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InteractionbetweenasingleInteractionbetweenasingleInteractionbetweenasingleInteractionbetweenasingleInteractionbetweenasingleInteractionbetweenasingleInteractionbetweenasingleInteractionbetweenasingle--------moleculemoleculemoleculemoleculemoleculemoleculemoleculemoleculemagnetMnmagnetMnmagnetMnmagnetMnmagnetMnmagnetMnmagnetMnmagnetMn1212121212121212 monolayerandagoldsurfacemonolayerandagoldsurfacemonolayerandagoldsurfacemonolayerandagoldsurfacemonolayerandagoldsurfacemonolayerandagoldsurfacemonolayerandagoldsurfacemonolayerandagoldsurface
KyungwhaKyungwhaKyungwhaKyungwhaKyungwhaKyungwhaKyungwhaKyungwha ParkParkParkParkParkParkParkPark
DepartmentofPhysics,VirginiaTech
SalvadorSalvadorSalvadorSalvadorSalvadorSalvadorSalvadorSalvadorBarrazaBarrazaBarrazaBarrazaBarrazaBarrazaBarrazaBarraza--------LopezLopezLopezLopezLopezLopezLopezLopez (postdoc)
MichaelC.AveryMichaelC.AveryMichaelC.AveryMichaelC.AveryMichaelC.AveryMichaelC.AveryMichaelC.AveryMichaelC.Avery (undergraduate)
SupportedbyJeffress MemorialTrustFund
NCSAclusters,VirginiaTechSystemX,VTclusters
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OutlineOutline Whataresingle-moleculemagnets(SMMs)?
Motivation Methodology:density-functionaltheory(DFT)
Reviewof ro ertiesofisolatedSMMMn
SMMMn12 depositedonagoldsurface
- Methodandmodel
- Changesinelectronicstructure(orbitalbroadening,chargetransfer)- Changesinmagneticproperties
BeyondDFT:effectofHubbard-likeUterm
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WhataresingleWhataresingle--moleculemagnets?moleculemagnets?Mn12Volumeofonemolecule:afewnm3
Singlemolecule:severaltransitionmetalionsstronglycoupledvialigands S=10
1.5nm
T.LisActaCryst.
Behavesassingle-domainmagneticnanoparticle
Largespinwithlargemagnetization
O CNClMn3+
Mn4+Mn4
S=9/2
B36,2042(1980)
D.HendricksonJ.Am.Chem.Soc.114,2455(1992)
Canformsinglecrystals(differentmoleculesarewellseparated)
Examples:Mn12,Mn4,Fe4,Fe8,Co4,
Ni4,cyanide-bridgedmolecules,Mn84torus,etc.
C&Enews,Dec13,2004
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Fe8
Mn84 torus
Mn5N3
Wieghartetal.,Angew.Chem.Int.Ed.Engl.23,77(1984)
S=6
S=10 S=11
SingleSingle--moleculemagnetsmoleculemagnets
Tasiopoulosetal,Angew.Chem.Int.Ed.43,2117(2004)
Lietal.,Inorg.Chem.44,4903(2005)
C.-I.Yangetal.,J.Am.Chem.Soc.129,456(2007)
S=3
Fe2Ni2
Single-chainmagnetMn-Ni-Mn unit
Coulonetal.,PRB69,132408(2004)
S=3
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MagneticAnisotropyBarrier&EasyAxisMagneticAnisotropyBarrier&EasyAxis(magnetizationreversalbarrier)
Energy
BarrierBarrierBarrierBarrier
ClassicalClassicalClassicalClassical
easyaxis
QuantumQuantumQuantumQuantummechanicalmechanicalmechanicalmechanical
0;2 >= DDmEnergy sSpinprojectionms
====
forB=0causedbyspin-orbitcoupling
EasyaxisEasyaxisEasyaxisEasyaxis"up""up""up""up""up""up""up""up""down""down""down""down""down""down""down""down"
Energ
Energ
BarrierBarrierBarrierBarrier
e.g.Mn12:Barrier=60K
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MagnetichysteresisMagnetichysteresis:essenceofquantumtunneling
Mn12 (S=10)at1.9K
0.04T/s
tobs=500sperdatapoint
On resonance
down up
Steps:tunnelingon
Plateaus:
MsIngroundstate
B.Barbaraetal.,J.Phys.Soc.Jpn.(2000);J.Friedmanetal.,PRL(1996);L.Thomas
etal.,Nature(1996)
Classicalferromagnetsat300K
unne ngo
down
Off resonance
up
HHHHLLLL (T)(T)(T)(T)
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AnotherevidenceofquantumtunnelingAnotherevidenceofquantumtunneling
Timedependenceofmagnetizationbecomesindependentoftemperature
(T)asT
0 =0 exp(U/kBT),
1
0 )]/[log(
C.Paulsenetal.,J.Mag.Mag.Mat.(1995)
A.Caneschietal.,Nature(1993)
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Magneticmeasurement:PropertiesofMn12monolayersdifferfromthoseofbulkMn12
Naitabdi et al., Adv. Mater. 17. 1612 (2005)
Salman et al., Nano Lett. (2007)
Motivation:deviceapplicationsMotivation:deviceapplicationsDepositionofSMMsonagoldor
siliconsurfaceSteckel et al., Nano Lett. (2004); Zobbi et al,
Chem. Comm. (2005); Fleury et al., Chem.
