buttheyareusuallyveryweakandnarrow,andaregenerally not observed experimentally [10]. A simulation of the muon's polarisationthroughthisavoidedcrossing,fromhereonintermed anALCcurve,isshowninFig.1(c).Theshapeandpositionofthis ALCcurvedependsonthehyperfinecouplingconstants(insolids, both isotropic and anisotropic). However, the presence of an electronspinrelaxationrate(eSR)alsohasaneffectontheALC curve, as can be seen in Fig. 1(c). For low values of the eSR (_5MHz),theALCpositionwithrespecttothexaxis(magnetic field)andthegeneralALCshapedonotchangeasafunctionofthe eSR but the ALC amplitude (loss of polarisation) enormously increases.WehavemodelledtheeffectofeSRthroughadensity matrixformalism,definedas

r

ðtÞ¼1₄ 1þpðtÞ

s

þpeðtÞ

t

þ X j;k PjkðtÞ

s

j

_t

k 2 4 3 5 (3)

where _p(t),pe(t) and P jk(t) are the muon, electron and mixed polarisations,respectively.Thetimeevolutionof

r

(t)isdescribed bytheequation

ihd_dt

r

¼½H;

r

 (4)

fromwhichthetimedependentpolarisationscanbeobtained[11]. Thegeneral solutioncanonly bedeterminednumerically.If an electronspinrelaxationmechanismispresentin thesystem its effectcanbetakenintoaccountphenomenologicallyby introduc-ingextraterms

l

peand

l

Pjkinthedifferentialequationsforthe polarisationsobtainedfromEq.(4)[12]:

dpe dt ¼...

l

pe; dPjk dt ¼...

l

P jk ₍₅₎ 3.Experimentalmethod

Tert-butyl-ethynyl anthradithiophene (TBu-ADT), tri-methyl-silyl-ethynyl anthradithiophene (TMS-ADT) and tri-ethygermyl-ethynyl anthradithiophene (TGe-ADT) were synthesized and puri_fied according to a published procedure [13,14] and were purified by repeated recrystallisation from dichloromethane/ ethanol. The only change in the chemical structure is the substitutionofthecentralatomintheside-groupwithC,Siand a)

b)

c)

0.00 0.12 0.24 0.36

Longitudinal Magnetic Field (T)

Energy (a.u.)

0.18 0.24 0.30 0.36

Longitudinal Magnetic Field (T)

Energy (a.u.)

ω0

0.2 0.6

Longitudinal Magnetic Field (T)0.3 0.4 0.5 0.6 0.5 0.4 1.0 Polarisation 0.9 0.8 0.7 0.0 MHz 0.1 MHz 0.5 MHz 1.0 MHz increasing eSR

Fig.1.(a)ThemuoniumBreit–Rabidiagramwithahyperfinecouplingconstantof A=80MHz.(b)Zoom-inregionoftheenergylevelsneartheALC.(c)Simulated muonpolarizationforseveraldifferentvaluesofelectronspinrelaxationrate.

Fig.2.TheALCresonancesfor(a)TBu-ADT,(b)TMS-ADTand(c)TGe-ADTfor10Kand300K,withtheassociatedmodellingtoextracttheeSRandhyperfineconstants.The molecularstructureisshownintheinsetof(c).Hydrogenisomittedforclarity.Onlythecentralatomintheside-groupmodified(blue).(Forinterpretationofthereferencesto colourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

2

Ge.Theyeachshareacommonback-bone,whichisanumberof fused rings mainlycomprising carbon and hydrogen, with the exceptionbeingtheendrings,whichcontainS.Theirstructuresare shown in the inset of Fig. 2(c). Analogous to the previously publishedworkperformedonthesubstitutedtriethylsilylethynyl (TES) and metal hydroxyquinolate (Xq3) series [5], performing targeted chemical substitutions can in principle identify the underlyingelectronspinrelaxationmechanism.

