Solid State Physics - Volume 65

605 Pages·2014·52.358 MB·English

by  Robert L. Stamps, Robert E. Camley

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CONTRIBUTORS
Numbersinparenthesisindicatethepagesonwhichtheauthors’contributionsbegin
AnjanBarman(1)
ThematicUnitofExcellenceonNanodeviceTechnologyandDepartmentofCondensed
MatterPhysicsandMaterialSciences,S.N.BoseNationalCentreforBasicSciences,Kolkata,
India
GustavBihlmayer(353)
PeterGru¨nbergInstitut(PGI-7),andInstituteofAdvancedSimulation(IAS-1),
ForschungszentrumJu¨lich,Ju¨lich,Germany
ZoeBudrikis(109)
ISIFoundation,Turin,Italy
ArabindaHaldar(1)
ThematicUnitofExcellenceonNanodeviceTechnologyandDepartmentofCondensed
MatterPhysicsandMaterialSciences,S.N.BoseNationalCentreforBasicSciences,Kolkata,
India
ThomasSaerbeck(237)
DepartmentofPhysics,andCenterforAdvancedNanoscience,UniversityofCalifornia
SanDiego,LaJolla,California,USA
WolfgangSpeier(353)
JARA-Fundamentalsof FutureInformationTechnology,ForschungszentrumJu¨lich,
Ju¨lich,Germany
KrzysztofSzot(353)
PeterGru¨nbergInstitut(PGI-7),ForschungszentrumJu¨lich,Ju¨lich,Germany,and
A.ChelkowskiInstituteofPhysics,UniversityofSilesia,Katowice,Poland
vii
PREFACE
Itisourgreatpleasuretopresentthe65theditionofSolid-StatePhysics.The
vision statement for this series has not changed since its inception in 1955,
and Solid-State Physics continues to provide a “mechanism ... whereby
investigators and students can readily obtain a balanced view of the whole
field.” What has changed is the field and its extent. As noted in 1955, the
knowledge in areas associated with solid-state physics has grown enor-
mously, and in 2014, its clear boundaries have gone well beyond what
wasonce,traditionally,understoodassolidstate.Indeed,researchontopics
in materials physics, applied and basic, now requires expertise across a
remarkably wide range of subjects and specialties. It is for this reason that
there exists an important need for up-to-date, compact reviews of topical
areas. The intention of these reviews is to provide a history context for a
topic that has matured sufficiently to warrant a guiding overview.
Thetopicsreviewedinthisvolumeillustratethegreatbreadthanddiver-
sityofmodernresearchintomaterialsandcomplexsystems,whileproviding
thereaderwithacontextcommontomostphysiciststrainedorworkingin
condensed matter. We have a wide range of research represented in this
volume. This includes work on magnetization dynamics in thin films and
nanostructures,thepropertiesofartificialspinicesystems,neutronscattering
as a probe for magnetic exchange, and a review of the recently discovered
resistiveswitchingphenomenawherevariousoxidescanbereversiblychan-
ged from a high-resistance state to a low-resistance state. Both editors and
publishershopethatreaderswillfindtheintroductionsandoverviewsuseful
andof benefit bothas summariesfor workersin these fieldsandastutorials
and explanations for those just entering.
