Spin Waves in Antidot Lattices: From Quantization to Magnonic Crystals

211 Pages·2011·7.75 MB·English

TECHNISCHE UNIVERSITA¨T MU¨NCHEN
Lehrstuhlfu¨rPhysikfunktionalerSchichtsysteme,E10
Spin WavesinAntidot Lattices:
From Quantizationto MagnonicCrystals
SebastianNeusser
Vollsta¨ndigerAbdruckdervonderFakulta¨tfu¨rPhysikderTechnischen
Universita¨tMu¨nchenzurErlangungdesakademischenGradeseines
DoktorsderNaturwissenschaften
genehmigtenDissertation.
Vorsitzender:Univ.-Prof.Dr.H.Friedrich
Pru¨ferderDissertation:
1.Univ.-Prof.Dr.D.Grundler
2.Univ.-Prof.Dr.R.Gross
DieDissertationwurdeam24.02.2011beiderTechnischenUniversita¨t
Mu¨ncheneingereichtunddurchdieFakulta¨tfu¨rPhysikam18.04.2011
angenommen.

Short Abstract
Spin-wave (SW) propagation was studied in periodic arrays of 120 nm
large holes, so called antidot lattices (ADLs). They were created by fo-
cused ion beam lithography into 25 nm thin permalloy Ni Fe films.
80 20
GHz SW spectroscopy was performed all electrically by micro- and
nanoscale coplanar waveguides. The ADL periodicity ranged from 300
to4000nm.For300nmperiodicity,coherentbackscatteringwasfoundto
causemagnonicminibandformationintheSWdispersionandlargegroup
velocitiesof 6 km/s. For 800nmperiodicityandlongSW wave lengths,
the ADL showed signatures of an unstructured plain film with effective
properties,i.e. metamaterialbehavior. Theseeffectivelycontinuousprop-
ertieswerealsofoundtodescribewellSWtransmissionintotheADL.
Es wurdeSpinwellen (SW)-Propagationin periodischenAnordnungen
von120nmgroßenLo¨chern,so genanntenAntidot-Gittern(ADL),unter-
sucht. DiesewurdenmittelsfokussierterIonenstrahllithographiein25nm
du¨nnen Permalloy Ni Fe Filmen erzeugt. GHz-SW- Spektroskopie
80 20
wurdereinelektrischmittelsmikro-undnanoskaligenkoplanarenWellen-
leitern durchgefu¨hrt. Die ADL Periodizita¨t reichte von 300 bis 800nm.
Bei 300nm-Periodizita¨t wurde koha¨rente Ru¨ckstreuung als Ursache fu¨r
magnonische Miniband-Bildung in der Spinwellen-Dispersion und hohe
Gruppengeschwindigkeitenvon6km/sgefunden. Bei800nm-Periodizita¨t
und langen SW-Wellenla¨ngen zeigte das ADL Kennzeichen eines un-
strukturierten Films mit effektiven Eigenschaften, d.h. Metamaterial-
Eigenschaften. Auf Basis dieser effektiv kontinuierlichenEigenschaften
wurdeauchdieTransmissionvonSWindasADLhineingutbeschrieben.
1

