1

Vacancy-drivennon-cubiclocalstructureandmagneticanisotropytailoringinFexO-Fe3-δO4nanocrystals

Alexandros Lappas,1,* Konstantinos Brintakis,1 George Antonaropoulos,1,2 MariannaVasilakaki,3 Kalliopi N. Trohidou,3 Vincenzo Iannotti,4 Giovanni Ausanio,4 AthanasiaKostopoulou,1MilindaAbeykoon,5IanK.Robinson6andEmilS.Bozin6

1Institute of Electronic Structure and Laser, Foundation for Research and Technology -Hellas,VassilikaVouton,71110Heraklion,Greece2DepartmentofChemistry,UniversityofCrete,Voutes,71003Heraklion,Greece3Institute of Nanoscience and Nanotechnology, National Center for Scientific ResearchDemokritos,15310Athens,Greece4CNR-SPINandDepartmentofPhysics"E.Pancini",UniversityofNaplesFedericoII,PiazzaleV.Tecchio80,80125Naples,Italy5Photon Sciences Division, National Synchrotron Light Source II, Brookhaven NationalLaboratory,Upton,11973NY,USA6Condensed Matter Physics and Materials Science Department, Brookhaven NationalLaboratory,Upton,11973NY,USA

*Correspondence:lappas@iesl.forth.gr;Tel.:+302810391344

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Abstract

In contrast tobulkmaterials, nanoscale crystal growth is critically influencedby size- andshape-dependentproperties.However, it is challenging todecipherhowstoichiometry, intherealmofmixed-valenceelements,canacttocontrolphysicalproperties,especiallywhencomplexbondingisimplicatedbyshortandlong-rangeorderingofstructuraldefects.Here,solution-grown iron-oxide nanocrystals (NCs) of the pilot wüstite system are found toconvert into iron-deficient rock-salt and ferro-spinel sub-domains, but attain a surprisingtetragonallydistortedlocalstructure.CationicvacancieswithinchemicallyuniformNCsareportrayedastheparametertotweaktheunderlyingproperties.Theselatticeimperfectionsare shown to produce local exchange-anisotropy fields that reinforce the nanoparticles’magnetizationandovercometheinfluenceoffinite-sizeeffects.Theconceptofatomic-scaledefectcontrolinsubcriticalsizeNCs,aspirestobecomeapathwaytotailor-madepropertieswithimprovedperformanceforhyperthermiaheatingoverdefect-freeNCs.

3

Introduction

Iron oxides are at the research forefront as they encompass important mixed-valentstates[1]thatimpacttheirphysicalpropertiesanditstechnologicalpotential,[2]extendingfrom energy storage devices to catalysts and electrochemical cells. Moreover, since theprincipal oxidation states (II-IV) of iron carry atomicmagneticmoments, spontaneous co-operativemagneticorderisstabilized,whichoffersahighlyexploitablemodality,extendingfromspintronicsandrecordingmedia[3] to therapidlydevelopingnanobiotechnology.[4]Inthelatterfieldofinterest,nanoscalemagneticparticlesforbiomedicalapplicationsdrawsignificant benefits from the volume-dependence of magnetism, and especially whensuperparamagnetism(astate notpermanentlymagnetized) isestablishedbelowacriticalparticlesize.[5]Consequently,thereishighdemandforcontrollingthecrossoveramongstdifferent states of magnetisation in order to improve the particles’ magnet-facilitatedperformance,formakingimagecontrastagents,heatemission“hyperthermia”systems,orevenmechanicalforcenanovectors.[6]

Morespecifically, radio frequencymagneticheatingof single-crystallinenanoparticles (i.e.nanocrystals), is emergingas anovel strategy for activating temperature-sensitive cellularprocesses,[7]butrequiresnon-toxicbiocompatiblenanomaterialsandunderstandinghowstructure-morphology relationships can be used as design parameters. Optimizinghyperthermia efficacy depends on magnetic loss mechanisms attributed to Néel-Brownrelaxations, which evolve with the magnetic anisotropy constant (K) and saturationmagnetization (MS).[8] Inpractice, relaxation times varyby changing intrinsicnanocrystalfactors, includingsize,[9]shape,[10]andcomposition[11].Whilesinglemagneticcoresofpure iron-metalparticlesmayoffersuperiorheatingefficiency, theirquestionablestabilityinbiologicalmedia,[12]hasledresearcherstodevelopiron-oxideparticles(e.g.ferrites:Fe3-δO4,γ-Fe2O3etc)asaversatileandbiocompatibleclassofmaterials.[13]

Thequestfornanocrystals(NCs)thatsurpasstheperformanceofasinglemagneticcoreismotivated furtherby thedesign-conceptofcontrolling thespatialdistributionofchemicalcompositionwithin a singlemotif,[14] suchas core@shell and thin-filmheterostructures.Distinct phases grown in a core@shell topology, with contrasting magnetic stateconstituents (e.g. antiferromagnetic (AFM), ferro- and/or ferri-magnetic (FM/FiM)subdomains),offerapowerfulwaytotunethenanoscalemagneticpropertiesandboosttheparticles’hyperthermia response.[10] This restson the important capability toadjust theparticle’sanisotropythroughtheinterfacialexchangeinteractionsbetweenthebi-magneticcomponentphases.[15]Theextenttowhichtheemergingexchange-bias(HEB)[16]playsakeyroleisregulatedbyvaryingthecore-shellvolumeratio,surface/interfacestructureandthecompositionitself.[17]Thus,optimaldesignofhyperthermiaagentsrequirestherightkind of defect-structure tomodulate favorablemagnetic relaxations. As we show in thiswork,thesemechanismscanbemodeledusingMonteCarlomethods.

In this endeavor solution-chemistry methods are widely used to develop size-[18] andshape-[19]controlledferrite-basednanocrystals,andfacilitatetheirinterfacialconnectivityonananoscalemotif,e.g.Fe@Fe3-δO4,[20]CoO@CoFe2O4,[21]FePt@MFe2O4(M=Mn,Fe,Co, Zn),[22] etc..Within these systems, unforeseenmagnetic properties are occasionallyreported,[23],[24],[25],[26]especiallywhenthermodynamicallymetastablephasessuchaswüstite[27]ornovelinterfacesareintroducedduringthenanoscaleparticlenucleation

4

andgrowth.Forexample,duringtheoxidativeconversionofAFMwüstite(FexO,Fig.1a)intoaFMspinelmagnetite (Fe3-δO4,Fig.1b), the internal structureof theas-madecore@shellFexO@Fe3O4NCsevolveswiththecompositiongradientsinfluencedbystresses.[28]WhileareductionintheAFM@FMinterfaceareaandcoreanisotropy,lowersHEB,[29]antiphaseboundaries(APBs) inthestructure,arefoundtoraisetheparticleanisotropy.Surprisingly,this paves the way to non-zero HEB even in the fully oxidized, Fe3-δO4-like derivatives ofwüstite.[25] It is interesting to note that APB defects are a favored low-energy growthpathway for Fe3O4-films[30] that modify the exchange interactions and give rise toanomalous magnetic behavior with important applications.[31], [32] These peculiarperformances, for NCs in the critical size range of 20-30 nm, were correlated withperturbations of the periodic potential of the iron atomic coordination by lattice defects,whicharehardtowaiveoutinpost-synthesistreatments,butarepreventablebystrategicredoxtuningoftheFe-valenceduringthereactionitself.[33]