ROBERT E. CAMLEY
Department of Physics, University of Colorado
Colorado Springs, Colorado, USA
ROBERT L. STAMPS
School of Physics and Astronomy
University of Glasgow, Glasgow, UK
ix
CHAPTER ONE
Time-Domain Study of
Magnetization Dynamics in
Magnetic Thin Films and
Micro- and Nanostructures
Anjan Barman, Arabinda Haldar
ThematicUnitofExcellenceonNanodeviceTechnologyandDepartmentofCondensedMatterPhysics
andMaterialSciences,S.N.BoseNationalCentreforBasicSciences,Kolkata,India
Contents
1. GeneralIntroduction 2
2. TheoreticalBackground 7
2.1 TimeScalesofMagnetizationDynamics 7
2.2 Laser-InducedUltrafastMagnetizationDynamics 8
2.3 LLGEquation 10
2.4 FerromagneticResonance 11
2.5 Spinwaves 15
2.6 Magneto-opticalKerrEffect 19
3. BackgroundofTRMOKE 25
3.1 BackgroundofTRMOKEExperiments 25
3.2 Laser-InducedUltrafastSpinDynamics 29
3.3 ImagingofPropagatingSpinWaves 32
3.4 Time-ResolvedKerrEffectMeasurementonSamplesDeposited
onOpaqueSubstrate 33
3.5 All-OpticalTRMOKEMicroscope 35
3.6 BenchtopTRMOKEMagnetometer 36
4. Time-ResolvedImagingofMagnetizationDynamicsinMicroscopicMagnetic
Elements 37
4.1 ImagingNonuniformPrecessionalDynamicsinSingleFerromagnetic
Microstructures 38
4.2 ImagingofNoisebyTime-ResolvedKerrMicroscopy 41
4.3 ImagingofSpin-WaveModesinFerromagneticMicrowires 42
4.4 ConfigurationalAnisotropyinPrecessionFrequencyandDamping 43
4.5 ExcitationandImagingIndividualResonantModesbyTime-Resolved
KerrMicroscopy 46
4.6 ImagingLargeAngleReorientationof2(cid:1)2mm2CoFe/NiFeElement 47
4.7 ImagingMagnetizationDynamicsofHardDiskWriters 47
SolidStatePhysics,Volume65 #2014ElsevierInc. 1
ISSN0081-1947 Allrightsreserved.
http://dx.doi.org/10.1016/B978-0-12-800175-2.00001-7
2 AnjanBarmanandArabindaHaldar
4.8 ConversionofFreeSpaceMicrowavetoMagnonicArchitecture:
TRSKMImaging 48
5. Time-ResolvedMagnetizationDynamicsofMagneticMultilayers 48
5.1 Time-ResolvedMagnetizationDynamicsofSpinValvesand
Exchange-CoupledBilayers 49
5.2 UltrafastMagnetizationDynamicsofMagneticMultilayerswithPMA 50
6. PrecessionalDynamicsofMagneticNanodotArrays 54
6.1 Size-DependentCrossovertoNonuniformPrecession 55
6.2 DynamicalConfigurationalAnisotropy 57
6.3 CouplingBetweenMagneticandElasticModes 57
6.4 CollectiveSpin-WaveDynamicsinArraysofNanomagnets 58
7. MagnetizationDynamicsinSingleNanomagnets 64
7.1 Cavity-EnhancedMagneto-OpticalMeasurementsofPicosecond
DynamicsofSingleNanomagnets 64
7.2 UltrafastThermalSwitching,Relaxation,andPrecessionofIndividual
FerromagneticDisks 67
7.3 EffectsofMagneticGroundStatesonMagnetizationDynamics
inSingleNanodisk 68
7.4 LargeAmplitudeMagnetizationDynamicsinaSingleNanomagnet 69
7.5 DetectingSingleNanomagnetDynamicsinVaryingMagnetostatic
Environment 70
8. MagneticVortexandDomainWallDynamics 71
9. Time-DomainCoherentControlofPrecessionalDynamics 79
9.1 CoherentSuppressionofPrecessioninMagneticThinFilms 80
9.2 CoherentSuppressionofPrecessioninMicroscaleThin-FilmElement 83
9.3 CoherentSuppressioninMagneticMicrostrips 85
10. Time-DomainPrecessionalSwitching 86
11. SummaryandFutureDirections 92
Acknowledgments 94
References 94
1. GENERAL INTRODUCTION
Magnetismisanoldsubjectwhoseorigingoesbacktoabout600BC
[1]. Since its early discovery, magnetism has been used to the benefit of
humansocietystartingfromitsuseinsurgerytotheuseofcompassfornav-
igation.Overtheyears,magnetismhasseendiscoveryofmanyfundamental
phenomenaandcontributedmanymodern-daytechnologiesinelectromag-
neticsindustry,healthscience,andmorerecentlyinminiaturizedsolid-state
devicesincludingmagneticdatastorageandmemorydevices.Themodern
Time-DomainStudyofMagnetizationDynamics 3
magnetismhasitsorigininthebeginningofnineteenthcentury,whichbegan
withtheseminalworksbyOersted,Ampere,Gauss,Biot-Savart,Faraday,and
Lorentz, which formed the basis of magnetostatics and magnetodynamics.