MuonexperimentswereperformedattheHIFIspectrometerat ISIS,RutherfordAppletonLaboratory.About200mgofthethree materialswereplacedinanenvelope(17mm17mm)madeof 25

m

mthicksilverfoil(99.99%pure).Anotherlayerofsilverfoil wasplacedinfrontofthesampleasadegrader,toassurethatthe muonsstopinthesample.ThesoftwareWimda[15]wasusedto extractthetime-integrateddataandplottheALCsasafunctionof appliedfield. Apolynomialbackgroundwas subtractedandthe ALCs weresubsequentlymodelledusingthesoftwareQuantum, with the eSR modelled using the density matrix formalism describedintheprevioussection[16].TheALCcurvesimulations presented in thefollowing areperformed consideringa muon-electronsystem.Nonucleiaretakenintoaccountastheirinfluence wasdiscoveredtobenegligible[7].Furtherdetailsofthemodelling canbefoundelsewhere[5–7,16].

4.Resultsanddiscussion

Fig.2showstheALCsmeasuredforthethreesamplesat10K and 300K. In all of the samples, four individual ALCs were observed,althoughweanticipatetheretobesixpositionsonthe moleculethatthemuoniumcouldbondto.Therecouldbeseveral reasonsfortherebeingtwounobservedALCresonances.Itcouldbe thattheformationprobabilityforthesetwoissigni_ficantlysmaller thantheobservedresonances,whichmaysimplyberelatedtoit notbeingenergeticallyfavourabletobondthere.Thiswouldresult inasmallamplitude,resultinginapotentiallyunobservableALC resonance. The missing resonances could also have hyperfine couplingparametersthataresimilartooneormoreoftheothers, resultinginmorethanoneALCmergingoroverlapping.Finally, there couldbe additional ALCs at higher fields that are as-yet undiscovered.

AsisexpectedinthelimitofatemperaturedependenteSR,the lowtemperaturedatahaveroughlyallthesameamplitudes[5,10]. However,incontrasttothepreviouslypublishedresultsintheTES

andmetal Xq3series[5],theALCamplitude at300Kdoesnot followastrongtrendasthemassofthesubstituentisincreased. SincetheamplitudeoftheALCisstronglyrelatedtotheeSR,with theamplitudebeingroughly proportionaltoeSRbelow around 1MHz,thisfirstobservationofthespectrasuggeststhattheeSR either slightly falls as a function of increasing mass of the substituentoritremainsroughlythesame.Thisisnotindicativeof aspinorbitmediatedmechanismforeSR,aspreviouslyreportedin similarmolecules[5].GiventhecomplexityofthespectrainFig.2, itismoreinformativetomodeltheresonancestoextracttheeSR. TheextractedhyperfinecouplingconstantsandeSRvaluesfor10K and300KareshowninTable1.

Withthesame methodologyusedpreviously[5–7],wehave plottedtheaverageeSRextractedfromtheALCsintheADTseries asafunctionofatomicnumber,Z,ofthe

substitutedatom(C,SiandGe).Thisisshownintheinsetto

Fig.3a,whereitcanbeseenthatthereisverylittlechangeasa function of Z of the substituted atom, within the error of the measurement.ThisisinconsistentwiththeZdependenceofeSRin theXq3

andTESseries,whereasignificantriseisobservedastheatomic numberofthesubstituentatomisincreased,asaresultofthespin orbitinteractiondrivingeSR.Thisinconsistencyisrelativelyeasyto explain.Itisrelatedtothepositionofthesubstitutedatomonthe ADTmolecule(thesidegroup)inrelationtothelocationof the electronicwavefunction,whichwillbepredominantlylocatedon thebackboneofthemolecule,withverylittlespindensityonthe sidegroups.Todemonstratethisfurther,wehaveperformedDFT calculations of the highest occupied and lowest unoccupied molecularorbitals(HOMOandLUMO,respectively)oftheseries of molecules,using B3LYP/6-31G(d)withthe GAMESS software package [17], shown in Fig. 3(b)_–(d). We can come to two conclusions from these calculations. Firstly, there is very little differenceintheHOMOorLUMOinthethreemolecules.Secondly, hardlyanyspindensityexistsfromtheHOMOorLUMOontheside groups,and we wouldexpect thatthemuonium electron (ina singularlyoccupiedmolecularorbital)tobesimilar.Thissupports ourconclusionthatwewouldnotexpecttheretobemuchchange intheeSRasin thedifferentmolecules, eveniftheunderlying mechanismis fromthespinorbitinteraction. Inthepreviously reportedstudy,thesubstitutionwasonthebackboneoftheTES series and in the centre of the Xq3 series, so the electronic wavefunctionhadsignificantoverlapwiththesubstitutedatom.It