The preceding discussion demonstrates that the properties of otherwise single-crystallineferrite particles are influenced by a significant fraction of atoms at the various particle“limits”, the surfaces and internal interfaces.[34],[35],[36] This necessitatescharacterization of the detailed atomic arrangements within the FexO-Fe3O4 phase-spaceavailabletothechemicalsynthesismethods.Effectively,researcheffortsfocusonsolvingamultiplelengthscaleproblem,[37]bycombiningsurface(e.g.electronmicroscopy)andbulk(e.g.powderdiffraction)sensitiveprobes.Totalscatteringexperimentsthough,coupledtoatomicpairdistributionfunction(PDF)analysis,canreachbeyondsuchlimitations.[38]Ourpresentwork reports on the added valueof thePDFmethod,which, in contrast tonear-neighborprobes likeEXAFSandNMR, isabletoprobearelativelywide fieldofview(∼10nm) in a single experiment by reporting how local (nanoscale) distortions are correlatedthroughoutthestructure.

Whilechemicalphaseandstoichiometryultimatelycontrolnanoscalemagneticproperties,therationalchoiceofthecriticalparticlesize,withoptimalmagneticanisotropy,[39]is∼20nm and determines the applications. [39],[40] In practice though, thermodynamic andkineticparametersatnanoscale surfacesand interfacesareexpected to triggernanoscalecrystalgrowthviaenergeticallyfavorablestructural-defectpathways.Thisservestorenderthecontrolofdefectsasanextratuningknob.Here,weinvestigatethenatureofstructuraldefectsestablishedduring thecourseof thespontaneous,oxidativeconversionofwüstiteintoFexO-Fe3O4NCs.WefocusonaseriesofNCswithincreasingparticlesizeintherange8-18 nm,which differ structurally andmorphologically. Our results establish a quantitativerelationshipbetweenfavorablevacancy-induceddisorderandtailoredmagneticproperties,apotentially important tweaking factorat subcriticalparticle sizes (<20nm).MonteCarlosimulations demonstrate broader implications for the right kind of defect structure tomediatethemagnetic lossmechanismsinfavorofefficientenergytransfer intoheatevenfor10nmNCs.

5

Results

1 Structuralinsights

1.1 Single-particlelocalstructure

Fournanoparticle samplesweremadeavailable for this study,with specimenof sphericalshape,entailingdiametersof8.1±0.6nmand15.4±1.3nmandofcubicshape,obtainingedge-lengthsof12.3±0.7nmand17.7±1.7nm(Fig.S1).Henceforth,thesearecalledS8,S15,C12andC18,where‘S’standsforsphericaland‘C’forcubicmorphologies.Moreover,high-resolution transmission electron microscopy (HRTEM) (Fig. 2a-d) suggests that thesmallerS8andC12NPsentailadomainofasingle-phasematerial,butthebimodalcontrastinthelargerS15andC18pointsthataboveaparticlesizeof∼12nmtwonanodomainsareattained.Thecoexistenceofdarkand light contrast features in theS15andC18couldbejustifiedassumingthattwochemicalphases,ofvaryingelectrondiffractingpower,sharethesame nanoparticle volume. Crystallographic image processing by Fast Fourier transform(FFT)analysisof the relevantHRTEM images results in theircorresponding (spot)electrondiffraction patterns (Fig. 2e-h). The unequivocal indexing of reflections in the S8 andC12specimenmay suggest that these adopt themagnetite type of phase (Fig. 2e, f). On theotherhand,asimilarconclusioncannotbemadeaftertheevaluationoftheFFTpatternsofthe apparently bimodal contrast S15 and C18 specimen as the cubic spinel and rock saltreflections(Fig.2g,h)appeartoberesolutionlimited.Thebehaviorappearsinlinewiththetendencyofbulkwüstiteforoxidativeconversion,[41],[42]andinfersaprocessanalogoustoitseliminationfrom∼23nmcore@shellFexO@Fe3-δO4nanoparticles.[25]

The long and short-rangemodulations of the selected (hkl) atomic planes could becomemore easily isolated with direct space images derived from the inverse FFT synthesis ofchosenfamiliesofreflections.Wefindthatthe(400)(or(200)forthecore@shellS15andC18NPs) familygeneratesperfectatomicplanes (Fig.S2.1-2.4)andtheirspacingcouldbeattributed to the Fe3-δO4 spinel (or Fe1-xO rock-salt) typeof structure.However, the (220)family(Fig.2i-l),deviatesfrombeingfaultless(Fig.S3).GeometricPhaseAnalysis(GPA)[43]of the (220) reflections depicts single-colored regions (Fig. 2m-p) that are internallyhomogeneous, showing no obvious inner side distortions. The results illustratehomogeneous structure for the S8 particle (Fig. 2m), but increasing degree of latticeheterogeneity with size (Fig. 2n-p). GPA has pointed before to a 5% crystal latticedeformationfrom(220)planesof∼23nmFexO@Fe3-δO4nanocubes,whilethatforthe(400)(or(200)forarocksalt)familyamountedtoonly∼1%.[25]

Insummary,theevaluationofthenumber(Nr)ofdefectsinvolvingthe(220)planes,impliesthatNPsofsphericalmorphology(S8,S15)carryalargernumberofdefectsintheirvolumethanthecubicones,andthoseofsmallersize(S8)aresomewhatmoresusceptibletolatticefaultsthanthoseoflargersize(Fig.S4;§S3.1andTableS1).Effectively,suchdistorted(220)atomic planes (Fig. 1b) impose tensile lattice strain as theoverall prevailing effect that ispronouncedforthesphericalmorphology(cf.from4-5%inthelatter,dropsdownto1-2%incubicshapeNPs;§S3.2andTableS2).

1.2 Ensemble-averagelocalstructure

With the aim to go beyond the HRTEM findings and acquire quantitative phase-specificstructural information froma largeensemble,wemeasured the synchrotronX-rayPDFof

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selected nanoparticle specimens and compared them to the bulk magnetite (Fig. 3). AsmoderateQ-spaceresolutionoftheexperimentalsetupusedlimitsthePDFfieldofviewinther-space(r>5-10nmlength-scalesmetinbulk),ouranalysisfocusesprimarilyonthelow-rregionintheatomicPDF(r=1-10Å).ThispracticallyallowstodescribethelocalstructurethroughinsightsonbondingandlatticedistortionswithintheFe3-δO4andFexOunitcells.