Based upon these works, Maxwell [2] in 1861–1862 formulated the well-
knownMaxwell’sequationsunifyingelectricity,magnetism,andoptics.
Magnetic domain theory was developed in 1906 by Weiss [3], who
suggestedthatalargenumberofatomicmagneticmomentsarealignedpar-
allelineachdomain.Weissexplainedthespontaneousalignmentofatomic
momentwithinaferromagnetic materialby Weiss’smeanfield theory.Ifa
system is in a single-domain state in equilibrium and the spins rotate uni-
formly during reversal, then it can be described by a macrospin model.
Quasisingle-domain systems may reverse by inhomogeneous modes, such
ascurling,fanning,buckling,andbytheformationof“C,”“S,”andvortex
states [4,5]. The simplest classical model describing single-domain systems
with coherent rotation was developed by Stoner and Wohlfarth [6] and is
commonly referred to as Stoner–Wohlfarth model. The aim of this model
istoanalyticallycalculatetheequilibriumdirectionsofthemagnetizationfor
a given anisotropy and a given applied field and its history. Further, for a
magnetic field applied along a given direction, one can calculate the field
value at which the magnetization reverses. As spatial variation of magneti-
zationisignoredinthismodel,theexchangeenergydoesnotplayaroleand
the magnetic switching is governed by the interplay between the Zeeman
energy and the effective anisotropy. In 1935, Landau and Lifshitz [7] gave
a theory of the dispersion of magnetic permeability in ferromagnetic body
andpredictedanequationofmotiondescribingprecessionofmagnetization.
TheLandau–LifshitzequationwaslatermodifiedbyGilbert[8],wherethe
original damping term was replaced by a dimensionless Gilbert damping
term. In 1946, Griffith [9] experimentally observed the ferromagnetic res-
onance(FMR)forthefirsttime.In1948,Kittel[10]derivedtheformulafor
theFMRfrequencyintermsofexternalmagneticfieldandtheinternalmag-
netic parameters famously known as Kittel formula.
Today,withtheinventionofvariousnewmagneticmaterials,synthetic
structures, micro- and nanostructures, and metamaterials, magnetism has
comealongwayandfoundapplicationsinarangeofmultidisciplinaryfields
inmodernandfuturenanotechnologieslikenonvolatilemagneticmemory
[11,12],magneticstoragemedia[13],magneticrecordingheads[14],mag-
netic resonance imaging [15], and biomedicine and health science [16,17].
Morerecently,emergingtechnologiesareproposedinthefieldsofspinlogic
[18,19], spin-torque nano-oscillators (STNOs) [20], and magnonic
4 AnjanBarmanandArabindaHaldar
crystals [21]. The new technologies demand the invention of new material
properties,whichmaynotalwaysbepossibletoachieveinasinglematerial
inthebulkorthin-filmform.Instead,structuringofknownmaterialsinone
andtwodimensionsatvariouslengthscalesandexploitingdynamicalmag-
netic properties over various time scales may potentially offer the desirable
material properties. An existing example is the patterned magnetic media,
which uses ordered arrays of lithographically patterned two-dimensional
arraysofbits,andthemagneticswitchingbehaviorsofsuchsystemsinclud-
ing switching field distribution have been thoroughly studied. An essential
criterion has been to eliminate magnetostatic interaction (crosstalks)
betweentheindividualbitsfortheapplicationinpatternedmagneticmedia.
Thesamesystemmaybeusedtotransmitmagneticexcitationsintheformof
collective long wavelength spin waves as information carrier in magnonic
crystals,whentheindividualmagneticelementsarestronglymagnetostatically
coupled.Forvariousapplications,explorationofavarietyofnewphenomena
isrequiredandthisrangesfromslowerprocessessuchasdomainwalldynamics
andmagneticvortexdynamicstofasterprocessessuchasspin-wavepropaga-
tion and localization and ultrafast demagnetization and relaxation. This also
introduces magnetic structures at various length scale such as nanodots,
microdisks, andfinally magnetic nanowires andnanostripes.
