Graphene-mediated exchange coupling between magnetic molecules and substrates:

a DFT view

Valerio BelliniCentro S3, Istituto Nanoscienze, CNR, Modena, Italy

Organic spintronics, spinterface and molecular spintronics

Non-magneticorganicmolecules Magneticsolidstatesystems

N.Atodireseietal.,Phys.Rev.Letters105,066601(2010)

The molecule-surface interaction couldbe exploited to tune the magneticpropertiesofthesubstrate.(Spinterface).E.g.H2Pcon2MLFe/W(110)

Organic layers can be employed to act astunneling barriers, but the spins resides instandard solid state leads (Organic spintronics).E.g.LSMO/Alq3/Co.

Z.H.Xiongetal.,Nature427,821(2004)

V.Dediuetal.,SolidStateCommun.122,

181(2002)

Weareinterestedinthecasewherethemoleculeitselfcontainsoneormore(native)magneticcenters,i.e.magneticmolecules

Why magnetic molecules?

• Magneticmoleculescanbethepenultimatelimitinthelowdimensionofamagneticdomain where to store binary information (0/1 = up/down) (the ultimate limit isrepresentedbysingleatomsorvacancies).

• Several advantages over “standard”magnetic nanoparticles, e.g.monodispersity isensuredbychemicalsynthesis.

• Themagneticpropertiesofthemoleculescansurvivetheevaporationprocessunderhigh-vacuum (molecular functionalization to toughen the molecule) and theinteraction with the surface (low-interacting substrates as Au or electronicdecouplinglayersareconsideredforthispurpose).

• Theycanself-assemblyonopportunesubstrates,offeringorderedarraysofmagneticunitsthatcan,inprinciple,beaddressedsingularlybylocalprobes.

• Thegoalistobuildfunctionalhybridorganic-inorganicdevices,onewouldideallybeable to switch themagnetic properties of themolecule or themolecule-substrateinteraction by external stimuli, e.g. electric or magnetic field, electronic current,electromagneticradiation,mechanicalorchemicalmanipulations.

Molecular magnetic (q)bits: some examples

Purelyorganicradicals Singlemolecule/chainmagnets

Lowspinmagneticmolecules2D/3Dmagneticmetalorganicnetworks

• Open-shell(neutral)molecules• Isotropicmagneticproperties

becauseofsmallspin-orbit

• Largespin(orbital)moment• Largemagneticanisotropy• Magneticstorage,spinvalves

• PredominantlyAFMinteractions• Small (or no, i.e. S=1/2 Kramer

doublet)magneticanisotropy• Q(uantum)bits,QuantumGates

• Spin-filteringlayer• Interplay between magnetic and

(semi)conductingproperties

Cobaltocene(CoCp2)

Tbdoubledecker(TbPc2)

Single ion magnetic molecules

Fephthalocyanine(FePc)

PRB88,144407(2013). JCPC118,17670(2014).

ACSNano4,7531(2010);Sci.Rep.6,21740(2016);ACSNano10,9353(2016).

MPcmagneticbuttons,M=4d,5d

ToappearinSci.Rep.(2017)

TbPc2-based molecular spintronics devices

Spintronicsdevicesobtained integratingTbPc2moleculewithcarbon-based leads (graphenedots,nanotubes)havebeenalreadypresentedintheliterature.

SpinvalveField-effect(spin)transistorA.Candinietal.,

Nanoletters11,2634(2011)M.Urdampilletaetal.,

NatureMaterials10,502(2011)

MorerecentlyithasbeendemonstratedthatthenuclearmagneticstatesoftheREioncouldbemeasuredandmanipulated[Science344,1135(2014);ACSNano9,4458(2015)].

The substrate’s choice: do we want interaction or not?

TbPc2onMgO

TbPc2onFMNi

C.Wackerlinetal.,Adv.Mat.28,5195(2016)

A.LodiRizzinietal.,Phis.Rev.Letters107,177205(2011)

TbPc2onAFMMnandCoO

A.LodiRizzinietal.,Nanoletters12,5703(2012)

Ln double decker (LnPc2)

• Ln3+valence+2Pc2-:electronunbalance• Ln4fmagneticmoment.• s=1/2 spin radical delocalized over thetwoPcs.

