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.