Thekeychallengestoinvestigateandtoapplythephysicalphenomenon
mentioned above are the synthesis or fabrication of high quality magnetic
materialsandtheircharacterization.Technologydemandsfabricationofmag-
neticultrathinfilmsandmultilayers(MLs)withhighsurfaceandinterfacequal-
ities.Applicationsinvariousmagnetoelectronicandmagnonicdevicesrequires
the fabrication of nanomagnets with narrow size dispersion arranged in an
orderedarrayoveramacroscopiclengthscale.Theseledtothedevelopment
ofanumberof“top-down”and“bottom-up”approachesinnanofabrication
methodsandmorerecentlyacombinationofthetwo.Whilethebottom-up
approachmainlyreliesuponsolutionphasecolloidalchemistry[22]andelec-
trochemistry using different templates such as track-etched polymer [23],
anodicalumina[24],anddiblockcopolymermembranes[25],thetop-down
approachreliesprimarilyonphysicalprocesses.Thisincludesdifferentkindsof
lithographictechniquessuchasphotolithography[26],electronbeamlithog-
raphy (EBL) [27], deep ultraviolet lithography (DUV) [28], X-ray lithogra-
phy [29], interference or holographic lithography (IL) [30], nanoimprint
lithography(NIL)[31],andionbeamlithography(IBL)[32].Scanningprobe
lithography[33],stepgrowthmethods[34],shadowmasks[35],andlaseror
ionirradiation[36]arealsoverypromisingtechniques.
Time-DomainStudyofMagnetizationDynamics 5
The quasistatic and ultrafast magnetization dynamics of magnetic thin
films,multilayers,andnanostructuresaredifferentfromtheirbulkcounter-
parts.Magnetizationdynamicsofthesesystemsstronglydependsupontheir
staticmagnetizationstates,whichdependnotonlyontheirintrinsicmaterial
parameterssuchasexchangestiffnessconstant,saturationmagnetization,and
magnetocrystallineanisotropy,butalsoontheirphysicalstructuresaswellas
theexternalparameterssuchasthestrengthanddirectionofthebiasmagnetic
field. To study the quasistatic and ultrafast dynamic properties of
nanomagnets, different kinds of sensitive characterization techniques have
been developed in last few decades [37]. Magnetic force microscopy
(MFM) [38] and Lorentz force microscopy [39] are two such examples,
which are now extensively used to map the gradient of the stray magnetic
fieldandthesamplemagnetization,respectively,withaspatialresolutionbet-
terthan10nm.ForMFM,thecontrastoftheimagescomesfrommagnetic
forcebetweenthescanningmagnetictipandthegradientofthestraymag-
neticfromthesample.Ontheotherhand,thedeflectionoftheaccelerated
electrons by Lorentz force after transmitting through thin magnetic speci-
menscreatesthemagneticcontrastincaseofLorentzmicroscopy.However,
it is not straightforward to extract quantitative information directly from
either of these imaging techniques. Electron holography [40] is another
imagingtechniquebasedupontheelectroninterference,bywhichtheampli-
tude and phase information of the spin configurations and stray magnetic
fields can be mapped with a very high spatial resolution down to 2nm.
Magneto-optical Kerr effect (MOKE) microscopy [41] is an old technique
and is widely used to map the sample magnetization with a sub-mm spatial
resolution.Thephotoemissionelectronmicroscopy(PEEM)[42]isaform
ofX-raymicroscopyandhasafarbetterspatialresolutionthanvisiblelight
imaging. Spin-polarized low-energy electron microscopy (SPLEEM) [43],
scanning electron microscopy with polarization analysis (SEMPA)[44],
spin-polarizedscanningtunnelingmicroscopy(SP-STM)[45],andballistic
electronmagneticmicroscopy(BEMM)[46]areotherimagingtechniques,
whichgiveexcellentspatialresolutionof10nmorbetter.Thesetechniques
usethespin-dependenttransmission,scatteringortunnelingofelectronsfor
imagecontrast.However,despitehavingverygoodspatialresolution,allthe
abovetechniquessuffer frompoorormoderatetemporalresolution.