Verystable.It could be functionalized to improvegraftingonsurfaces(pyrene).Strong spin-orbit coupling, that leads tosingle-magnetbehavior.It has been demonstrated to work as amolecularbit(qbit)intransistorandspin-walvegeometries.Its nuclear magnetic states could beaddressed.

a dream for experiments…

Itisaratherlargemolecule(113atoms).It contains a rare-earth ion, and theimportantphysicsisonthe4forbital.Inneutral form, it has a localized inorganic(4f)andadelocalizedorganic(radical)spins,thatmustbeaddressatthesametime.Thereisnotmuchwork intheliteraturebyDFTtocomparewith.Multiple spins means multiple magneticstates:CDFTneeded!

…a nightmare for DFT!

IshikawaInorg.Chem.43,5498(2004)

Theoretical approach and some (few) technical details

Computationaldetails

• Density-functionaltheory(DFT)calculations,GGA(GGA+U)functionals.• PAWpseudopotentials(precisionhigherthanstandardpseudo≈all-electronmethods)• Nospin-orbitcouplingisincluded,i.e.welookatisotropicexchangeonly.• Grimmedispersioncorrectionshavebeenaddedtodescribemoreaccuratelythemolecule-surfaceinteraction(DFT-D2,DFT-D3).

• The surface is simulated by a finite size slab, typically composed of 5-6 monolayers(magneticmomentinthecenterhastobebulk-like).

• Structuralrelaxationsofthemoleculeandtopsurfacelayer(nodynamics).• Extractionof themolecule-surfaceexchangeenergies required, despite the large in-planecell,asamplingontheK-pointsinthe2DBrillouinzone(2x2).

• SupercomputersattheCINECAcenter(Bologna)andHLRN(Hamburg)havebeenemployed.

TbPc2: Wien2k vs Quantum Espresso, LDA+U

Wien2K QuantumEspresso

AllElectron PAWpseudopotential

Ingas-phasecalculations,avalueofU=9eVandJ=1eVhasbeenconsidered,followingtheworkofLarsonetal.,Phys.Rev.B75,045114(2007)onrare-earthnitrides.

ForthemoleculesonsubstratesthelinearresponsemethodofCococcionietal.[Phys.Rev.B71,035105(2005)]hasbeenused,andwehavefoundavalueofU=6eV.

LnPc2, Ln=Tb, Dy, Er in the gas phase: a DFT view

LDOSanalysis

A.Candinietal.,“Spin-communicationchannelsbetweenmolecularnanomagnetsandamagneticsubstrate:thecasestudyofLn(III)bis-phthalocyaninesonNi(111)surface”,ScientificReport6,21740(2016).

Spindensity

• 5dorbitalson the Ln ions gets spinpolarizedduetothepresenceofthe4fmoment.

• They are more extended in space and thisleadstoanhybridizationwiththeN2porbitalsin the Pcs (see for instance peaks at -3.5eVand-2.5eV)

4f-Pcinteractionsisbridgedbythe5dorbitals

XMCD experiments of LnPc2, Ln=Tb, Dy, Er on Ni(111)

XMCDanalysisforTb

The magnetization could be fitted considering adirectTb-NiAFMexchangeterm.

A.Candinietal.,“Spin-communicationchannelsbetweenmolecularnanomagnetsandamagneticsubstrate:thecasestudyofLn(III)bis-phthalocyaninesonNi(111)surface”,ScientificReport6,21740(2016).

Theintensityofthemagneticcoupling(AFM)behavesasthespinpolarizationofthe5dorbitaloftheLnion.

Ni(111):eithersinglecrystal(magneticmultidomain)orthinfilmsonCu(singlemagneticdomain,differentanisotropyvs.thickness).

