Ab initio all electron full potential linearized augmented plane wave method for one-dimensional systems [Elektronische Ressource] / vorgelegt von Yuriy Mokrousov

AbinitioAll-electronFull-potentialLinearized
tedAugmenPlane-waveMethodforOne-dimensionalSystems

VonderFakult¨Rheiniscatf¨urh-Westf¨aliscMathematik,henTechniscInformatikhenHoundchschuleNaturwissenscAachenhaftender
zurErlangungdesakademischenGradeseinesDoktorsderNaturwissenschaften
Dissertationgenehmigte

onvorgelegtv

ScienceofMaster

vMokrousouriyY

(Ukraine)Kievaus

Berichter:Universit¨atsprofessorDr.StefanBl¨ugel
Universit¨atsprofessorDr.PeterHeinzDederichs

Tagderm¨undlichenPr¨ufung:24.05.2005

DieseDissertationistaufdenInternetseitenderHochschulbibliothekonlineverf¨ugbar

Abstract

Inrecentyearswewitnessedanenormousprogressinthechemicalsynthesis,growthand
thedevelopmentoftechnologyallowingthefabricationofarichvarietyofone-dimensional
(1D)structures.Theyincludesinglewalled(SWNT)andmulti-walled(MWNT)one-
dimensionaltubularstructures,madeofcarbon,GaN,BN,TiO,VOandothercom-
pounds,thinmetallicquantumwires,quasi-1Dmolecularmagnetsetc.Theyinvolve
elementsfromtheentireperiodictableandshownewphysicalphenomenasuchasquan-
tizedconductance,chargeandspinseparation,intriguingstructuralandmagneticprop-
ertiessuchashighspin-polarizationandlargespin-scatteringlengths.Inmanycasesthe
transportpropertiesofthesesystemscanbeeasilytunedbychoosingsuitablestructural
parameterssuchasthediameterorchirality.Moreover,thediametersofmanyexperimen-
tallyobserved1Dstructuresaremuchsmallerthanmostsemiconductordevicesobtained
sofar,andthusonecanimaginethatthesmallestpossibletransistorsarelikelytobe
basedonthem.Inordertounderstandthestructure-propertyrelationinthesenewma-
terialsonthebasisoftheelectronicstructure,abinitiocalculationsbasedonthedensity
functionaltheoryplayanimportantrole.
Inthisworkwehavepresentedanextensionofthefull-potentiallinearizedaugmented
plane-wave(FLAPW)methodtotrulyone-dimensionalsystems.Thespaceispartitioned
intothreeregions,themuffin-tinspherearoundtheatom,avacuumregionsurrounding
acylinderandtheinterstitialregionbetweentheatomsandthevacuumregion.Ineach
regionoptimalbasisfunctionsforthewavefunctions,chargedensityandpotentialareused.
Thespin-orbitinteractionisincludedtoinvestigatetheorbitalmomentsandthemagnetic
anisotropy.Despitetheplane-waverepresentationintheinterstitialregionwewereable
toincludeawideclassofchiralsymmetries,characteristicforone-dimensionalsystems.
Theone-dimensionalFLAPWmethodwasimplementedasextensionoftheFLAPWcode
FLEURandparallelizedforsupercomputingapplications.Duetotheefficientlyadjusted
basisfunctionsandpartitioningofspace,1Dcodeallowstoachieveasignificantspeed-
up,forinstance,approximatelybyafactorof150formonowires,ascomparedtothe
super-cellapproachinthebulkcode.
Theaccuracy,precisionandcorrectnessofthecodewasvalidatedonasetof1Dstruc-
tures,alreadycalculatedpreviouslywithothermethods.Wefocusedonthesystemsof
alargecurrentinterestinthefieldofnanophysics.Wereportedonthecalculationsof
3d-and4d-monowires(Ti;Y,Zr,Nb,Mo,Tc,Ru,RhandPd).Forthesemonowires
weinvestigatedtheferro-andantiferromagneticinstability,calculatedequilibriuminter-
atomicdistances,magneticandorbitalmoments,magnetocrystallineanisotropyenergies.
Wefoundthatacrossthe4d-transition-metalseries,YandNbexhibitanonmagnetic
ground-state,MoandTcareantiferromagneticandZr,Ru,RhandPdareferromagnetic
atequilibriumlatticeconstants.FortheRu,RhandPdsystemiswasfoundthatthe
easyaxisisperpendiculartothewireforRuandPdandalong-the-wireforRh.
Furtherweconsidereda(6,0)nanowireofgoldatoms,andahybridstructureofaniron
monowireinsideagold(6,0)tube,showingthattheFemonowireispronetothePeierls
dimerization.ForthehybridsystemFe@Au(6,0)wefoundahighspin-polarizationatthe

Fermilevel,proposing,therefore,thissystemasapossiblecandidateforspin-dependent
applications.orttranspUsingasuper-cellapproachwithintheone-dimensionalFLAPWmethodweinves-
tigatedasetofone-dimensionalmultiple-deckersandwichesofbenzeneandvanadium,
whichareforthepast20yearsofgreatinterestinthefieldoforganometallics.Thecalcu-
latedstructuralresultsobtainedareingoodagreementwithexperimentalandtheoretical
results.Afterthecalculationoftotalenergies,magneticmoments,orbitalinteraction
schemes,onecanfinallyconclude,thatwiththeincreasingnumberofthevanadiumatoms
inthemolecule,themagneticmomentsofvanadiiprefertoorderferromagnetically,which
wasrecentlyobservedexperimentally.

