magnon scattering in the transport coefficients of cofe thin...
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Magnon scattering in the transport coefficients of CoFe thin films
ExperimentalandAppliedPhysics,RegensburgUniversity*Dept.ofChemistry,Ludwig-MaximilianUniversity,Munich
S.Srichandan,M.Kronseder,S.Wimmer*,M.Vogel,C.Back,H.Ebert*,C.Strunk
SpinCat
Spin, charge and energy transport in novel materials Hvar 2017
manynewtypesofspin-dependenttransporteffects:
• spin-Hallandinversespin-HalleffectsKatoetal.,Science2004;Wunderlichetal.,PRL2005;Saitohetal.,APL2006
• transverseandlongitudinalspin-Seebeckeffects Uchidaetal.,Nature2008;Jaworskietal.,Nat.Mat.2010;Uchidaetal.,Nat.Mat.2010
• spin-PelXerandspin-NernsteffectsFlipse,etal.,Nat.Nanotech.2012;PRL2014;Meyeretal.,Nat.Mat.2017
Spin - caloritronics
howwelldoweunderstandthemoreconvenXonaltransportphenomena?
• spin-dependentresisXvity?
• spin-dependentthermopower?
• spin-effectsinthermalconductance?
someXmesaneffectcandisappearagain...M.Schmid,S.Srichandan,C.S.,C.Backetal.,PRL2013
differenttypesofquasi-parXclescontributetoandaffecttransportofcharge,spinandheatinferromagnets:
• electronswithmajorityandminorityspins
• phonons
• magnons
Magnon scattering in itinerant ferromagnets
Canweseparatetheeffectsfromdifferentsub-systems?
studiedinthe1950's–1970's,butnodetailedunderstandingatthatXme
–Xmetotakeafreshview:
• preciseroleofspin-degreesoffreedom?
• systemaXcchangeofelectrondensityascontrolparameter
• comparisontostate-of-the-artmodelcalculaXons
Device fabrication
AuPdheater
CoFefilm
Althermometers
etchedarea
plainSiNmembrane 1stEBLstep 60-80nmCoFe
2ndEBLstepAlcontacts+thermometersAuPdheaters
RIEetchinginCHF3+O2
3rdEBL
4thEBL
AlcontactstomeasureresisXvityandthermopower
SiN based suspended microcalorimeter
XRDcharacterizaXonofCoFefilms:
§ xCo=0.22,0.22:singlebccphase,§ xCo=0.36,0.7:mixedbcc+fccphase
50µm
AuPdheater
CoFefilm
Althermometer
Alcontacts
topviewofdevice
etchedarea
seealsoA.D.Avery,etal.,PRL2012
Electrical resistivity
§ monotonicdecreasewithdecreasingelectrondensity
§ temperaturedependentpart:Δρ=ρ(296K)-ρ(25K)~2-5μΩcm,comparabletootherexperimentalgroup1.
§ ΔρsmallerthantheΔρofbulkFe2(10.41μΩcm)andofCo3(6.23μΩcm),respecXvely.
1C.Ahnetal.,Jour.Appl.Phys.108,023908(2010)2M.Rubinsteinetal.,Phys.Rev.B37,15(1988)3J.W.C.DeVriesetal.,ThinSolidFilms167,25-32(1988)
Resistivity as a function of Co concentration
• besideschemicaldisorderstrongcontribuXonfromgrainboundaryscapering
• violaXonofMaphiessen'srule
1M.Rubinsteinetal.,Phys.Rev.B37,15(1988)2J.W.C.DeVriesetal.,ThinSolidFilms167,25-32(1988)3P.P.Freitasetal.,Phys.Rev.B37,6079(1988)
Understanding the effects of different scattering processes
§ measureT-dependenceofdifferenttransportcoefficientswhilesyste-maXcallytuningtheFermilevelthroughthe(pseudo)bandstructure
§ comparisontomicroscopictheory(Ebertgroup,LMUMunich)
1. ForbandstructurecalculaXon,MunichSPR-KKR-programpackagehasbeenused.ThisincludesthefullyrelaXvisXcKorringa-Kohn-RostokermulXplescaperingGreen‘sfuncXonformalismtoevaluateKubo‘sformula. H.Ebertetal.,Rep.Prog.Phys.74,096501(2011)
2. TemperaturedependentcalculaXonforresisXvityusingalloy-analogymodel(AAM)basedoncoherentpotenXalapproximaXon(CPA)includingvertexcorrecLons. H.Ebertetal.,Phys.Rev.B91,165132(2015)
ThermopowerfromgeneralizedMopmodelusingtemperaturedependencefromelectricalconducXvityandFermi-DiracdistribuXon.