XMCD results in agreement with otherexperiments of TbPc2 on Ni thin films onCu(100) and Ag(100) substrate [Lodi Rizzinietal.,Phys.Rev.Letters107,177205(2011)]

Existence and interaction of the spin-radical

Schwoebeletal.,Nat.Commun.3,953(2012)spinpolarizationofLUMObySTS/STM

FMcouplingoftheorderof0.3T.(0.03meV)

Urdampilletaetal.,ACSNano9,4458(2015)

• Which is thesizeandsignofthecoupling with the Ln ion? Is itinfluencedbytheenvironment?

• Does the spin radical in the PcALWAYS survive when themolecule is adsorbed on thesurface?

• Ln4fmagneticmoment.• s=1/2spinradicaldelocalizedoverthetwoPcs.

TbPc2 on Ni(111): DFT results

TbPc2isolatedmolecule

Thechargetransferissolargethatthespinradicaliscompletelyquenched.Initssteadaspinpolarization takes place at the lower Pc plane due to contact interaction with the Ni(111)substrate,itchangessignmovingfromanatomtoanother,andithasanextrinsicnature.

TbPc2/Ni(111)

Sohowdoesthe4fspininteractwiththeNimagnetization?

Let’sseewhathappensifwefliptheTbmagneticmoment

NotethedifferentcolorsontheatomsonthelowerPcplane!

TbPc2 on Ni(111): DFT results

TbPc2 on Ni(111): DFT results

TbPc2 on Ni(111): DFT results

The spin polarization on the lower Pc is pinned to the Ni substrate. If Tb spin is reversed, amodification in the polarization of theN atoms takes place, the interactionwith the remnantspinpolarizationinthePcplane,resultsintoadifferentenergy,i.e.magneticinteraction!

Note that a spin polarization, but no radical, has been also found in the STMexperiments of,Schwoebeletal.,Nat.Commun.3,953(2012),forTbPc2onCo/Ni(111)!!!

The graphene/Ni(111) substrate

top-fcc top-bridge

W.Zhaoetal.,J.Phys.Chem.Letters2,759(2011)

HR-XPS (200K)showsthattop-fcc is themostabundant stacking (60%), while top-bridge isthe second most abundant one. DFTcalculationsalsoshowthattop-fccandbridgetoparethelowestenergyconfiguration.

Itgetsspin-polarizedbycontactwithNi

dGr-Ni=2.1Å

GraphenegrowspseudomorphicallyonNi(111)andlatticemismatchisminimal(1.2%)

• Graphene-passivatedNickelasoxidation resistantelectrode forSpintronics [B.Dlubaketal.,ACSNANO6,10930(2012)]

• Graphenelayerasanelectronicdecouplinglayer[J.Choetal.,NanoLett.12,3018(2012)]• Itallowsmagneticcouplingbetweenmagneticlayers[V.M.Karpanetal.,Phys.Rev.Lett.99,

176602(2007)]

TbPc2 on Ni(111) and Graphene/Ni(111)

Chargetransferisreducedto0.75e-fromthemoleculeto the surface, and the spin radical is partiallyquenched (from 1.00𝜇B to 0.25𝜇B). It has an intrinsicnature, thatmeans that it couldbestabilized inboththespindirection.

TbPc2isolatedmolecule

The charge transfer is so large that the spinradical is completely quenched. In its stead aspin polarization takes place at the lower PcplaneduetocontactinteractionwiththeNi(111)substrate, it changes signmoving from an atomtoanother,andithasanextrinsicnature.

TbPc2/Ni(111) TbPc2/Graphene/Ni(111)

ThePcspinradicalsurvivestheinteractionwiththesubstrateandshouldthusbeconsideredwhenfittingXMCDmagnetizationdatabyspin-modelHamiltonian!

Spin model Hamiltonian: Tb radical Ni

Threespinsystem:Tb,Pcspinradical,Nimagnetization

Themagneticcouplingcouldberationalizedasduetoarelay-likeexchangemechanism,i.e

Tb-radical+radical-Ni

,

Asafurthereffortwetriedtoreducethenumberoffitting parameters, obtaining either Jexch or K bycalculations.

• CASSCFfindsJexch=−0.24meV(FM),andthefittoXMCDmagnetizationdataleadstoK=+0.22meV(AFM).