1.2.1 Localstructuredistortions

Bulk magnetite was taken as a reference system against which subtle distortions of theatomic lattice planes in the nanoparticles could be identified. Initial refinements wereperformed with the simplified, normal spinel, cubic configuration of magnetite,(Fe3+)8[Fe3+,Fe2+]16O32,[44] where the round brackets represent tetrahedral (Td) and thesquarebracketsoctahedral(Oh)coordinationbyoxygencrystallographicsites(i.e.model#1;this assumes no Fe2+/Fe3+ inversion between Td/Oh sites). The atomic PDF in the low-rregionforthebulksampleat300Kisdescribedwellbythistextbookmodel(Rw=8.8%).Asomewhat lowerqualityofthefitat80K(Fig.4a;Rw=9.6%)mayinfersomesensitivitytoacentric distortions, beyond the r-space resolution of our measurements, caused by theVerweytransitionofbulkmagnetite.[45]

Thesametextbookmodel(#1)wasthenutilizedtomodelthexPDFdatafornanoparticlesofvariablesizeandmorphology.Whatisparticularlystrikingisthatbetween300Kanddownto80K,thiscubicmodel,systematicallyfailstofitthepeakatr∼3Å(sampleS8:Fig.4b,Rw=18.1%; sample C12: Fig. S5a, Rw= 11.9%). Importantly, this corresponds to the closestdistance between the iron atoms that are octahedrally coordinated by oxygen in thestructure of magnetite (forming a pyrochlore-type sublattice, Fig. 1b). Moreover, thenearestdistanceofapairofFe-Feinwüstiteisalsojustabove3Å.ItmaybeexpectedthenthatifadetectablylargevolumefractionofwüstitephaseispresentintheNPs(cf.HRTEMforS15)thentheintensityofthepeakatr∼3Åshouldbeincreased.Inanefforttoexplorethis,atwo-phasecubicrock-saltandspinel(FeO-Fe3O4)modelwasemployed.Thisanalysisshowed that either in smaller nanocrystals (S8 and C12) or larger NPs (S15), the cubicsymmetry model (Fig. 4c; Rw= 13.6%), is somewhat misplaced with respect to the 3 Åobserved radial distance distribution. Per present analysis and assessments of fits overbroaderr-rangesitappearsthatthesenanoscalesamplesarehighlynon-uniformintermsofdefects(vide-infra),andtheirstructureisnotquitecubicathigh-r,andisneithersolocallytoo.

Forthesereasons,thepossibilityofthenanoparticlelocalstructuredeviatingfromtheidealcubic lattice configurationhasbeen factored-in.However, themodestQ-space resolutionforresolvingsymmetry-loweringconfigurationsbeyondthe localscale,and inturn limitedPDFfieldofview, ledustoutilizeapproximations implementedbyspacegroupsofhighersymmetry. The exemplary case of maghemite (γ-Fe2O3) drove this effort as it can beconsidered as Fe2+-deficient magnetite, 3212218 ]OFe,[Fe(Fe)

32

31 〉〈 (FeOh-vacancies

represented by the angular 〉〈 brackets)[46], [47]. Under this defect-based schemerandomlydistributedvacanciesresultinanfcclattice(model#1),butwhentheirorderingisfavored, either a primitive cubic (P4332 symmetry, model #2)[48],[49] structural variantcouldbestabilized,orasymmetry-loweringlatticedistortionistriggered(P43212tetragonalsymmetry,model#3)[50],[51].

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Amongstthese,onlymodel#3madeamarkedimprovementinthedescriptionofthePDFpeakpositions fromroomtemperaturedownto80K (Fig.4d,Fig.S5b,Fig.S6c).ThePDFintensitieswere accurately describedwhen the Fe-site occupancies (η)were refined. Theoutcome indicates that nanoparticle samples of spherical morphology display the leastoccupiedFe-sites,namely:η-S8<η-S15<η-C12[i.e.16.4(1)<18.2(1)<20.0(1),outof24Fe-atoms/unitcell;Fig.S7,§S7].Alongthis trendcomestheexpansionof the in-plane(a-b)lattice dimensions and the contraction of the c-axis, which suggest a more pronouncedtetragonal compression for the spherical (S8, S15 c/a∼ 0.975) rather than the cubic (C12,c/a∼0.985)morphologyNPs.

Thoughthelocalsymmetrychangemaybeseenasamanifestationofthecouplingbetweenelasticandexchangeenergyterms,[52]whicharelikelyoptimizedbytheapparentlylargerstrain in thenanospheres, subtle crystallineelectric fieldeffectsdue to a local tetragonalJahn-Teller distortion, lifting the orbital degeneracy in Fe2+ (3d6),[53] cannot be eitherresolvedorruled-outbythestructuralxPDFprobeonthisoccasion. Moreover,whilewecannot completely discard the contribution of valence-swap induced distortion [with afractionof Fe2+ atomsoccupying Fe3+ sites and vice versa {cf. (Fe3+)8[Fe3+,Fe2+]16O32}],[54]we emphasize that vacancy-driven effects are a plausibility as the relative G(r) peakintensitiesof FeOh-FeOh (r∼ 3.0Å) andFeOh-FeTd (r∼ 3.5Å) changeappreciably (vide-infra),whereas the one-electron difference between the Fe2+ and Fe3+ electronic configurationswould effectively be unobservable in the xPDF peak heights. It is therefore inconceivablethat observed dramatic changes in relative PDF peak intensities originate from inverted-spinel-likeelectronicconfigurations.

Recapitulating theabovePDFanalysis, it is important to recognize the sensitivenatureoftheNPs,andespeciallythosewithsphericalshape,inlocalstructurenon-stoichiometry.Inparticular,Fe-vacanciesstabilizeatetragonallydistortedlocalstructure,whilethetendencyfortetragonalicityseemstobeenhancedforthesphericalparticlemorphology, inferringarelationtothelargernumberofdefectsinthevolume,asimplicatedbytheHRTEMbasedanalysisaswell.

1.2.2 Wherethedefectsarelocated

The question as of how structural vacancies relate to different cation lattice sites is nowtackled by comparing the observed, normalizedG(r) patterns of theNPs against the bulkmagnetite(Fig.5a).Twotypesofradialdistancepopulations,representedbytheG(r)peak-intensity, are considered. (a) FeOh-FeOh separations (r∼ 3.0Å):When the single-phaseNPspeak-intensitymaximumiscomparedtothatinthebulkstoichiometricFe3O4ameasureofthepresenceofOhvacancies iswitnessed.Withtheratiobeing∼0.8and∼0.9, for theS8andC12NPs,respectively,moreOh-Fevacanciesaresupportedinthenanospheres.ForthelargerNPs (S15) the enhancedG(r) suggests an increased rock-salt type of phase in theirvolume(§1.2.1).(b)FeOh-FeTdseparations(r∼3.5Å):TheprogressivediminutionoftheG(r)peak-intensity advocates also that the spherical nanoscale morphology (S8, S15) adoptsnoticeably more empty lattice sites than the cubic one (C12), conferring that theirabundanceisashape-dependentphenomenon.[10]

Withthepurposeofevaluatingfurtherifthevacancieshaveasite-specificpreference,xPDFpatternswere simulated,while the ratioof Fe-vacancypopulationat theOhandTd siteswasvaried.Thetrendissimilarassumingeitherthesymmetry-loweringmodel#3(Fig.5b)