Subsequently,differentkindsofexperimentaltechniqueshaveemerged
to investigate fast magnetization dynamics of magnetic thin films and
nanostructures. The conventional FMR [47] and vector network
analyzer-based broadband ferromagnetic resonance (VNA-FMR) [48]
6 AnjanBarmanandArabindaHaldar
techniquesareveryefficienttomeasurethehigh-frequencymagneticreso-
nance,permeability,andlossfromMHztotensofGHzregimelimitedonly
by the instrumental bandwidth with a very good spectral resolution. Later,
Tamaruetal.[49]developedthespatiallyresolvedFMRtoimageresonant
modeprofilesofconfinedmagnetic elements.Pulsedinductivemicrowave
magnetometry (PIMM) [50] is an oscilloscope-based time-domain tech-
niquetomeasurethemagnetizationdynamicswithtensofpicosecondtem-
poral resolution. Brillouin light scattering (BLS) is based upon the inelastic
lightscatteringfromspinwavesandotherquasiparticlesandisconvention-
allyused to studythespinwavesin thewavevectordomain[51].Thefre-
quencydispersionofthespinwaveswiththeirwavevectorcanbemeasured
directlybyvaryingtheangleofincidenceoflightwithrespecttothesample
planeusingthistechnique.Recentlyspace-resolvedandtime-resolvedBLS
techniqueshavebeendevelopedtoobtainsub-mmspatialresolutionandfew
ns temporal resolution [52]. The best spatiotemporal resolution is obtained
from time-resolved magneto-optical Kerr effect (TRMOKE) micro-
scope [53]. They are used to probe the ultrafast magnetization dynamics
in time domain and can achieve tens of femtosecond temporal resolution
limited only by the pulse width of the laser. The magnetoresistive
methods[54]andX-raymicroscopy[55]alsohavethepotentialtoachieve
very good spatiotemporal resolution similar to TRMOKE. Time-resolved
scanning Kerr microscopy (TRSKM) is a variant of TRMOKE, which is
used to image the time evolution of magnetization excited by a time-
dependent magnetic field.
Here,wewillreviewthetime-domainstudyofmagnetizationdynamics
inmagneticthinfilmsandnanostructures.Theremainingpartofthereview
will be divided into 11 subsections. In Section 2, we will describe the
backgroundtheoryofmagnetizationdynamics.InSection3,wewillrevisit
the development of TRMOKE experiments from early 1990s to cater the
need of various measurement systems and properties starting from funda-
mental science to industrial needs. We will discuss some milestone instru-
mental development and investigation of new phenomena using this
technique.InSections4–9,wewilldescribethetime-domainmeasurements
of precessional dynamics in some specific and important magnetic systems.
This includes microscopic elements (Section 4), magnetic multilayers
(Section 5), magnetic nanodot arrays (Section 6), single nanomagnet
(Section 7), and magnetic vortex and domain wall dynamics (Section 8).
InSection9wereviewthecoherentsuppressionofmagnetizationdynamics
usingmagneticfieldpulseshaping,andinSection10wereviewtheprogress
Time-DomainStudyofMagnetizationDynamics 7
inprecessionalswitching.Finally,weconcludeanddiscussthefuturedirec-
tions in the study of time-domain magnetization dynamics (Section 11).
2. THEORETICAL BACKGROUND
2.1. Time Scales of Magnetization Dynamics
Magnetization dynamics can occur over a wide range of time scale.
Figure 1.1 shows various kinds of magnetization dynamics with their
characteristictimescales[56].Thetimescales(t)aredeterminedbytheinter-
actionenergies(E)viaHeisenbergrelationt¼h/E.Thefastestprocessisthe
fundamental exchange interaction, which occurs within 10fs. The spin–
orbit coupling and spin-transfer torque occur in the time scale of 10fs–
1ps. Laser-induced ultrafast demagnetization occurs within few hundreds
offs.Thefastremagnetizationtimefollowingtheultrafastdemagnetization
covers the time scale of 1–10ps. The magnetic writing which is done via
reversalofspinhasatimescaleoffewpstofewhundredsofps,whereasvor-
texcoreswitchingoccursfromfewtensofpstonstimescale.Theprecession
of magnetization occurs within few ps to few hundreds of ps whereas the
dampingassociatedwithmagnetizationprecessionoccursfromsub-nstotens
Figure1.1 Characteristictimesscalesofvariouskindsofmagnetizationdynamics.