• DFTcalculationsfindsK=−45meV(FM),andthefitleadstoJexch=+0.03meV(AFM)

AFMcouplingbetweenTbandNiisobserved

S. Marocchi et al., “Relay-like exchange mechanism through a spin radical between TbPc2 molecules andgraphene/Ni(111)substrates”,ACSNano10,9353(2016).

Pc rotation upon quenching of the radical

36°41°

TbPc2/Graphene/Ni(111) TbPc2/Ni(111)

Komedaetal.,NatureCommunication2,217(2011)

Our results are fully compatiblewiththeonesshowninapreviouspaper on STM measurements ofTbPc2/Au(111)

Cobaltocene(CoCp2)

Tbdoubledecker(TbPc2)

Single ion magnetic molecules

Fephthalocyanine(FePc)

PRB88,144407(2013). JCPC118,17670(2014).

ACSNano4,7531(2010);Sci.Rep.6,21740(2016);ACSNano10,9353(2016).

MPcmagneticbuttons,M=4d,5d

ToappearinSci.Rep.(2017)

Cobaltocene(CoCp2)

Tbdoubledecker(TbPc2)

Single ion magnetic molecules

Fephthalocyanine(FePc)

PRB88,144407(2013). JCPC118,17670(2014).

ACSNano4,7531(2010);Sci.Rep.6,21740(2016);ACSNano10,9353(2016).

MPcmagneticbuttons,M=4d,5d

ToappearinSci.Rep.(2017)

Structural, electronic spin and states of metalloces

Structural, electronic spin and states of metalloces

metallocenemolecule,MCp2,M=V,Cr,Mn,Fe,Co,NiCp=cyclopentadienyl,C5H5

MCH

dz2

dxy , dx2-y2

dxz , dyz

S = 3/2 1 1/2 0 1/2 1

Y. Li, et al., Phys. Rev. B, 83, 195443 (2011)

CoCp2 is the member which more strongly binds, i.e. Eads = 0.2 eV (physysorption) to graphene, and that shows largest charge transfer to graphene, i.e. Q=0,28 e-

Trends in charge transfer between metallocenes and unsupported graphene

K.-F. Braun, et al., PRL 96, 246102 (2006)

B. Heinrich, et al., PRL 107, 216801 (2011)

FeCp2 on Au(111)

FeCp2 on Cu(111)

Dissociation!

NO Dissociation!

J. Choi et al., Surf. Sci. 600, 2997 (2006) CoCp2 on Cu(111)

Dissociation!

CoCp2 vs. FeCp2 -  additional electron occupies the anti-

bonding orbital. -  H-L energy gaps is smaller. CoCp2 has larger chemical reactivity (used

as redox agent in catalysis)

Experiments on metallocenes on metallic substrates

ButFeCp2isnotmagnetic!

WhataboutCoCp2?

In this case the presenceof a graphenedecouplinglayermightbecriticaleventopreservetheintegrityofthemolecule!

Top-Fcc Bridge-Top

HOMO 2B2 HOMO 2A2 Hollow

Top

Bridge 1

Bridge 2

a)

b)

c) dyz dxz

Unit cell: cobaltocene on graphene deposited on a 4 layer thick Ni (111) slab. Structural characterization follows three lines: a) Molecule conformation b) graphene stacking c) preferred adsorption site

CoCp2 on graphene/Ni(111) substrate

S.Marocchi,P.Ferriani,N.M.Caffrey,F.Manghi,S.HeinzeandV.Bellini,“Graphene-mediatedexchangecouplingbetweenamolecularspinandmagneticsubstrates”,Phys.Rev.B.88,144407(2013).

CoCp2 on graphene/Ni(111) substrate

(meV) (meV) (Å) Configuration

ΔE = Energy difference with respect to GS d = Co-graphene distance (dCo-Ni=d+2.1Å)

Eex= E( ) – E( )

The magnetic coupling is AFM and of around 10 meVs. It is not that small! dCo-Ni = 6.4Å !!!

