Magnonic Devices: Numerical Modelling and Micromagnetic Simulation Approach

89 Pages·2023·3.2 MB·English

by  C. S. Nikhil Kumar

SpringerBriefs in Materials
C. S. Nikhil Kumar
Magnonic Devices
Numerical Modelling and
Micromagnetic Simulation
Approach
SpringerBriefs in Materials
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C. S. Nikhil Kumar
Magnonic Devices
Numerical Modelling and Micromagnetic
Simulation Approach
C.S.NikhilKumar
AdamMickiewiczUniversity
Poznan´,Poland
ISSN 2192-1091 ISSN 2192-1105 (electronic)
SpringerBriefsinMaterials
ISBN 978-3-031-22664-9 ISBN 978-3-031-22665-6 (eBook)
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Preface
Magnonics—thestudyofspinwaves—hasseenaremarkablescopeforthecreation
of magnetic field-controlled devices with properties tailored on the nanoscale. It
aims to control and manipulate spin waves in ferromagnetic material. Spin wave
caneffectivelycarryandprocessinformationinmagneticnanostructures.Themost
controllabilityoftheirfunctioningisbyanexternalmagneticfield.
The magnonic devices which are periodically modulated in space are seen as
very promising devices because of the possibility of tunning their band structure.
Periodically modulated magnonic devices can also be called as “magnonic crys-
tal”magneticcounterpartofphotoniccrystal,withspinwaveactingasinformation
carrier.Magnoniccrystalsarebettercandidatesforminiaturization,sincethewave-
lengthofspinwaveisseveralordersofmagnitudeshorterthanthatofelectromagnetic
wavesofthesamefrequency.Anexampleofone-dimensionalmagnoniccrystalis
amultilayeredmagneticstructureconsistingofalternatedferromagneticlayers.The
basic advantage of a such device is that frequency position and width of the band
gaparetunablebyanappliedfieldandthroughmaterialproperties.Thedispersion
propertiescanbetunedbychangingthedimensionsofmagnonicwaveguide.
Spectrumofmagnoniccrystalshowsbandgapsinwhichspinwavecannotprop-
agate.SuchbandgapshavebeenexperimentallystudiedusingBrillouinlightscat-
teringspectroscopy[1,2]andtime-resolvedscanningKerrmicroscopy[3].Thestudy
ofmagnoniccrystalisfirstproposedin[4].PuszkarskiandKrawczykhavetheoreti-
callycalculatedthemagnonicbandstructureof2DMCsconsistingofinfinitelylong
cylindricalFerodsperiodicallyembeddedinayttriumirongarnet(YIG)background
[5].ThematerialsFeandYIGwereselectedfortheirlargedifferenceinmagnetic
properties, as it has been predicted that the larger the difference, the wider would
bethebandgapwidth.Theyinvestigatedthepositionandwidthofbandgapsinthe
spinwavespectrumversusperiodofthestructureandmagneticproperties.
Apopularmethodtoinvestigatethebandstructureofperiodicstructureisplane
wave expansion method. Plane wave method has been successfully implemented
in both photonic [6], phononic [7] and magnonic crystals [5, 4, 8]. We follow the
main idea behind the plane wave method to investigate the band structure of peri-
odicallymodulatedmagnonicwaveguide.Theequationofmotionforaperiodically
vii
viii Preface
magnetic structure is transformed into reciprocal space using Fourier transforma-
tionandBloch’stheorem.Theequationofmotionisthenreducedtoaneigenvalue
problem. The numerical solutions were found out for such an eigenvalue problem
bystandardnumericalroutines.Thesolutionyieldeigenfrequenciesthathelptofind
thebandstructureandeigenvectoryieldsspinwaveprofileinsidetheperiodicmate-
rial. One of the main objectives of this thesis is to follow the plane wave method
in order to investigate the spin wave spectrum of the striped magnonic crystal in
backwardvolumeconfiguration.Theresultispublishedin[9].Weinitiallyinvesti-
gated the magnetostatic field insidethegeometry usingtheidea presented in[10].
TheobtainedmagnetostaticfieldisusedinthegoverningLandau-Lifshitzequation.
This helps us to reduce the equation in to an eigenvalue problem. This eigenvalue
problemissolvednumericallyinordertoinvestigatethespinwavespectrum.The
eigenvectorconceptisusedtoinvestigatethespinwaveprofileinsidethestructure.
This book describes the dispersion relation of dipolar spin wave in a magnonic
curvedwaveguide.Walker’sequationincylindricalcoordinatesissolvedwithappro-
priateboundaryconditions.Thedispersionofexchangespinwavesisthencalculated
using perturbation theory. We validated our results by investigating the dispersion
relationforahigherbendingradiusandcomparedittothatofastraightwaveguide
forhigherbendingradius.Byintroducingsymmetryabouttheazimuthaldirection,
wealsoobtainanalyticalsolutionsforWalker’sequationandthemodeprofilechar-
acteristics of dipolar spin waves in a magnonic ring. Perturbation theory is used