Abstract
Nanomagnetismisafieldofresearchwhereoneaimsformodificationand
controlofmagneticpropertiesthroughtailoredgeometryonthenanoscale.
Nanostructured ferromagnets offer broad functionality due to manifold
magnetization states they exist in [Sta10]. Dynamic phenomena in such
systems in the GHz rangehave generatedincreasingscientific interestin
recentyears. Herespinwaves(SWs)ormagnonsareofparticularattrac-
tion. Magnons are the particle-like quantized spin excitations, whereas
theirwave-likecounterpartisreferredtoasspinwaves. Advancementsin
patterningtechniqueshaverecentlyallowedtopreciselytailortheseexci-
tations[Neu09].
Inthisthesis, 22to 30nmthinfilmsof permalloy,i.e. Ni Fe , with
80 20
saturationmagnetizationM rangingfrom760to830kA/marenanos-
Sat
tructured by focussed ion beam lithography to create a periodic square
arrayofcircularholes,i.e. anantidotlattice(ADL).Fromsampletosam-
ple, the edge-to-edgeseparationis variedbetween40 and4000nm. The
holediameteris86 120nmInthisparameterregime,thefollowingphe-
−
nomenahavebeenobserved:
Quantization and localization of spin waves. For, both, large
•
edge-to-edgeseparationsandperiodicitiespoftheADL,SWquan-
tizationisobserved. Differenteigenmodesareresolvedexperimen-
tally, which reside in different parts of the ADL. A propagating
modeisfoundtoextendthroughthelatticeinspin-wavenanochan-
nels formedin between neighboringholesperpendicularto the ex-
ternalfield. Themeasuredpropagationcharacteristicsofthismode
showastrongcharacteristicanisotropy.Groupvelocitiesv between
g
2.5 and 3.5 km/s are measured. Furthermore, a localized mode
is found to exist in between neighboringholes parallel to the field
(v =0).
g
Effectively continuous material properties. For SW excitations
•
of wavelength λ , which are much larger than the periodicity p,
SW
it is found that a p = 800 nm ADL behaves as being an effec-
tivelycontinuousplainfilmwithareducedsaturationmagnetization
M⋆ = 600 kA/m. The holes have a diameter of d = 120 nm.
Sat
This is verified in an experiment where long-wavelength SWs are
injected into such an ADL. Reflectivity and transmittivity are well
describedbythewavevectormismatchoftwo(effectively)contin-
uous materials of different magnetic properties. The ADL is thus
foundtoactasametamaterialforspinwaves.
Magnonicproperties. Movementinaperiodicpotentialisknown
•
toalterthepropagationpropertiesofwave-likeexcitations. Thisis
investigated in this thesis for spin waves. Allowed minibands and
forbiddenfrequencygapsareprovokedby,e.g.,coherentbackscat-
tering. Results on SWs suggest that, starting from large edge-to-
edge separation (large p), localized modes residing close to holes’
edges become coupled for sufficiently small p. Being similar to a
tight-binding approach, this is in contrast to the mechanism based
on coherent backscattering from periodic holes and pitches as re-
ported for photonic, plasmonic, and phononic crystals. Advanta-
geouslylargegroupvelocitiesv = 5 to 6 km/s are foundfor the
g
magnonicmodewhichisinexcessoftheplainfilmvalueatthesame
magneticfieldvalue.
Experimentalmethodsusedtoobtaintheseresultsincludedallelectrical
spin-wave spectroscopy (AESWS). Highly sensitive and electromagneti-
callyisolatedSWemittersanddetectorswithmicro/nanoscaleextensions
were designed and fabricated using electron-beam nanolithography. For
thefirsttimeSWspropagatingthroughferromagneticnanostructureswere
observed all electrically using a broadband magnetic probe station. Ex-
perimentsweremodeledusingmicromagneticsimulations. Inthecourse
of this thesis, scientific collaborations were initiated. Providing tailored
ferromagneticnanostructurestoexperimentalgroupsinRegensburg,Ger-
many1, and Perugia, Italy,2 spin-wave propagationwas studied using the
spatiallyandtimeresolvedmagneto-opticalKerreffectandBrillouinlight
1Institutfu¨rExperimentelleundAngewandtePhysik,Universita¨tRegensburg,D-93040Re-
gensburg,Germany
2CNISM,DipartimentodiFisica,UniversitadiPerugia,ViaA.Pascoli, I-06123Perugia,
Italy
4
scattering, respectively. In the theory group of M. Krawczyk in Poznan,
Poland,1 theso-calledplanewave methodwasdevelopedfurtherandap-
pliedtotheantidotlatticesinvestigatedhere. Thetechniquesandthethe-
oreticalapproachwereappliedtogainfurthermicroscopicinsightintothe
spin-wavephysicsatthenanoscale.
1SurfacePhysicsDivision,FacultyofPhysics,AdamMickiewiczUniversity,Umultowska
85,Poznan´61-614,Poland
5