P.S. FeP on Co/Cu: Eex≈ 50meV (dFe-Co=3.4Å)

Top-Fcc

2B2

hollow

CoCp2 on graphene/Ni(111) substrate

(meV) (meV) (Å)

The extension of the magnetic orbital of Cobaltocene is clearly a critical factor in determining the magnetic coupling

Configuration

dyz dxz

HOMO

2B2 2A2

ΔE = Energy difference with respect to GS d = Co-graphene distance (dCo-Ni=d+2.1Å)

Eex= E( ) – E( )

CoCp2 on graphene/Ni(111) substrate

(meV) (meV) (Å) Configuration

The stacking of graphene is not critical. That’s surprising since: •  mC-top = - 0.02 μB mC-fcc = + 0.03 μB •  mC-bridge = +0.002 μB

The coupling does not depend on the size of the magnetic moment induced on graphene

Top-Fcc Bridge-Top

ΔE = Energy difference with respect to GS d = Co-graphene distance (dCo-Ni=d+2.1Å)

Eex= E( ) – E( )

CoCp2 on graphene/Ni(111) substrate

(meV) (meV) (Å)

ΔE = Energy difference with respect to GS d = Co-graphene distance (dCo-Ni=d+2.1Å)

Eex= E( ) – E( )

Variation in the adsorption site leads to some variation in the coupling.

The coupling in all the above cases is

ANTIFERROMAGNETIC

Configuration

dyz spin-polarized HOMO is pinned at the Fermi level. Only a small shift is observed upon adsorption of CoCp2

Clear hybridization between the C sp-states of graphene and the d states of Ni! Hybridization around the Fermi level is more effective for the C atom on the fcc position and involves both dz2 and dxy/dx2-y2 Ni states.

In general, electronic or magnetic coupling between two orbitals is re levant i f energy and spat ia l overlapping is effective. In our system AFM coupling is favored

Exchange mechanism revealed by LDOS analysis

1 monolayer of Fe or Co is intercalated below graphene.

[Intercalation has been demonstrated experimentally, and it’s a way to avoid the difficulties of growing graphene on metals, see rev. of M. Batzill, Surf. Sci. Rep. 67, 84 (2012)]

Ni slab

Fe/Co ML

Graphene

WHY?

NièFeèCo progressive depopulation of the minority spin leads to smaller DOS at EF and larger spin moment.

(meV)

Tuning of the magnetic coupling by intercalation

Cobaltocene(CoCp2)

Tbdoubledecker(TbPc2)

Single ion magnetic molecules

Fephthalocyanine(FePc)

PRB88,144407(2013). JCPC118,17670(2014).

ACSNano4,7531(2010);Sci.Rep.6,21740(2016);ACSNano10,9353(2016).

MPcmagneticbuttons,M=4d,5d

ToappearinSci.Rep.(2017)

Cobaltocene(CoCp2)

Tbdoubledecker(TbPc2)

Single ion magnetic molecules

Fephthalocyanine(FePc)

PRB88,144407(2013). JCPC118,17670(2014).

ACSNano4,7531(2010);Sci.Rep.6,21740(2016);ACSNano10,9353(2016).

MPcmagneticbuttons,M=4d,5d

ToappearinSci.Rep.(2017)

Molecular Button

J.Am.Chem.Soc.131,3639(2009)

Shuttlecockgeometry

Sn

SnPc

Transient oxidation by STM current (via hole injection)induces a Sn2+➜ Sn3+ transition, reducing the Sn ionicradius, and promoting the switching between the twostructuralconformationsofaSnPcmoleculeonAg(111).

Switching can be irreversible or reversible dependingwhethertheSnPmoleculeisdirectlyadsorbedonAgorifitisadsorbedonabufferlayerofSnPcmolecules.

Constant-currentSTMimagesat7K

Let’s make it magnetic!

Requirements: ItmustcontainanelectronicmagneticmomentItmustpresenttwostablestructuralconformations

Let’s make it magnetic!

Magneticionsbelongtothe3d,4dor5dseries,ortothe4fseries

Let’s make it magnetic!