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orthecubicspinelmodel#1(Fig.S8b,c;§S8).Theprogressiveintensitydiminutionatr∼3.5Å,whenrawandsimulatedpatternsarecompared,corroboratestoasignificantvolumeofvacanciesalsoat theTdFe-sites (∼10-20%;Fig.S7), inferringa limited lengthofstructuralcoherence.[55] This is in contrast to bulk spinel sampleswhere intrinsicOh Fe-vacanciesmediate the structure and properties.[56] The significant content of vacancy distributionresolvedbyxPDFmayinferemergingstrains/stresses(Fig.S9and§S9),remindingthoseinFexO@Fe3O4nanocubesprobedbysingle-particlelocalstructuretechniques.[28],[25]

Overall, PDF indicates that during the self-passivation of wüstite, smaller NPs are single-phase,whilelargeronesattainatwo-phasecharacter.Thissize-mediatedphaseevolutionisinagreementwiththeHRTEMfindings,whichalsoindicatethatparticlesofsphericalshapeaccommodatelargernumberofdefectsintheirvolume[cf.refinedFe-siteoccupancyη-S8<η-S15<η-C12 [i.e.16.4(1)<18.2(1)<20.0(1),whereη=24Fe-atoms/unit cellof thebulkcubicspinel;Fig.S7].Besides,PDFuncoversthatinadditiontovacanciescommonlyfoundatthe Oh sites, Td-Fe is largely absent, fostering local tetragonal lattice distortions. Theseobservationstriggerquestionsabouttheimpactofvacanciesontheobservedproperties.

2 Nanometerscaleeffectsonproperties

2.1 Magneticbehavior

In view of the nanoparticles’ deviation from perfect structural ordering their magneticbehavior isevaluatedherebecauseof itsdirect relevancetohyperthermiaapplications.Abroad maximum in the dc magnetic susceptibility, χ(T), with an irreversibility betweenZFC/FC curves (Fig. 6a-c), marks a characteristic temperature, TB, that separates thesuperparamagneticstatefromtheblockedstate.[5]Inaddition,theχ(T)forthecore@shellNPs(S15;Fig.6c)pointstoasuddendropduetotheparamagnetictoAFMtransition(TN)inwüstite and a subtle anomaly nearing the Verwey transition (TV) of bulkmagnetite.[29],[34],[35]Furthermore,theevolutionsofthehysteresisloopcharacteristics(Fig. S10, Table S3; §S10) suggest that a processes beyond the coherent reversal ofM isinvolved. Inthis,M(H)experimentsunder field-cooling (Hcool=5T;Fig.6d-f,Fig.S11,S12),supportthedevelopmentofamacroscopic,exchange-biasfield(HEB)[16].ThequickriseofHEB for the S15 NPs, against the single-phase S8 and C12 (Fig. 7, Fig. S13, §S13), impliescompetingexchangeinteractionsduetodifferentkindsofinterfaces.

Inaddition,alltheNPspresentadiscontinuousstep-likevariationofthemagnetizationnearzero field (Fig. 6d-f, Fig. S12). The two-switching fielddistributions,markedbymaxima indM/dH,resemblethe inhomogeneousmagneticbehaviorarising fromcoexistingmagneticcomponentsofcontrastingHCs (e.g.ofmixtureofparticlesizes[57]orcompositions[58]).Herethough,theHRTEMstudyoftheFexO-Fe3O4NPsconferstheirsinglecrystalcharacterandnarrowparticlesizedistribution(Fig.S1).However,xPDFresolvesFe-sitevacancies[V=(η-S8orη-S15orη-C12):ηisthemodeling-derivedcontentperunitcellvolume,η=24Fe-atoms / cell of bulk cubic spinel], with V-S8 (33%) > V-S15 (25%) > V-C12 (17%). Theexistenceof thesedefectsseemstoestablishaspatialvariationof thecompositionat thelocallevelthat‘turnson’theobservedinhomogeneousmagnetism.

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2.2 Couplingofstructuraldefectstomagnetism

To shed light on how atomic-scale defects (e.g. Td Fe-lattice sites vacancies and localtetragonaldistortions)coupletomagnetismweutilizedMonteCarlo(MC)simulations.Forthis purpose, our systems were approximated by a microscopic “core-surface”model,[59],[60] however,with random defects introduced in the nanoparticle structure.ThesedefectsweredescribedasweaklycoupledFMpairsofspinswithstronganisotropy,inferred from the symmetry-lowering local structure (§1.2.1) of the NPs. Their soft FMcharacter[61] was chosen to resemble that of V4-Td clusters of defect-units [due tocoalescenceof4FeOh-vacancies(V)aroundanFe3+Td-interstitial](Fig.1a)[41]outofwhichspinelmagnetitehasbeenclaimedtonucleateduringtheoxidativeconversionofFexO.[62]Assuming that the fraction of the FM pairs of spins (pinning bonds) is a tunable particleparameter,theevolutionof(a)thelow-fieldjump(ΔM/MS,estimateshowmanymagneticmomentsareswitched)and(b)theexchange-bias(HEB)hasbeenquantified(Fig.8).

Withthepurposetoassesstheformer,ΔM/MS,wenotethatthesurfaceisalargepartforthe smaller nanoparticles, i.e.∼50%of the S8 and∼35%of theC12 specimens, andbothmay assume a two-phase magnetic nature. The ΔM/MS changes may then be amanifestation of the character stemming from the exchange-coupled hard and softferro/ferri-magneticphasesinthetwonanodomains.[63]Asthenumberofpinningbondsincreases in the main body of these NPs, MC calculations point that the defects’ strongrandom anisotropy leads to exchange randomness rendering their two-phase magneticnature more disordered. This leads to less prominent, ΔM/MS changes in the hysteresisloops (Fig. 8).What is concernedwith the evaluationof the latter,HEB,wenote that thedefect-induced spin disorder within the core-like sub-domains reduces the overallmagnetization (Fig. S11, S12), but supports extra pinning centers that could impede easycoherentreversal[64]ofthesurroundingmoments.InlinewiththisaretheMCsimulationswhich indicate that insmallS8andC12NPswithoutdefects,exchange-bias isabsent,butwith increasingnumberofpinningbonds, theweaklybondeddisordereddefectscompetewiththeorderedspinsenvironmentinthecoreandinduceextraanisotropy,resultinginnetexchangebias(Fig.8).

Thebehaviorisdepictedinthemagneticmomentsnap-shotsofdefected(Fig.9a-c)versusdefect-free(Fig.9d-f)NPs.Whilefornon-defectedNPsthesoftanisotropiccorefollowstheappliedfieldreversal,theexistenceofdefectsgeneratesantiparallelspincomponentsthatpromotethecantingofthecoretowardsthexy-plane(Fig.9,S14,S15).Thenanospheres’more defected internal structure generates adequate conditions that endorse exchange-coupling so that HEB-S8> HEB-C12 (while HC-S8< HC-C12, due to differences in the NPs’magneticvolumes).AsmagnetizationstatesatthedifferentkindsofinterfacesareadjustedbyHcool,foramatterofconsistency,itisworthpointingoutthatMCsimulations(Fig.S16)reproducefairlywelltheexperimental (Fig.7)evolutionofthehysteresis loopparameters(HEB,HC,ΔM/MS)evenforthelargerS15NPs(§S16).

