Influence of the electronic structure on the transport properties of some iron pnictides

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F. Rullier-Albenque.

Influence of the electronic structure on the transport properties of

some iron pnictides.

Comptes Rendus Physique, Centre Mersenne, 2016, 17, pp.164 - 187.

properties

of

some

iron

pnictides

Influence

de

la

structure

électronique

sur

les

propriétés

de

transport

de

quelques

pnictures

à

base

de

fer

Florence Rullier-Albenque

Servicedel’ÉtatCondensé,IRAMIS,CEA,CNRSUMR2464,UniversitéParis-Saclay,OrmedesMerisiers,CEASaclay,91191Gif-sur-Yvettecedex, France

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Articlehistory:

Availableonline11November2015

Keywords: Ironpnictides Transportproperties 122family 111LiFeAscompound Mots-clés : Pnicturesdefer Propriétésdetransport Familledes122 Compose111LiFeAs

Animportant featureoftheiron-basedpnictides istheirmulti-bandelectronicstructure withbothelectronand holebandsattheFermilevel. Thesizeofthesepocketscan be changedbydifferenttypesofsubstitution,resultinginavarietyoforiginalmagneticand electronicproperties.Thecontributionsofbothtypesofcarrierswillthushaveimportant consequencesontheevolutionofthetransportpropertiesversustemperatureanddoping. IthasbeenpointedoutthatHund’sruleinteractionplaysaprominentroleinthephysics ofthesecompoundsbyallowingastrongorbitaldifferentiationbetweenthe3dFeorbitals. Asaresult,adescriptionintermsofmoreorlesscorrelatedelectronswasproposedand may have important consequenceson the scattering lifetimes of the different carriers. Finally,thepresenceofveryflat bandsatthe Fermilevelmay inducea semiconductor-like behavior, with a change in carrier concentration with temperature. In this paper, wewill reviewthe evolution of transport properties with chemical doping/substitution in iron pnictides. We will more particularly focus onthe 122 family (Ba(Sr,Ca)Fe2As2) and the 111LiFeAs compound for whichsizeable single crystalsrequired for transport measurementsare available. Thecombined resistivity,Hall effectand magnetoresistance datawillbeanalyzedinassociationwithelectronicstructurecalculations,angle-resolved photoemissionmeasurements and quantumoscillations. Inspite ofthe strong interplay betweenantiferromagnetismand superconductivityinmostpart oftheirphasediagram, directsignaturesof spinfluctuations are difficulttoidentifyin thetransport properties ofironpnictides.Wewillshowthatmeasurementsofthelongitudinalmagnetoresistance provideapowerfultoolforstudyingthecouplingbetweenthechargecarriersandthespin degreesoffreedom.

©2015Académiedessciences.PublishedbyElsevierMassonSAS.All rights reserved.

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Unecaractéristiqueimportantedespnicturesàbasedeferestleurstructureélectronique « multi-bandes » présentantàlafoisdesbandesd’électronsetdetrousauniveaudeFermi. La taille de ces poches peut être changée par différents types de substitution, ce qui entraine unegrande diversitéde propriétésmagnétiques etélectroniquesoriginales. On

E-mailaddress:florence.albenque-rullier@cea.fr.

http://dx.doi.org/10.1016/j.crhy.2015.10.007

sont disponibles. Les données combinées de résistivité, effet Hall et magnétorésistance seront analysées en association avec les calculs de structure électronique, les mesures de photoémission résolues en angle et oscillations quantiques. En dépit de la forte interaction entre antiferromagnétisme et supraconductivité dans la plus grande partie de leurs diagrammes de phase, la signature des fluctuations de spin n’apparait pas directementdanslespropriétésdetransportdespnicturesdefer.Nousmontreronsquela mesuredelamagnétorésistancelongitudinalefournitunesondeintéressantepourétudier lecouplageentrelesporteursdechargeetlesdegrésdelibertédespin.

©2015Académiedessciences.PublishedbyElsevierMassonSAS.All rights reserved.

1. Introduction

Despitethestrongsimilaritiesbetweenthephasediagramsofhigh-Tc cupratesandiron-basedsuperconductors(FeSC), acrucialdifferencecomesfromthefactthattheformeraresingle-bandmaterialswhileallthedorbitalsofironparticipate inthe electronic structure atthe Fermilevelfor FeSC.Thisusually results forall theFeSCs infive Fermisurface sheets: threeholepocketsaroundthecenteroftheFe2As2Brillouinzoneandtwoelectronpocketsaroundthecornersaspredicted bybandstructurecalculationsandevidencedbyangleresolvedphotoemissionspectroscopy(ARPES)[1–3].