Comm. (2005).
PhotoemissionspectraonMn12monolayers:Mn12 dorbitalsinvalence
STMimage
an sares m ar o ose or u n12
delPenninoetal.,Surf.Sci.(2006);Vossetal.,PRB(2007)
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Motivation:deviceapplicationsMotivation:deviceapplicationsElectronictransportmeasurementsthroughSMMMn12
- Joatel.NanoLett(2006)- Hendersonetal.,J.Appl.Phys.(2007)
TheoriesontransportthroughSMM:- G.H.KimandT.S.Kim,PRL(2004).- Romeikeetal.PRLs(2006)
- ElsteandTimm,PRB(2005),PRBs(2006)
- LeuenbergerandMucciolo,PRL97,126601(2006).
- MisiornyandBarnas,cond-mat/0706.2315
Nofirst-principlescalculationsonSMMsdepositedonasurfaceorbridgedbetween
electrodes
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Interactingmany-electronproblem:H=Ewhere =(x1,y1,z1,...,xN,yN,zN)
H=Hkin +Hn-e +He-e
Cost:M3N forMxMxMgrids
30
HowtosolvemanyHowtosolvemany--bodyproblemsquantumbodyproblemsquantum
mechanicallyusingDensitymechanicallyusingDensity--FunctionalTheory(DFT)FunctionalTheory(DFT)
. . ,
Nnon-interactingsingle-electronproblems:Hi=ii wherei=i (x,y,z)
H= whereVeff(r)isaneffectivepotential
Cost:NM3 forMxMxMgrids
(e.g.:10x103 forN=10,M=10)
)(V2/ eff2 r
r
+
DFT
Totaldensityofelectronsisthe
same
Kohn&Pople(1998,Nobelprize
inchemistry)
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HowtodoelectronicstructurecalculationsHowtodoelectronicstructurecalculations
Initialassignment(geometry,totalcharge,spinconf.,totalmoment)
PlaceGaussiansoneachatomasabasissetforanatomicwavefunction
SolveNnonnonnonnon----interactinginteractinginteractinginteracting one-electronequations
])(exp[)(2
kkkk RrfCr
r
rr
=
Veff(r)=Vnucl+VH[(r)]+Vxc[(r)]
iiir =+ )](V2/[ eff2 rEnergyisEnergyisEnergyisEnergyis
converged?converged?converged?converged?
Calculateforces,(r),geometry
Forceissmall?Forceissmall?Forceissmall?Forceissmall?Geometry
isoptimized!