The defect-rich NPs discussed here broaden the picture that growth-approach mediatedsubtle, structural microscopic factors,[65],[24],[32] foster local-scale anisotropy thatfacilitatesexchangebiasinotherwisephase-pure,monocrystallineNCs.

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2.3 Defect-drivenmagneticheating

Ferritenanocrystals,inmagnetically-mediatedbiomedicalapplications,drawtheirversatilityfrom the critical particle size (∼20 nm), [39] a factor which varies with the magneticanisotropy.[40]Inthepresentworkwehavedemonstratedthatsurfaceatomscanresponddifferentlythanthecoreones,aprominenteffectforthesmallerfullyoxidizedderivatives(≤12 nm) of the FexO-Fe3-δO4 NCs. Although defect-elimination during synthesis can yieldnanomagnetic agents (≥20 nm) with enhanced, concurrent diagnostic imaging andthermoresponsiveperformances,[33]structuraldefectsatsub-criticalparticlesizesappeartoofferadifferentexploitablepathway,compatible thoughwith thebiological limits (e.g.setbytoxicityandpatientdiscomfort).[66]Here,vacanciesinself-passivatedironoxidesofsubcritical size (≤12 nm), act as pinning centers that favour the competition of exchangeinteractions,thusfosteringlocalanisotropyenhancement.BenefitsfromtheNPs’extendedanisotropicpropertiesmay raise theirapplicationpotential, as forexample toaffordheatgenerationbeyondthebaresusceptibilitylosses(Néel-Brownrelaxation)mediatedbyfinite-sizeeffectsalone(§S17).[39]

TheMCsimulationssupportthatforsmalldefectedNPs(S8),wheretheeffectiveanisotropyincreases 5 times compared to the defect-free ones, the heat dissipation (specificabsorptionrate=SAR)israisedalmostten-fold,i.e.∼450W/gvs.∼50W/g,at500kHzunder37.3kA/m(Fig.9g).Forcomparison,itisworthnotingthatexperimentally,defect-free9nmFe3O4NPs,exhibitaSARof152W/g.[14] It canbeenvisagedthenthatnanoparticleself-passivationleadstoadequateperturbationoftheperiodicpotentialoftheironcoordinationby vacant lattice sites that in turn tweak the core to surface magnetic anisotropy ratio.Whetherthismightbeanavenuetoboostthethermalenergytransferatsubcriticalparticlesizes(≤10nm)bysynergisticrelaxationprocesses,warrantsfurtherexploration.EvenintheabsenceofextendedburiedAFM/FMinterfaces,[14]wherebeneficialexchangeparametersattain efficient heat sources, smaller, heterogeneous nanocrystals (S8, C12) may beuncoveredasusefulheat-therapeuticagents.

3 Conclusions

Theself-passivationofnanoscalewüstite(FexO)hasbeeninvestigatedasatestinggroundtoexplore the consequences of thermodynamically unstable interfaces formed during thenucleation and growth of nanostructured iron-oxides. As conventional oxidation evolves,grown component phases give rise to single-crystal nanoscale entities with sub-domainFexO-Fe3-δO4interfacialconnectivity.However,whenthesynthesisparametersarevariedtoattain smaller-size nanocrystals (≤12 nm) a spinel-like phase is nucleated alone. Thecompositionalandstructuralcomplexityoftheseiron-oxidenanostructuresiswitnessedbysingle-particle transmission electron microscopy and complementary, phase-specificstructural information, attained from a large ensemble by high-energy synchrotron X-raytotalscatteringexperiments.Theseuncoverthatdefects(withasignificantvolumeresidingattetrahedralFe-sites)alleviateasurprisingtetragonallatticecompressioninthespinel-likephases.Thedefectsentailstructuralvacancieswithanincreasednumberdensitywhenthenanoscale morphology changes from cubic to spherical and the particle size shrinks.Moreover, magnetometry and Monte Carlo calculations show that the nanostructures’heterogeneous character reflects in a core-surface type of spin-configuration that favors

11

twoswitchingfielddistributions.EvenwithoutacontributionfromuncompensatedspinsatconventionalAFM/FMburied interfaces,as in largercore@shellFexO-Fe3-δO4nanocrystals,exchange-bias is unexpectedly evident, though much reduced, in the smaller size, fullyoxidized particles. The latter, in linewith the non-cubic local symmetry of the nucleatedspinelphases,expresses the influenceof local anisotropy fields,whichapparentlydeviatefromtheeasy-axissymmetrymetincommoniron-oxides,favoringcantingintothexy-plane.The results corroborate that size-dependent evolution of themetal-cation valence state,producespinningdefectswhichpromote the competitionof theexchange interactions atsubcriticalsizes(<20nm).Theconceptraisedherepointsthatatomic-scaledefectcontrolinsmall particles (∼10 nm), typically hampered by the superparamagnetic limit, may act infavor of anisotropic properties for improved magnetism-engineered functionalities (cf.heatingagentsandthermo-responsivecellularprocesses).

Methods

4.1 Materials

Allreagentswereusedasreceivedwithoutfurtherpurification.Oleicacid(technicalgrade,90%), absoluteethanol (≥98%),octadecene (technical grade, 90%), hexane (ACS reagent,≥99%) and sodium oleate powder (82%) were purchased from Sigma Aldrich. Iron (III)chloride (FeCl3·6H2O, ACS Reagent) was purchased fromMerck. Iron (III) acetylacetonatewaspurchasedfromAlfaAesarandoleylamine80-90%waspurchasedfromAcrosOrganics.

4.2 Synthesesprotocols

Colloidalsyntheseswerecarriedout in100mLround-bottomthree-neck flasksconnectedvia a reflux condenser to a standard Schlenk line setup, equipped with immersiontemperature probes and digitally controlled heating mantles. The reactants were storedunderanaerobicconditions inanAr-filledglovebox (MBRAUN,UNILab),containing<1ppmO2andH2O.

A gas mixture of 5% H2/Ar has been used as a protective/reductive atmosphere. ThereductiveatmospherecanhelptomaintaintheFexO(wüstite)phaseinsteadoftheoxidizedFe3O4 (magnetite) and/or γ-Fe2O3 (maghemite) forms. Previous studies have shown thatFexO crystallites formed under these synthetic conditions become rapidly oxidized afterremoving the reducing agent and exposing them to ambient air.[67] Very small particlestend to be fully oxidized to the spinel structure. A minimum diameter over ∼13 nm isneededforthenanoparticletomaintainitscore@shellstructure.