S. Wimmer et al., Phys. Rev. B 88, 201108 (R) (2013); Phys. Rev. B 89, 161101 (R) (2014)
Band structure (Bloch spectral function)
0.2
0.25
0.4
0.5
xCo
§ redlines:shapeofd-likebandofthespin-upchannel
§ 0representstheFermienergyEF
§ EFinreaseswithrespecttobandswhenelectrondensityincreases
S.Wimmeret.al.(2016)
Separation into electron-phonon and electron-magnon scattering contributions
§ phononandmagnonenergyscalesdifferbyafactor10
§ electron-magnonscaperingcontribuXonissmall
M.V.Kamalakaretal.,Appl.Phys.Lep.95,013112(2009)
§ chemicalandvibronicdisorderscaperingcontribuXonincalculaXonsunderesXmatestheresidualresisXvityandoveresXmatesthetemperaturedependence
S.Wimmeret.al.(2016)
pureFe:Raquetetal.2002
MagneXccontribuXontoresisXvityremainingauersubtracXonofBloch-Wilsonfit(?)
Thermopower S(T)
§ S(T)ismostlynegaXveinsign.
§ monotonicincreasewithdecreasingelectrondensity.
§ visiblechangeofsignofcurvatureatlowertemperatures.
Separation of Mott-like and magnon drag contributions
2/3'')( TSTSTS dragMagnonMott −+=
S.J.Watzmanet.al.,Phys.Rev.B94,1444(2016)
fromWatzmanetal.
70%Co
WitharXficialdisorder
3NCo
lowenergymagnonnumber~T3/2
Separate magnon drag and Mott-like contributions
§ conjecturedSMoPextractedfromexperimentislinearinTbyconstrucXon.
§ thermoelectricparameterη=-3eSMo%TF/π2kB=5.2forfilmwithxCo=0.2iscomparablewithη=7.6forliquidFeK.Hirataetal.J.Phys.F:MetalPhys.7,3(1977)
§ maximumSmagnon-dragis15μV/Kat296KforfilmwithxCo=0.2.
§ Smagnon-dragchangessignfromnegaXvetoposiXvefollowingsignofbulkCoandFe
S.J.Watzmanet.al.,Phys.Rev.B94,1444(2016)
origin of the sign change of magnon drag thermopower?
§ Smagnon-dragmaycontaininformaXononthespintransfertorqueparameters
§ relaXontoSmagnon-dragsignchange?
( ) magnondragmagnonS καβ 3−∝−
hydrodynamicdraglike Gilbertdampingparameter,
Berryphaselike
Y.Tserkovnyaketal.,J.Magn.Mag.Mat.320,1282(2008)
B.Flebusetal.arXiv1605.06578
Mott-like contribution compared to microscopic calculation
§ CalculaXonusinggeneralizedMoprelaXonshowsbandstructureeffects.
§ Mop-likecontribuXontothermopowerextractedfromphenomenologicaldecomposiXon ( )( ) ( )
( ) ( )∫
∫
∂∂−
∂∂−
−−=
εεµε
εσ
εεµε
µεεσ
dTf
dTf
eTS ,,
,,1
S D (m
V/K)
-30
-20
-10
0
T (K)0 100 200 300
20
22
365070
Residual thermopower
§ Sresidue(T)=S–SD–SMis(much)smallerthanSMandSD
§ ForfilmswithxCo=0.2and0.22,SresidueissimilartophonondraginbulkNi(andAlreferenceleads)
§ ForfilmswithxCo=0.36,0.5and0.7,effecXvein-elasXcscaperingandphonondrageffect
E.Shapiraet.al.,Nanotechnology18,48(2007)
Thermal platform model for thermal conductance
thermalbathT0
TH TC PC=0
PH=IHVH
KB=KSiN+KCoFeKL KL
VHIH
hotisland coldisland
SoluXonof1DthermaldiffusionequaXon
( ) ( ) HBLL
BCH
BLL
BLH P
KKKKTTP
KKKKKTT
2,
2 00 ++=
+
++=
P.Kimetal.Phys.Rev.LeM.87,215502(2001)R.Sultanetal.J.Appl.Phys.105,043501(2009)
KB=bridgeconductanceKL=leadconductancePH=heaterpower
SiN based suspended microcalorimeter
50µm
AuPdheater
CoFefilm
Alcontacts
AlThermo-meter
etchedarea
topviewofdevice
Comparison with microscopic calculation results
§ theoryreproducesnicelytheconcentraXondependence§ numbersareafactortwolargervaluesofκ-mostprobablyconnectedtounderesXmaXonofρintheory
§ theoryworksbeperthanforρandS.
%Co
experimentcalculaLonwithvibronicdisorder
Lorenz ratio and violation of Wiedemann-Franz law
§ LorenznumberL(T)/L0=κ(T)ρ(T)/T§ L>L0:ForfilmswithxCo=0.2and0.22duetothesignificantphonon(magnon?)
contribuXontothermalconducXvity(nofccphaseprecipitaXon)§ L<L0:ForfilmswithxCo=0.36,0.5and0.7duetoenhancedinelasXcscapering
ofelectronswithphononsandmagnons(withfccphaseprecipitaXon)
experiment theory
Conclusions
§ Experimentalpla|ormenablesstudyofalltransportcoefficientsoftheverysamefilm
§ TheorysignificantlyunderesXmatescomposiXondependentresisXvity
§ ThermopowerisphenomenologicallydecomposedintoMop-likeandMagnondragterms-thelaperchangessignforlargeCo-concentraXons
§ ThermalconducXvityismainlyelectronic
§ SignificantdeviaXonsfromWiedemann-Franzlawobservedinexperiment.