YESYESYESYESYESYESYESYES
NONONONO
NONONONO
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MnMn1212: [Mn12O12(O2CCH3)16(H2O)4]
1.5nmT.LisActaCryst.B36,2042(1980)
y
x
Experimentaldata
Mn4+
Mn3+
O
Totalground-state spin:S=8x2 4x3/2=10
Singlemolecule:S4 symmetry
4Mn4+ (3d3,S=3/2)ionsincube
8Mn3+ (3d4,S=2)ionsinoutercrown
Easyaxis:zaxis
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Electronicstructure&MagneticanisotropyElectronicstructure&Magneticanisotropy
forisolatedMnforisolatedMn1212M.R.Pederson&S.N.Khanna,PRB60,9566(1999)
All-electrondensity-functionaltheory(DFT)
calculationsusingNRLMOL
Allligandswereincluded
Total round-states inS=10
Mn(I)
[Mn12O12(O2CH)16(H2O)4]
SpindensityislocalizedonMnions
MajorityHOMO-LUMOgap=0.45eV
MinorityHOMO-LUMOgap=2.08eV
(2nd order)magneticanisotropybarrier=55.7K
Mn(II)
Mn(III)
c.f.Expt:55.6K A.Fortetal.,PRL(1998)
NRLMOL:M.R.Pederson&K.A.Jackson,PRB(1990);ibid,PRB(1991);K.A.Jackson&M.R.Pederson,PRB(1990);D.Porezag&M.R.Pederson,PRB(1996)
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HowdoesaHowdoesametalsurfacemetalsurfaceaffectelectronicaffectelectronic
structureandmagneticanisotropyofMnstructureandmagneticanisotropyofMn1212??
goldsurface
ExperimentExperimentExperimentExperimentExperimentExperimentExperimentExperiment
Monolayerof
Considerslabcalculation: Mn12-S2-
goldsurface
~20nm
TheoryTheoryTheoryTheoryTheoryTheoryTheoryTheory
L.Zobbietal.,Chem.Comm.1640(2005).
S.Barraza-Lopezetal.,Phys.Rev.
B(2007).
surface
shortlink
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Method&ModelMethod&ModelSpinpolarizeddensity-functionaltheory(DFT)
UseViennaab-initiosimulationpackage(VASP)
PBEGGAforexchange-correlationpotential
Projectoraugmented-wave(PAW)pseudopotentials[Blchl,PRB(1994);Kresse &Joubert,PRB(1999)]
- All-electronwavefunctions areavailable
- Totakeintoaccountspin-orbitcoupling
- Accuracyisimprovedinmagneticmaterials
Au:s1d10
Mn: 3p64s23d5O:s2p4
C:s2p2
S:s2p4
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NochemicalbondingbetweenAuandMn12 sotwoSatomslink
Mn12 toAuAllligands areincludedinoursimulations
Method&Method&ModelModel(continued)(continued)
Mn12+linker+Auslab:Total2886 valenceelectronsperunitcell
OptimizeAuslabandMn12separatelytocreateawholegeometry
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Computeequilibriumlatticeconstantforbulkgold(4.175)
Withthecalculatedlatticeconstant,weconstructAumonolayers
Checkconvergencewith#ofkpointsandenergycutoffforplanewaves
Au(111Au(111)slab)slab
TocoverMn12,atleast36surfacegoldatomspermonolayerareneeded
Usesixgoldmonolayers (36x6=216goldatomsasatotal)
Relaxgoldslab(w/omolecule)untilmaxforcesarelessthan0.01eV/
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IsolatedSIsolatedS--terminatedMnterminatedMn1212 Mn12 withthelowermostHatomsreplacedbySatoms,isadsorbedonAu
TotalmagneticmomentofS-terminatedMn12 ingroundstate:18181818BBBB(c.f.groundstateofMn12:20B)
H H
ByaddingHbelowsulfur,themagneticgroundstategoesbackto20B
Geometry3Geometry3Geometry3Geometry3
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DensityofStates:Geometry2DensityofStates:Geometry2
SSSSpinpinpinpinpolarizationpolarizationpolarizationpolarization ofsulfurevidentfromthedensityofstates(DOS) HOMO-LUMOgapiscreatedbysulfurpgapiscreatedbysulfurpgapiscreatedbysulfurpgapiscreatedbysulfurp----orbitalsorbitalsorbitalsorbitals
SulfurSulfurSulfurSulfurpppp----orbitalsorbitalsorbitalsorbitalshybridizedhybridizedhybridizedhybridized
withwithwithwithMnMnMnMn dddd----,Op,Op,Op,Op----orbitalsorbitalsorbitalsorbitals
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BuildingBuildingwholewholestructurestructure Unitcell17.7x17.7x34.03
6Aulayers+S6Aulayers+S6Aulayers+S6Aulayers+S6Aulayers+S6Aulayers+S6Aulayers+S6Aulayers+S22222222 +Mn+Mn+Mn+Mn+Mn+Mn+Mn+Mn1212121212121212 (Geo2)+(Geo2)+(Geo2)+(Geo2)+(Geo2)+(Geo2)+(Geo2)+(Geo2)+10vacuum10vacuum10vacuum10vacuum10vacuum10vacuum10vacuum10vacuum
DistancebetweenclosestHatomsinneighboringmolecules:3.35.Interactionsbetweenmoleculesareweak.