4.2.1 Preparationofironoleateprecursor

Iron (ΙΙΙ) - oleate was prepared before each nanoparticle synthesis and used as an ironprecursorsubsequently.Specialcarewastakentoprotectitfromthelight.ThemetaloleateprecursorisformedbythedecompositionofFeCl3·6H2Ointhepresenceofsodiumoleateat60 oC,basedona slightlymodified literatureprotocol.[68]16mmolofFeCl3·6H2Osaltand48mmolofsodiumoleateweredissolved inamixtureofsolvents inaroundbottomflask.56mLhexane,32mLethanoland24mLdistilledwaterwereusedas solvents.Themixturewasheatedto60-65oCunderAratmospherefor4hoursandthenlettocooldownto room temperature. The organic phase containing the metal oleate complex was

12

separated from the aqueous phase using a separatory funnel, thenwashedwith∼30mLdistilledwaterandseparatedagain.Thisprocesswasrepeated4timesandattheendthemetalorganiccomplexwasdriedunderstirringandmildheatingforseveralhours,resultinginaviscousdarkredoleate.Thefinalproductwasstoredinadarkplacetoprotectitfromlight.Somemildheatingtoensureitsfluidnessmaybeneededjustbeforeitsuseforeachnanoparticle synthesis. The successful fabrication of the ferric oleate complex has beenidentifiedbytheFTIRdata(Fig.S18).[69]

4.2.2 Synthesisofiron-oxidenanoparticles

The nanoparticles (NPs) were synthesized by employing modified literatureprotocols[69],[34],[70],[18] aiming to produce the wüstite type of oxide (Fe1-xO). In atypical synthesis2-7mmolof ironoleateweredissolved inoctadecene in a flaskunderareductive atmosphere. Oleic acid was used as surfactant and protective ligand, in aproportion1:2withrespecttotheironprecursor.Theamountsofreactantsweretunedsothat a final Fe-oleate molar ratio of 0.2 mol/kg solution was achieved. The synthesisprotocol includes three major steps. First, a degassing step at 100 oC for 60 min undervacuumisrequiredforthecompleteremovalofanywaterandoxygenresidues.Thenthemixture is heated to 220 oCwith aheating rateof∼10 oC·min-1. At this temperature thatlasts for 60 min the so-called nucleation step allows for the crystal seeds[92] to begenerated for the successive formation of the nanocrystals (NCs). At the final stage, themixtureisheatedto320oCwherethenanocrystals’growthtakesplace.AttheendofthesynthesisthecolloidalmixturewaslefttocooldownatroomtemperatureandtheNCswereprecipitateduponethanoladdition.Theywereseparatedbycentrifugationat6000rpmfor5min,re-dispersedinhexaneandthencentrifugedoncemoreafteraddingethanolina1:1ratio with respect to the hexane. The process was repeated two more times at acentrifugation speedof 1000 rpm.Additionof sodiumoleatewasproved topromote theformationofcubicNPs,asproposedinearlierstudies.[70]Wefoundthatametalprecursorto sodium oleate ratio of 8:1 to 5:1 is adequate enough to realize such a shapetransformation.Minorvariationsinthistwo-stepheatingprotocolallowsthetuningoftheparticle’ssizeandthecontroloftheirsizedistribution.[18],[71]TheprotocolgivesrisetoNPswithdiametersupto20nm,withsize-controlattainedbymodifyingthegrowthtime(40< t< 90min) at the final stage. An extended stay here produces even larger NPs, butbeyond60minsmaller-sizeparticlesareafforded,likelyduetoaripeningmechanism.Fouriron-oxide colloidal nanostructures, with varying size and morphological features (vide-infra), S8,C12, S15,C18 (S: spherical, C: cubic)were finally grownand storedas colloidaldispersionsin∼4mLhexaneinsepta-sealedvials.

4.3 Characterizationtechniques

4.3.1 HighResolutionTransmissionElectronMicroscopy(HRTEM)

Low magnification and high resolution Transmission Electron Microscopy (TEM) imageswere recorded, using a LaB6 JEOL 2100 electronmicroscope operating at an acceleratingvoltageof200kV.AlltheimageswererecordedbytheGatanORIUSTMSC1000CCDcamera.ForthepurposesoftheTEManalysis,adropofadilutedcolloidalnanoparticlesolutionwasdeposited onto a carbon-coated copper TEM grid and then the hexane was allowed toevaporate. In order to estimate the average size, statistical analysis was carried out onseverallowmagnificationTEMimages,withthehelpofthededicatedsoftwareImageJ.[72]

13

The structural features of the nanoparticles were studied by two-dimensional (2D) fastFouriertransform(FFT)imagesacquiredandanalyzedbyImageJ.

With thepurpose tohighlight thedefect structureof thenanoparticlesweemployed theGeometric Phase Analysis (GPA) method of Hÿtch et al..[43] The HRTEM images wereFouriertransformedandaregionaroundoneofthe{220}peakswasselectedwithacircularwindow. This diffraction pattern was re-centered and inverse Fourier transformed toprovide a real-space imagewhose phase (Fig. 2m-p), represents the projection (onto the{220}reflectionchosen)ofthelatticeshiftofthatparticularregionofthecrystalrelativetothe average lattice. The single-colored regions are internally homogeneous, showing noobviousinternaldistortions,buthavedifferentphaseshiftsfromtheirneighbors.

4.3.2 X-rayPairDistributionFunction(xPDF)

X-ray synchrotron-basedPDFdatawere acquired at the28-ID-1beamlineof theNationalSynchrotronLightSourceII,BrookhavenNationalLaboratory.Eachnanoparticlepowderwasencapsulatedina∅1.0mmkaptoncapillary,sealedatbothendswithepoxyglue.The28-ID-2inPDFmodeusesaPerkin-Elmer2Dimageplatedetectorforfastdataacquisition,butofrelativelymodestQ-spaceresolutionwhich,inturn,limitsthePDFfieldofviewinr-space.Datawere collectedbetween80<T<400K,makinguseof thebeamline’s liquidnitrogencryostream(OxfordCryosystems700),withincidentX-rayenergyof68keV.Bulkmagnetitepowder(Fe3O4)wasutilizedasareference.

TheatomicPDF[38]givesinformationaboutthenumberofatomsinasphericalshellofunitthicknessatadistancerfromareferenceatom,andisdefinedas:

]ρ)ρ([4π 0−= rrG(r) (1)

where ρo is the averagenumber density, ρ(r) is the atomic pair-density, and r representsradial distance. The raw 2D experimental data are then converted to 1D patterns ofintensity versus momentum transfer, Q (= 4π sinθ/λ), which are further reduced andcorrectedusingstandardprotocols,andthenfinallyFouriertransformedtoobtainG(r):

)sin(1])([)(2/πmax

min

∫ −=Q

QdQQrQSQG(r) (2)

S(Q) istheproperlycorrectedandnormalizedpowderdiffraction intensitymeasuredfromQmin toQmax.TheexperimentalPDF,G(r),cansubsequentlybemodeledbycalculatingthefollowingquantitydirectlyfromapresumedstructuralmodel:

0ijij 2

ji ρ4π)]δ(f

ff

1[ rrrr

G(r) −−∑><

= (3)

here, f stands for the X-ray atomic form factors evaluated at Q= 0, rij is the distanceseparatingthei-thandj-thatoms,andthesumsareoveralltheatomsinthesample.Inthe28-ID-2 experiments, elemental Ni powder was measured as the standard to determineparameters, such as Qdamp and Qbroad, to account for the instrument resolution effects.Experimental PDFs, based onmodest Q-space resolution and aQmax= 25 Å-1 raw powderdiffractiondata,werefittedwithstructuralmodelsusingthePDFgui[73]softwaresuite.