”UsinganequalityduetoBogolyubov,MerminandWagner

haveprovedrigorouslytheabsenceofbothferromagnetism

andantiferromagnetisminone-dimensionalspinsystems.”

M.B.WalkerandT.W.Ruijgrak,PhysicalReview,171,513

still...still...”still...

MilesDavistohismusiciansin

GingerbreadBoy,album”MilesSmiles”,Columbia

still...”

CL

2601

(1968)

(1966)

4

tstenCon

ductiontroIn1

2DensityFunctionalTheory
2.1DensityFunctionalTheory...........................
2.2SpinDensityFunctionalTheory........................
2.3TheLocalSpinDensityApproximation....................
2.4TheGeneralizedGradientApproximation(GGA)..............

3FLAPWApproachtoOne–DimensionalSystems
3.1FLAPWMethod................................
3.1.1TheAPWMethod...........................
3.1.2TheConceptofLAPW........................
3.1.3TheConceptofFLAPW........................
3.2ChiralSymmetries...............................
3.2.1HexagonalIn-PlaneLattice......................
3.2.2TriangularIn-PlaneLattice......................
3.3Implementation.................................
3.3.1Geometry................................
3.3.2Symmetries...............................
3.3.3ChargeDensityandPotential.....................
3.3.4CoulombPotential...........................
3.3.5BasisFunctions.............................
3.3.6EigenvalueProblem..........................
3.3.7Timing..................................

ProblemaluevEigen44.1RelativityinValenceElectronCalculations..................
4.1.1TheKohn-Sham-DiracEquation....................
4.1.2TheScalarRelativisticApproximation................
4.2ConstructionoftheHamiltonianMatrix...................
4.2.1HamiltonianandOverlapMatricesintheSpheres..........
4.2.2InversionSymmetry..........................
4.2.3HamiltonianandOverlapMatricesintheInterstitial........

5

9

1313161718

21212223252627293031323435373838

4142434446475052

CONTENTS64.2.4HamiltonianandOverlapMatricesintheVacuum.........54
4.3FermiEnergyandBrillouinZoneIntegration.................58
61yDensitCharge55.1GenerationoftheStartingDensity......................61
5.2GenerationoftheChargeDensity......................63
5.2.1“l-like”Charge.............................64
5.2.2DeterminationoftheOptimalEnergyParameters..........65
5.2.3GenerationoftheChargeDensityintheSpheres...........65
5.2.4GenerationoftheChargeDensityintheInterstitial........66
5.2.5GenerationoftheChargeDensityintheVacuum..........67
69tialotenP66.1CoulombPotential...............................69
6.1.1ThePseudo-ChargeScheme......................69
6.1.2SolutionofthePoissonEquationintheVacuumandInterstitial..71
6.2Exchange–CorrelationPotential........................79
σσ6.2.1CalculationofandVintheInterstitial.............79
xcxcσσ6.2.2CalculationofandVintheSpheres...............80
xcxcσσ6.2.3CalculationofandVintheVacuum...............80
xcxc83Results77.1MonowiresofTiand4dtransitionelements.................83
7.1.1TiMonowire..............................85
7.1.2Monowiresof4dtransitionelements.................88
7.2Gold(6,0)Nanowire..............................99
7.2.1ComputationalDetails.........................99
7.2.2GeometricalStructure.........................101
7.2.3ElectronicStructure..........................101
7.2.4ChargeDensity.............................102
7.3HybridStructureFe@Au(6,0).........................103
7.3.1GeometricalStructure.........................104
7.3.2MagneticProperties..........................105
7.3.3ElectronicStructure..........................106
7.3.4ChargeDensity.............................108
7.4One-DimensionalMultipleBenzene-VanadiumSandwiches.........108
7.4.1ComputationalDetails.........................112
7.4.2V(Bz)Complex.............................113
7.4.3V(Bz)Complex............................118
217.4.4V(Bz)Complex............................122
327.4.5V(Bz)Complex............................126
437.4.6Conclusions...............................129

CONTENTS

8

Conclusions

7

131

8

CONTENTS

Chapter1

ductiontroIn

tiveDuringandthefastestlastgrodecadewingfieldsresearchofonmothedernphnanoscaleysics.devOneelopreasonedtoisonecertainlyofthethemostinnoenormousva-
alloprogresswingthewitnessedfabricationintheofcarichemicalhvarietsynythesis,ofgronanomaterialswthandthewithdevunprecedenelopmentoftedtecnewhnologyprop-
erties.Asthescaleofnanomaterialscontinuetodecreasefromthemesoscopicregime
totheatomicscale,one-dimensional(1D)nanometerscalesystemssuchascarbonnan-
licotubquanes[38],tumwiresradially[49,and29,113axially]momovedindulatedtothefocussemiconductorofattennanotion.wiresThe[71],excitemenandthintinmetal-these
quantizedone-dimensionalconductance,structureschargeisfueledandbspinytheirwseparation,ealthofinnewtriguingphysicalstructuralphenomenaandsucmagnetichas
propthereisertiesasucgeneralhashighconsensusspin-pontheolarizationexpectationandlargethatthespin-scatteringquantumnaturelengthsin[115].materialsTodayis,