Nofurtherrelaxationofthewholestructure
4k-pointsin6x6x1Ausupercell
Chargeprofilewascomputed;chargefromAuslabhasatailgoingallthewaytothelowersectionofmagneticmolecule
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EnergylevelsaroundtheFermilevelandchargeEnergylevelsaroundtheFermilevelandchargetransfertransfer
ThelocationoftheHOMOlocationoftheHOMOlocationoftheHOMOlocationoftheHOMO----LUMOLUMOLUMOLUMO fortheisolatedS-
terminatedMn12,relativetotheFermienergyofbulkAu,determinesthedirectionofdirectionofdirectionofdirectionof
AuAuAuAu Fermilevel
LUMOLUMOLUMOLUMO
c arge rans erc argetrans erc argetrans erc arge rans er, rom u orom utorom utorom u othemagneticmoleculethemagneticmoleculethemagneticmoleculethemagneticmolecule
AuFermilevelisabove
majorityspinLUMObutbelowminorityspinLUMO.
HOMOHOMOHOMOHOMO
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DensityofDensityofstatesstates::WholestructureWholestructure
Uponadsorption,spinspinspinspinpolarizationofpolarizationofpolarizationofpolarizationofSSSSatomsisatomsisatomsisatomsislostlostlostlost
Differentscale
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OrbitalbroadeningOrbitalbroadeningMn12molecularorbitals broadenuponadsorption
Isolated
Orbitalbroadeningismuchlessthanchargingenergy
WeakcouplingWeakcouplingWeakcouplingWeakcoupling
Isolated
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CalculatedspindensityCalculatedspindensity
Topview
Sideview
Red:up Blue:down
SpindensityislocalizedonMn
monoclinicunitcell17.7x17.7x34.03
Mn(I):inner, -2.588B
Mn(II):outer,3.524B
Mn(III):outer,3.543B
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SpatialchangeofmagneticmomentsSpatialchangeofmagneticmoments
2.02.02.02.0
Whole- 2 Fromtheplane-averagedmagneticmomentsalongthez-direction,wefindanincreaseof2B between
theS-terminatedMn12 andthewholestructure
ThewholestructurehasaThewholestructurehasaThewholestructurehasaThewholestructurehasa
Barraza-Lopez,AveryandPark:PRB76767676
224413(2007)
magneticmomentof20magneticmomentof20magneticmomentof20magneticmomentof20BBBB.
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MagneticAnisotropyinSMMsMagneticAnisotropyinSMMs
-ev
z
x
y
Mn
O
)(
2
122LS
========
r
r
rrr
pS
cm
BS
mc
eV
Spin-orbit
coupling
: Coulombpotentialduetoatomicnucleiandelectrons
)(vv ========r
r
r
r
r
EB
Anisotropic
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MagneticanisotropybarrierforSMagneticanisotropybarrierforS--terminatedMnterminatedMn1212
Tocomputemagneticanisotropybarrier,weconsiderspin-orbitcouplinginDFTself-consistently.
AlthoughtotalmagneticmomentdiffersforMn12andGeo.2(S-terminatedMn12),theMABofordinaryMn12isthesameasthatof
H H
Mn12 Geo 2 Geo 3
66.7 66.9 60.7
MAGNETICANISOTROPYBARRIER(K)MAGNETICANISOTROPYBARRIER(K)MAGNETICANISOTROPYBARRIER(K)MAGNETICANISOTROPYBARRIER(K)
eo.
MagneticanisotropybarrierforGeo.3getsreducedbyabout9%
Geometry3Geometry3Geometry3Geometry3
HHHHSSSS
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MagneticanisotropyMagneticanisotropybbarrierforwholestructurearrierforwholestructure
ThespatialchargeandmagneticmomentdistributesinasimilarwayforwholestructureandGeo.3.
So[magneitc ansiotropy barrier(MAB)ofGeo3]=[MABofwholestructure]
2.02.02.02.0
Whole- 2
Whole Geo2Geo3- Geo2
2.0B
Themagneticanisotropybarrierforthewholestructureisreducedby9%ofthatfortheisolatedMn12.