14

4.3.3 Magneticmeasurements

The magnetic characterization was conducted using a vibrating sample magnetometer(VSM, Oxford Instruments,Maglab 9T), operating at a vibration frequency of 55 Hz. Themeasurementsofthetemperaturedependentmagnetization,M(T),werecarriedoutat50Oe at a fixed temperature rate of 1 K min-1 after either zero-field cooling (ZFC) or fieldcooling(FC)in50Oefrom300Kto5K.SelectedM(T)measurementswerealsocarriedoutat a different applied field (100 Oe). Hysteresis loops, M(H), were obtained at roomtemperatureandat5Kbysweepingtheappliedfieldfrom+50kOeto-50kOeandbackto+50kOeaftercoolingthesamplefrom300Kto5KunderZFCoranappliedfield0<Hcool≤50kOe(FC). IntheFCprocedure,oncethemeasuringtemperaturewasreached,thefieldwasincreasedfromHcooltoH=50kOeandthemeasurementoftheloopwaspursued.

Whileprecautionsweretakentomaintainthe integrityof thesamples, theirspontaneouschemical evolution led us to exclude one specimen from the in-depth discussion wheremagnetism and structural properties are correlated (§2). This is because while TEMstructural investigations were pursued soon after the sample growth, neither xPDF normagnetic characterizations were readily available (due to remote facility timeline accessrestrictions) near the initial life-time of the samples. So, while four iron-oxide colloidalnanostructuresweregrowninitially,theirself-passivationintoFexO-Fe3O4nanocrystals,ledustodiscussmagneticdataonlyforthreesamples(i.e.S8,C12,S15)foracoherentpictureofstructure–propertyrelations.

4.4 MonteCarlosimulations

The simulations approximate the nanoparticles (NPs) by a microscopic “core-surface”model.[59],[60] Three nanoparticle model systems were considered, with somewhatdifferentmorphologicalfeatures,asthesewereprobedexperimentally intheS8,C12,andS15 specimens. The spins in the NPs were assumed to interact with nearest-neighborHeisenberg exchange interaction, and at each crystal site they experience a uniaxialanisotropy. [35],[74],[75] Under an externalmagnetic field, the energy of the system iscalculatedas:

E=-Jcore Sii,j∈core

·Sj - Jshell Sii,j∈shell

·Sj - JIF Sii∈core,j∈shell

·Sj

-Ki∈core Si·ei2 - Ki∈shell Si·ei

2 - H Si (4)

ii∈shelli∈core

Here𝑆! istheatomicspinatsiteiandêiistheunitvectorinthedirectionoftheeasy-axisatsite i.Thefirst,secondandthirdtermsgivetheexchangeinteractionbetweenspinsintheAFMcore,intheFiMshellandattheinterfacebetweenthecoreandtheshell,respectively.TheinterfaceincludesthelastlayeroftheAFMcoreandthefirstlayeroftheFiMshell.ThefourthandfifthtermsgivetheanisotropyenergyoftheAFMcore,KC,andthatoftheFiMshell,Kshell,correspondingly;thelasttermistheZeemanenergy.

Parameterswerechosen(§S18)aftercarefulanalysisoftheexperimentalmagneticbehaviorandMonteCarlo (MC) simulationswere implementedwith theMetropolisalgorithm.[76]The hysteresis loops,M(H), were calculated upon a field cooling procedure, starting at a

15

temperatureT=3.0 JFM/kB anddown toTf = 0.01 JFM/kB, at a constant rateundera staticmagneticfieldHcool,directedalongthez-axis.Thehysteresisloopshiftonthefield-axisgaveusanestimateoftheexchange-field,HEB=-(Hright+Hleft)/2.ThecoercivefieldwasdefinedasHC=(Hright-Hleft)/2.HrightandHleftarethepointswheretheloopintersectsthefield-axis.ThefieldsH,HCandHEBaregivenindimensionlessunitsofJFM/gμB,thetemperatureT inunitsJFM/kBandtheanisotropycouplingconstantsKinunitsofJFM.Inthiswork104MCstepsperspin (MCSS) were used at each field step for the hysteresis loops and the results wereaveragedover60differentsamples(namelyrandomnumbers).

Acknowledgements

This research used beamline 28-ID-1 of the National Synchrotron Light Source II, a U.S.DepartmentofEnergy(DOE)OfficeofScienceUserFacilityoperatedfortheDOEOfficeofSciencebyBrookhavenNational LaboratoryunderContractNo.DE-SC0012704.AL thankstheFulbrightFoundation-GreeceforaVisitingScholarawardtoundertakeresearchworkatBrookhavenNationalLaboratory,USA.

SupplementalMaterial

Supplementary Information accompanying this paper includes: TEM size-distributions,HRTEMinverseFFTsynthesis,Calculatedparametersfordefects,Sizeandshapedependentstrain, xPDF fits for the C12 and S15 nanoparticles, Simulations of the defect-dependentchangesinG(r),Sizeandshapedependentvacancycontent,Cell-sizeT-evolutionforS8andS15, ZFC and FC hysteresis loops, Magnetic anisotropy, ZFC and FC hysteresis loopscharacteristics and their first derivative, Cooling-field dependence ofM(H) for S15, FTIRspectra, Monte Carlo calculations of theM(H) parameters, spin-configuration snap-shotsandSARfordefectedS8anddefect-freenanoparticles.

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[75] G.F.Goya,T.S.Berquó,F.C.Fonseca,andM.P.Morales,J.Appl.Phys.94,3520(2003).[76] K.BinderandD.Heermann,MonteCarloSimulationinStatisticalPhysics:AnIntroduction,5th

ed.(Springer-Verlag,BerlinHeidelberg,2010).

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FIGURES

Figure 1. Illustrations of the Fe-site arrangement in archetype face-centred cubic crystal types ofbulk iron oxides: (a) the FexO (wüstite) rock-salt, defect-mediated structure, with octahedrallycoordinated(byoxygen-notshownforclarity) ferrous(Fe2+)sites(Oh)representedbydarkgreenspheres,withlargelightgreenspheresdepictingtheinterstitialferric(Fe3+)tetrahedralsites(Td)inthepresenceof fourvacant (V) ironpositions (lightgreen),givingrisetothesmallestV4-Tddefectcluster(oxygenisdepictedbyredspheres);theircoalescenceisalikelypathwayfor(b)theFe3-δO4(magnetite),representingtheferro-spinelfamily,whereOhFe-sitesarecharacterizedbydarkgreenspheres,TdFe-sitesbybrightgreenspheresandavacancy-bearing(220)latticeplaneishighlighted.BothstructuraltypesaccommodatetrigonalpyramidsofFe-atoms,asacommonbuildingblock.