Table1

Simulationparametersforthethreesamples,TBu-ADT,TMS-ADTandTGe-ADT.Fistheweightingin%,andthehyperfinecouplingparameters(A:isotropic;D1/D2: anisotropic)andelectronspinrelaxationrate(eSR)aregiveninMHz.Errorsareestimatedfromthesensitivityofthesimulationonparameters,statisticalerrorbarsofthe data,andaccuracyofthebackgroundsubtraction.

10K 300K

ALC1 ALC2 ALC3 ALC4 ALC1 ALC2 ALC3 ALC4 TBu-ADT F 240.3 280.3 420.3 60.3 240.3 280.3 420.3 60.3 A 1071 1371 1611 2011 1071 1281 1541 2011 D1 40.1 80.1 100.1 50.1 40.1 60.1 90.1 70.1 D2 50.1 90.1 120.1 50.1 50.1 30.1 130.1 70.1 eSR 0.020 0.020 0.020 0.020 0.020.02 0.150.02 0.820.02 0.780.05 TMS-ADT F 180.3 250.3 500.3 70.3 180.3 250.3 500.3 70.3 A 1071 1391 1581 2011 1061 1321 1531 2051 D1 40.1 60.1 100.1 50.1 1061 1321 1531 2051 D2 40.1 60.1 90.1 50.1 1061 1321 1531 2051 eSR 0.020 0.020 0.020 0.020 0.450.03 0.150.02 0.500.02 0.900.02 TGe-ADT F 310.3 440.3 180.3 70.3 310.3 440.3 180.3 70.3 A 1331 1621 1801 2380.1 1301 1511 1781 2881 D1 70.1 110.1 90.1 100.1 60.1 90.1 70.1 80.1 D2 70.1 90.1 40.1 110.1 30.1 90.1 80.1 110.1 eSR 0.020 0.020 0.020 0.020 0.200.02 0.320.02 0.350.02 0.500.05 3

http://doc.rero.ch

is therefore more appropriate to plot this against the atomic numberoftheheaviestatomonthebackbone,inthiscaseS,as showninthemainpanelofFig.3(a).Thisfitsverynicelyonthe trend.

5.Conclusions

WehavereportedeSRmeasurementsonamolecularseriesbased onananthradithiophene,withtargetedchemicalsubstitutiononthe sidegroups.WefoundverylittlechangeintheaverageeSRasthe massofthesubstituentatomincreases,whichcanbeexplainedby theelectronicwavefunctionbeingmainlylocatedonthebackboneof themolecule,whichdoesnotundergoanychangesintheseries. Thereisthereforeverylittleelectronicwavefunctionoverlapwith thesubstitutedatomonthesidegroup,suchthatsubstitutingoneof theatomswithaheavierspeciesdoesnotsigni_ficantlyincreasethe spinorbitinteraction,whichhasbeenshowntobeaveryeffective mechanismofeSRinorganicmolecules[5].

Acknowledgements

AJDwouldliketoacknowledgefinancialsupportfromtheUK EngineeringandPhysicalSciencesResearchCouncil,grantnumber EP/G054568/1, the European Union Seventh Framework Pro-grammeprojectNMP3-SL-2011-263104‘HINTS’andtheEuropean Research Council project ‘Muon Spin Spectroscopy of Excited States(MuSES)’proposalnumber307593.SZandLSacknowledge financialsupportfromtheNationalScienceFoundationofChina, grantnumbers61307039and61404088.

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Fig.3.(a)TheaverageeSRoftheADTseriesplottedagainsttheatomicnumberoftheback-boneheaviestatom(Sulphur),whichshowsexcellentagreementwiththe previouslypublishedtrendintheaverageeSRoftwootherorganicsemiconductors[5].Inset:noZdependenceoftheaverageeSRisobservedwhenplottedagainstthe substitutedatomoftheADTseries.(b)–(d)TheHOMOandLUMOlevelsofthethreemoleculesintheseries.

4