Magnon scattering in the transport coefficients of CoFe thin...
Transcript of Magnon scattering in the transport coefficients of CoFe thin...
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.