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Figure2.High-resolutionTEMimages in the[001]zoneaxes forsphericalS8 (a),S15 (c)andcubicC12(b),C18(d)morphologynanocrystals.Thecorrespondingdiffractionpatterns(e,fandh,g)afterFast Fourier Transform (FFT) analysis of each micrograph are shown beneath. Green and yellowcirclesmark setof reflections that couldbe indexedon thebasisof eitherwüstite (green)or/andmagnetite (yellow)rock-saltandcubicspinelcrystalunitcells (seetext fordetails).Representativereal space images of the (220) atomic lattice planes (inverse FFT synthesis; filtered from specificplane orientations) for the samples S8 (i), C12 (j), S15 (k) and C18 (l), respectively. Lattice planeshave been colored with red (possible presence of atomic plane) and green (possible absence ofatomic plane) pseudo-chrome acquired after inverse FFT process. Lattice phase contrast imagesobtainedby theGPAmethod (see text) after re-centering thediffraction aroundoneof the (220)reflectionsforsamplesS8(m),C12(n),S15(o)andC18(p).

S8 C12 S15 C18

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Figure3.Experimental atomic xPDFdataat80K for the single-phaseS8,C12andcore@shell S15nanoparticles plotted as a function of the radial distance, r up to 50 Å. The corresponding xPDFpattern for the bulk magnetite, measured under the same exact conditions, is provided as areference material. The line over the data is the best fit based on the cubic spinel atomicconfigurationmodel(Fd-3msymmetry;model#1),andbelowthecorrespondingdifferencebetweenobservedandcalculatedxPDFsforbulkmagnetite.

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Figure4.RepresentativexPDFfits(T=80K)ofthe“low-r”regionfor(a)thebulkmagnetiteassumingthecubicspinelatomicconfiguration(Fd-3m,model#1;a=8.3913(2)Å,Rw=9.6%),(b)thesingle-phase S8 nanoparticle sample with the same cubic model (Rw= 18.1 %), (c) the two-phase S15nanoparticlesamplewiththecubicrock-saltandspinel(Rw=13.6%)crystallographicmodels,and(d)the single-phase S8nanoparticle sample in the tetragonal (P43212,model #3; aSp=bSp=8.4052(1)Å,cSp=8.1951(1)Å,Rw=7.5%)crystallographicconfiguration(seetextfordetails).Thebluecirclesandredsolid linescorrespondtotheobservedandsimulatedatomicPDFsrespectively.TheblacksolidlinesbelowarethedifferencecurvesbetweenobservedandcalculatedPDFs.Thequalityoffitfactor(Rw) isgiven inbracketsforeachcase.VerticaldashedlinesmarkthepositionsoftypicalFe-OandFe-Febonddistances;TdandOhrepresenttetrahedralandoctahedralcationsites,respectively.

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Figure 5. (a) Adequately normalised, observed G(r) patterns (T= 80 K) of the low-r region for allnanoparticle samples (single-phase, S8 & C12 and two-phase, S15) compared against the bulkmagnetiteand(b)thesimulatedxPDFpatternsonthebasisofthesymmetry-lowering(tetragonal)atomic configuration. As a proof of concept, the optimally chosen set ofmodels assumes a sub-stoichiometricOhFe-siteoccupancy(η;keptconstantat75%,anaverageoccupationderivedfromrefinementsoftheG(r)dataacrossthesamples),whiletheTdFe-siteoccupationlevelwasvariedinastep-wisemanner(60<η<100%).VerticaldashedlinesmarkthemodificationofthedistributionoftheFeOh-FeOh(r∼3.0Å)andFeOh-FeTd(r∼3.5Å)separationsfrombulktonanoscalesamples.

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Figure6.Thetemperatureevolutionofthezero-fieldcooled(ZFC;solid lines)andfield-cooled(FC;dotted lines) susceptibility curves for the single-phase S8 (a), C12 (b) and core@shell S15 (c)nanoparticlesunderamagneticfieldof50Oe.OrangeandgreendashedlinesindicatetheVerwey(TV) and Néel (TN) related transition temperatures anticipated for bulk, stoichiometric Fe3O4 andFexO,respectively;thearrowsmarktheobservedTVandTNvalues.Partofthenormalizedhysteresisloops (M/MS) at 5 K for the single-phase S8 (d), C12 (e) and the core@shell S15 (f) nanoparticlestakenunderzero-andfield-cooled(Hcool=5T)protocols.Thepanelsbeneaththeloopspresentthedifferentialchange (dM/dH)of thenormalized, isothermalmagnetizationwhen it is switched frompositivetonegativesaturation.Insets:theM(H)loopsbetween-50<H<+50kOe.

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Figure7.Theexperimentallydeterminedexchange-bias(HEB;opensymbols),coercivefield(HC;half-filledsymbols),low-fielddemagnetization(ΔM/MS;colouredhatchedsymbols,righty-axis-red)andMr/MS (Mr,remanence:stars,righty-axis-black)obtainedatvaryingcooling-fieldstrengths(Hcool).Plotsymbols:circularforsphericalcore-shell(S15)nanoparticles,triangular(S8)anddiamond(C12)forsingle-phasesphericalandcubicshapenanoparticles.

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Figure8.MonteCarlocalculations(Hcool=5JFM/gμB)oftheeffectofpinningbonds(vacancy-driven)onthelow-fieldmagneticmomentswitching(ΔM/MS;filledsymbols,leftaxis)andtheexchange-bias(HEB; open symbols, right axis) of self-passivated FexO-Fe3O4 nanocrystals with differentmorphologies.Plotsymbols:circularforsphericalcore-shell(S15)nanoparticles,triangular(S8)anddiamond(C12)forsingle-phasesphericalandcubicshapenanoparticles.

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Figure9.MonteCarlo(MC)simulationoftheM-H loopsmadeafterfield-cooling(Hcool=5JFM/gμB),andbyassuminganuppermaximumfractionofpinningbonds,as thiswas identifiedby thexPDFrefinements.Snap-shotsofthespin-ensembleduringM-HloopcalculationforasmallferrimagneticsphericalnanoparticleofR=5latticeconstants:(a-c)afullyoxidized,defectednanocrystal(S8),and(d-f)adefect-freecase,assumingacore-surfacetypeofMCmodel.Spinconfigurationsareshowninthezy-plane(x=–1)forpositivefield(H=+8JFM/gμB)magnetizationsaturationandafterfieldreversal(H=–0.2JFM/gμB,H=–2.0JFM/gμB)towardsnegativesaturation.Thearrowcolor-codingstandsfor:core (red), surface (blue),defects (black)magneticmoments. (g)SpecificAbsorptionRate (SAR)ofsmall defected (S8) versus defect-free nanoparticles on the basis of susceptibility losses (AC fieldamplitude,H0and f= 500 kHz), calculated according to the Linear Response Theory of amodifiedNéel-BrownrelaxationMonteCarlomodel.

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