Mn12 Geo 2 Geo 3 Whole
66.7 66.9 60.7 60.7
MAGNETICANISOTROPYBARRIER(K)MAGNETICANISOTROPYBARRIER(K)MAGNETICANISOTROPYBARRIER(K)MAGNETICANISOTROPYBARRIER(K)
Additi l i l i fAdditi l i l i f l tl t l tl t
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Takesintoaccounttheorbitaldependenceofstrongon-sitecorrelations(inLSDAorinGGA),whichisabsentinstandardDFT.
Hubbard-likeUtermplaysimportantroleforlocalizedd- orf-electrons.
d- orf-orbitals aremorelocalizedandenergygapincreases.
AdditionalinclusionofAdditionalinclusionofelectronelectron--electronelectron
correlations:LSDA+Umethodcorrelations:LSDA+Umethod
ValueofUterm:dependsonlocalenvironments,determinedbyexperimentorstandardDFTcalculationsbyvaryingtheoccupancyofd-orf-orbitals.
V.I.Anisimov etal.,PRB 44444444,943(1991)V.I.Anisimov etal.,J.Phys.:Condens.Matter9999,767(1997)
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Effectofcorrelation:GGA+UEffectofcorrelation:GGA+U
Electronic
level (eV)U=6* PBE GGA
Mn12HOMO
Mn12LUMO
-6.13 -7.04
-4.78 -4.77
-5.08 -6.45
-4.84 -4.50
On-siteU=6eV isconsideredforMn d-orbitals
OrdinaryMn12:HOMOlevels
areshifteddown.HOMO-LUMOgapgreatlyincreasesduetoHOMOandLUMOthat
-
Barraza-Lopez,AveryandPark,J.Appl.Phys.(2008)
gap 1.35 0.24
Geo 2HOMO
Geo 2LUMO
gap
-6.37 -6.66
-6.05 -5.51
0.32
-5.37 -6.07
-5.22 -4.84
0.15
(*)Boukhvalov etal,PRB75757575,014419(2007)
.
S-terminatedMn12 (Geo2):
HOMO,LUMOarefromSp-orbitals sothegapdoesnot
changemuch.
DirectionofchargetransferdoesnotchangewithU
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SummarySummaryModeledamonolayerofMn12 adsorbedonaAusurfaceviaathiol groupusingDFT
Electronicstructure:broadeningofmolecularorbitals wassmall,weakcouplingbetweenMn12 andaAusurfaceevenwiththeshortlink
arge rans er rom u o n12
Totalmomentforwholestructurebackto20B
Magneticanisotropybarrierforwholestructureisreduced
by9%comparedtothatforisolatedMn12 moleculeEffectofon-siteUonorbitals forisolatedmolecules
Barraza-Lopez,AveryandPark:PRB76767676 224413(2007),JAP103103103103 07B907(2008)
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Bulkgold:Equilibriumlatticeconstant=4.175
Exp:4.078,difference:2.8%
Checkconvergencewith#ofkpointsandenergycutoffforplanewaves
Withcalculatedlatticeconstant,wevary#ofAula ersand#ofverticalvacuumla ers
Bulkgold&Au(111)slabBulkgold&Au(111)slab
Ausurfaceenergysaturateswith8Aumonolayers and7vacuumlayers
TocoverMn12,atleast36surfacegoldatomspermonolayerareneeded
Usesixgoldmonolayers (36x6=216goldatoms)
Relaxgoldslab(w/omolecule)untilmax
forcesarelessthan0.01eV/
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vacuumlayerz
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ProjecteddensityofstatesforMnProjecteddensityofstatesforMn1212onAuslabonAuslab
Blue:IsolatedMnBlue:IsolatedMnBlue:IsolatedMnBlue:IsolatedMn12121212
Red:MnRed:MnRed:MnRed:Mn12121212 onAuslabonAuslabonAuslabonAuslab
3d
Mn(I):inner,Mn(II),Mn(III):outer
3d
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BroadeningoforbitalsismuchlessthanCoulombcharging
ProjecteddensityofstatesforMnProjecteddensityofstatesforMn1212onAuslabonAuslab
3d
Mn(I):inner,Mn(II),Mn(III):outer
energy:
WeakcouplingWeakcouplingWeakcouplingWeakcouplingWeakcouplingWeakcouplingWeakcouplingWeakcoupling2p
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+2.0+2.0+2.0+2.0
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