Afirstskimmingcanbeobtainedsimplyrealizingthat3dionaresmallenoughtobeaccommodatedwithinthePcplane,andthat4fionsaresolargethatthemoleculeisstabilizedonlybysandwichingitbetweentwoPcplanes(e.g.TbPc2)

Let’s make it magnetic!

A second skimming can be obtained by some systematics aimed to find outwhether the ion is accommodated in thePcplaneor if it is pushedoutof ituponstructuralrelaxation.Weareleftwith4candidates.

Energy barrier for MPc, where M=Zr, Nb, Hf, Ta

Redcurves(rightscale)depicttheTMmagnetic moment (Lowdin charges).Nominally it isS=1/2 (1𝜇B) for1st rowionsandS=1(2𝜇B)for2ndrowions.

Black curves (left scale) depict theenergybarrier, calculatedmoving theTM ions along theperpendicular to aflatPcmolecule.

Outward relaxations d amounts to0.4-0.7Å,whileenergybarriersrangesfrom0.35to1.1eV.

Spin(polarizedcharge)density

Total spin of themolecule is S=1 forZrPc/HfPcandS=3/2forNbPc/TaPc

Cu111

Effect of the molecule-substrate interaction on the energy barrier between the two conformations

NbPcmoleculeadsorbedonCu(111)surface

∆zinthex-axisofthefigureisthedisplacementoftheNbionfromtherelaxed‘up’conformationtowardsthesurface.

∆z

Cu111

Effect of the molecule-substrate interaction on the energy barrier between the two conformations

NbPcmoleculeadsorbedonCu(111)surface

∆z

∆zinthex-axisofthefigureisthedisplacementoftheNbionfromtherelaxed‘up’conformationtowardsthesurface.

Cu111

Effect of the molecule-substrate interaction on the energy barrier between the two conformations

NbPcmoleculeadsorbedonCu(111)surface

∆z

∆zinthex-axisofthefigureisthedisplacementoftheNbionfromtherelaxed‘up’conformationtowardsthesurface.

TheinteractionwiththeCu(111)substratequenchesthebarrieranddestroythebistability

ZrPc on Graphene/Ni(111)

ZrPc(HfPc)attainsabistablestructuralconformationongraphene/Ni(111).Inthe‘up’case,anintrinsicmagneticmomentpersistsinthemolecule,anditcouplesAFMwiththeNisubstrate(∆E=-16meV).In the ‘down’ case, the Zr spin is quenched and a spin polarization isinducedonthePcligand.

Energy barrier by Nudge Elastic Band (NEB) method

• The‘down’conformationis1.5eV(ZrPc)-1.8eV(HfPc)morestablethanthe‘up’one☞Stillratherstronginteractionwiththesubstrate!

• IntheHPccasethe‘up’to‘down’transitionseesabarrierof0.1eVwhichmightnotbesufficienttopreservethe ‘up’state instandardexperimentalconditions,while intheZrPccasethebarrierisof0.3eV.

• TheZr(Hf)magneticmomentsisquenchedinthe‘down’state.

Spin density analysis during the ‘up’ to ‘down’ transition

Energy barrier for instant oxidation/reduction

Calculationshavebeendonefortheisolatedmolecule

ForSnPc,abarrierof2.5eVwascalculated,thatcouldbediminished upon reduction(-1e-)to1.5eV.

The ZrPc (HfPc) shows two stablestructural conformation, with differentmagnetic properties, and the energybarrier between them could be modifiedbyinstantreduction/oxidation.

Molecularmagneticbutton

COLLABORATORS

AndreaCandini,MarcoAffronte,ValdisCorradini,ValentinadeRenzi,RobertoBiagi,UmbertodelPennino,HeikoWende(Duisburg-Essen),MarioRuben(Karlsruhe)

SimoneMarocchi,FilippoTroiani,FrancaManghi,AlessandroSoncini(Melbourne),PaoloFerriani,StefanHeinze(Kiel)

MAGMANET(NoE),MolSpinQIP(STREP),THE-SIMS(ProgettodiInternazionalizzazioneCassadiRisparmiodiModena),MOQUAS(FETProactive)

FUNDINGS

EXP

THEORY

Thank you for your attention!