toinvestigatethemodeprofilecharacteristicsofmagnonicring.Finally,analytical
dispersionrelationofcurvedwaveguideiscomparedwithmicromagneticsimulation.
Wecouldseeareasonableagreementoffundamentalmodebetweensimulationand
analyticalresultsandattributethedifferencestothelargeexchangeinthesimulation
andtheweakexchangeinperturbationtheory.
Thisbookalsodescribesnanocontact-drivenspinwaveexcitationsinmagnonic
cavity. A spin-polarized electric current injected into Permalloy (Py) through a
nanocontactexertsatorqueonthemagnetization,leadingtospinwave(SW)exci-
tation. We considered an array of nanocontacts on a Py film for an enhanced SW
excitation.Wedesignedanantidotmagnoniccrystal(MC)aroundthenanocontactto
formacavity.TheMCwasdesignedsothatthefrequencyoftheSWmodegenerated
bythenanocontactliesinthebandgapoftheMC.Thenanocontactswereplacedina
linedefectcreatedintheMCbyremovingarowofantidots.TheSWtimeseriesand
powerspectrumwereobservedattheoutputofthecavity.WeobservethattheSWs
decay in the absence of the MC cavity, and when the nanocontacts are within the
antidotMCcavity,theSWamplitudeisamplifiedandstable.Thisisalsoreflectedin
theSWspectrumobtainedattheoutputport.Finally,Qfactorofthedeviceiscalcu-
latedusingdecaymethodandobservedahighQfactor Q =3.8×105foracurrent
of7.8mA.TheproposeddevicebehavesasaSWASER(spinwaveamplificationby
thestimulatedemissionofradiation).
Poznan´,Poland C.S.NikhilKumar
Preface ix
References
1. Tacchi S, Madami M, Gubbiotti G, Carlotti G, Tanigawa H, Ono T, Kostylev MP (2010)
Anisotropic dynamical coupling for propagating collective modes in a two-dimensional
magnoniccrystalconsistingofinteractingsquarednanodots.PhysRevB82:024401.
2. TacchiS,MadamiM,GubbiottiG,CarlottiG,GoolaupS,AdeyeyeAO,SinghN,Kostylev
M.P(2010)Analysisofcollectivespin-wavemodesatdifferentpointswithinthehysteresis
loopofaone-dimensionalmagnoniccrystalcomprisingalternative-widthnanostripes.Phys
RevB82:184408.
3. KruglyakVV,KeatleyPS,NeudertA,HickenRJ,ChildressJR,KatineJA(2010)Imaging
collectivemagnonicmodesin2darraysofmagneticnanoelements.PhysRevLett104:027201.
4. VasseurJO,DobrzynskiL,Djafari-RouhaniB,PuszkarskiH(1996)Magnonbandstructure
ofperiodiccomposites.PhysRevB54:1043.
5. PuszkarskiH,KrawczykM.(2003)Magnoniccrystals-themagneticcounterpartofmagnonic
crystal.SolidStatePhenomena94:125.
6. JoannopoulosJD,JohnsonSG,WinnJN,MeadeRDPhotonicCrystals:MoldingtheFlowof
Light(SecondEdition).PrincetonUniversityPress,2ed.,Feb.
7. BenchabaneS,KhelifA,RauchJ-Y,RobertL,LaudeV(2006)Evidenceforcompletesurface
wavebandgapinapiezoelectricphononiccrystal.PhysRevE73:065601.
8. KrawczykM,PuszkarskiH(2008)Plane-wavetheoryofthree-dimensionalmagnoniccrystals.
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9. KumarN,PrabhakarA.(2013)Spinwavedispersioninstripedmagnonicwaveguide.IEEE
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Contents
1 Introduction .................................................... 1
References ...................................................... 4
2 BackwardVolumeSpinWavesinaRectangularGeometry .......... 7
2.1 SolutiontoWalker’sEquation ................................. 7
2.1.1 DispersionCharacteristicsforDipolarSpinWaves ......... 10
2.1.2 DispersionCharacteristicsofExchangeSpinWaves ........ 10
Reference ....................................................... 11
3 MagnetostaticWavesinMagnonicCrystals:APWMApproach ..... 13
3.1 MagnetostaticWavesin1DMagnonicCrystal ................... 17
3.2 Walker’sEquationinaOne-DimensionalMagnonicCrystal ....... 17
3.3 DispersionCharacteristicsofBackwardVolumeSpinWaves ....... 20
References ...................................................... 22
4 FieldLocalizationinStripedMagnonicCrystalWaveguide .......... 23
4.1 GeometryandMethodofAnalysis ............................. 24
4.2 StaticDemagnetizingField ................................... 26
4.3 SpinWaveMagnonicBand ................................... 28
4.4 SpinWaveLocalizationsinStripedMagnonicWaveguide ......... 32
4.5 Convergence ................................................ 33
4.6 Conclusion ................................................. 34
References ...................................................... 34
5 Walker’sSolutionforCurvedMagnonicWaveguideandResonant
ModesinMagnonicRing ......................................... 37
5.1 SpinWaveDispersionforCurvedMagnonicWaveguide .......... 37
5.1.1 GeometryandAnalysis ................................ 38
5.1.2 DispersionRelationofCurvedMagnonicWaveguide ....... 42
5.1.3 Validations ........................................... 44
5.1.4 ModesinaMagnonicRing ............................. 46
xi