Contents
1 MotivationandStateofResearch 13
2 Theory 17
2.1 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . 17
2.1.1 Phenomenology . . . . . . . . . . . . . . . . . . 17
2.1.2 Magnetizationandtotalenergy . . . . . . . . . . 19
2.1.3 Magneticmoment . . . . . . . . . . . . . . . . . 20
2.1.4 Exchangeinteraction . . . . . . . . . . . . . . . . 22
2.1.5 Energycontributions . . . . . . . . . . . . . . . . 23
2.2 FerromagneticDynamics . . . . . . . . . . . . . . . . . . 28
2.2.1 Landau-Lifshitzequationofmotion . . . . . . . . 28
2.2.2 LinearizedLandau-Lifshitzequation . . . . . . . 30
2.2.3 Ferromagneticresonance . . . . . . . . . . . . . . 32
2.2.4 Relaxationanddamping . . . . . . . . . . . . . . 34
2.3 DipolarSpinWaves . . . . . . . . . . . . . . . . . . . . 35
2.3.1 Dispersionrelation . . . . . . . . . . . . . . . . . 35
2.3.2 Planewavemethod . . . . . . . . . . . . . . . . 40
2.3.3 Micromagneticsimulations . . . . . . . . . . . . 42
2.4 MicrowaveExcitation . . . . . . . . . . . . . . . . . . . 49
2.4.1 Transmissionlinemodel . . . . . . . . . . . . . . 49
2.4.2 ScatteringParameters. . . . . . . . . . . . . . . . 52
2.4.3 Voltageinductionandmeasuredquantities . . . . 53
2.4.4 Electromagneticfieldsimulation . . . . . . . . . . 56
3 ExperimentalSetupandTechniques 57
3.1 MeasurementApparatusandSampleDesign . . . . . . . . 57
3.1.1 Broadbandmicrowaveprobestation . . . . . . . . 57
3.1.2 Sampledesign . . . . . . . . . . . . . . . . . . . 60
3.2 MeasurementTechniques . . . . . . . . . . . . . . . . . 64
3.2.1 VNAferromagneticresonancetechnique . . . . . 64
3.2.2 Allelectricalspin-wavespectroscopy . . . . . . . 65
7
Contents
3.2.3 MagnetoopticalKerreffecttechnique . . . . . . . 66
3.2.4 Brillouinlightscatteringspectroscopy . . . . . . 71
4 Preparation 73
4.1 OpticalLithographyPreparation . . . . . . . . . . . . . . 73
4.2 ElectronBeamLithographyPreparation . . . . . . . . . . 75
4.3 FocussedIonBeamLithographyPreparation. . . . . . . . 77
5 ElectromagneticPropertiesofaCPW 81
5.1 MeasuredScatteringParameters . . . . . . . . . . . . . . 82
5.2 ModeledScatteringParameters . . . . . . . . . . . . . . 82
5.3 ModelingofthespatialFieldProfile . . . . . . . . . . . . 85
5.4 ElectromagneticCrosstalk . . . . . . . . . . . . . . . . . 87
6 PlainFilmMeasurements 91
6.1 Phenomenology . . . . . . . . . . . . . . . . . . . . . . . 91
6.2 InterpretationandAnalysis . . . . . . . . . . . . . . . . . 95
6.2.1 Susceptibilityandinhomogeneousbroadening . . 95
6.2.2 Wavevectorselectiveanalysis . . . . . . . . . . . 99
6.2.3 Propagationvelocity . . . . . . . . . . . . . . . . 100
6.2.4 Relaxationanddamping . . . . . . . . . . . . . . 102
7 AntidotLattices: StaticandDynamicCharacterization 107
7.1 StaticMagnetization . . . . . . . . . . . . . . . . . . . . 107
7.1.1 MagnetizationReversal . . . . . . . . . . . . . . 108
7.1.2 MicromagneticGroundState . . . . . . . . . . . 109
7.2 PhenomenologyofMagnetizationDynamics. . . . . . . . 114
7.2.1 VNA-FMRstudy . . . . . . . . . . . . . . . . . . 115
7.2.2 AESWSforlargeperiodicities(p 400nm) . . . 117
≥
7.2.3 AESWSforsmallperiodicities(p<400nm) . . . 122
7.2.4 ComparisonofAESWSdatafordifferentp . . . . 125
7.3 QuantizationandLocalizationofSpinWaves . . . . . . . 125
7.3.1 p=800nmADL:localizedandextendedmodes . 127
7.3.2 p=300nmADL:edgemode . . . . . . . . . . . 129
7.3.3 p=120ADL:modehybridization. . . . . . . . . 129
7.4 ModeBehavior . . . . . . . . . . . . . . . . . . . . . . . 134
7.4.1 Internalfieldanalysis . . . . . . . . . . . . . . . . 134
7.4.2 AnalysisofBLSdata . . . . . . . . . . . . . . . . 136
8