Thisrathercomplexmulti-band electronicstructure isoneofthekey ingredienttounderstandthe physicalproperties of theFeSCs and hasimportant consequences on thesuperconducting and normalstate propertiesof thesecompounds. Inthe undopedcompoundsthe spindensitywave (SDW)ordering belowTN iswidelyattributedto thenesting between electronandholequasi-cylindricalbands,whichleadstoareconstructionoftheFermisurfaceandastronglypeakedspin susceptibilityattheantiferromagnetic (AF)wavevector QAF.Itwas argued veryearly thatSC could bealso mediatedby spinfluctuationsatthesamewavevector,resultinginanextendeds-wavepairingwithsignchangeoftheorderparameter betweenelectronandholesheets[4,5].

Thetransportpropertiesarealsoexpectedtobevery sensitivetoanymodificationsoftheFermipocketsasafunction oftemperature, doping or pressure.As amatter of fact,resistivity measurements providethe simplestexperimental way tofollowtheevolutionofthephysicalproperties.ThisisforinstanceillustratedinFig. 1wherethetemperatureresistivity curvesarereportedasafunctionofCosubstitutionintheBa

(

Fe1−xCox

)

2As2 compound[6].Startingfromtheparent com-pound BaFe2As2 wherethemagnetostructuraltransitionisevidenced bythe sharpdropoftheresistivityat TS

=

TN,one canthen easilyfollowthe decreaseinTS andTNandtheappearance ofsuperconductivitywithCosubstitution, allowing one to constructthe phasediagram. We can alsonotice that amarked change inthe evolutionof

ρ

(

T

)

occurs atabout

x

=

0

.

03,forwhichsuperconductivityappears.

Itappearsmuch morecomplicatedtounderstandthetemperaturedependenceoftheresistivityanditsevolution with Cosubstitution.Forinstanceitisstrikingtoseethatthehigh-T partsoftheresistivityshiftdownwardsparalleleachother forweak Co substitution (dashedcurvesin Fig. 1a). This clearly cannot be understoodwithin a one single band picture. Indeedinthatcase,usingasimpleDrudeformulaandMatthiessen’srule,theresistivity

ρ

writesas:

ρ

=

m∗

/

ne2

τ

=

m∗

/

ne2

(

1

/

τ

e

+

1

/

τ

in

(

T

))

(1)

withm∗,n and

τ

e and

τ

in,theeffectivemass,numberofcarriersandelasticandinelasticscatteringtime ofthecarriers respectively. Knowingthat Coelectron dopesthesystem, onewouldexpect changes oftheslope oftheresistivity curves withCosubstitution,contrarytowhatisobserved.

Thus thetransport propertiesofFeSCswill dependina non-trivialmanneronthe numberofcarriersinthe different Fermipocketsandtheirrespectiveintra- andinter-bandscatterings.Thescope ofthispaperisto reviewtheevolutionof their transport properties– resistivity, Hall effect andmagnetoresistance – in relationship withwhat is known on their electronicstructureeithertheoreticallyby bandstructurecalculationsorexperimentallyby ARPESorquantumoscillations studies.Wewillrestrictourselvestotheironpnictidesandmoreparticularlytothoseforwhichsizeablesinglecrystalscan be synthesized,a prerequisite togetgood measurementsof transportproperties.Mostofthe paperwillbe thusdevoted

Fig. 1. (a) Resistivitycurvesofthe122-compound Ba(Fe1−xCox)2As2 for differentCo concentrations(from[6]).The evolutionofthe superconducting transitionscanbeeasilydetermined.Anomaliesoftheresistivityallowonetodetermineboththestructuralandthemagnetictransitiontemperaturesby lookingatthetemperaturederivativeofresistivityasshownin(b)andtobuildupthephasediagramofthiscompoundasafunctionofCosubstitution (c).

to theveryrich 122BaFe2As2 familywhichhasbeenthemostextensivelystudied systemsince superconductivitycanbe obtained by verydifferent routes– electronor holedoping, isovalent substitution andpressure.Another compoundthat is particularlyinteresting isthe111compound LiFeAssince itisthe onlynearly stoichiometriccompound,together with NaFeAsandKFe2As2,whichissuperconductingwithoutanysubstitution.Moreover,duetotheneutralsurfaceofLiFeAsafter cleaving, onedoesnotexpect anyinfluence ofthe surfaceonthe electronicstates.Thereforethedataofsurface sensitive probessuchasangleresolvedphotoemissionspectroscopy(ARPES)areverywellrepresentativeofthebulkproperties[7].

2. 122compounds

Among the 122system,BaFe2As2 appearsasthe prototypicalironpnictide compoundassuperconductivity canbe in-duced eitherby substitution onthe iron site (electrondoping by Co orNi [8–10]; isovalent substitution by Ru [11,12]), substitutionontheBasite(holedopingbypotassiumsubstitution[13])orsubstitutionontheAssite(isovalentphosphorus substitution[14–16])(morereferencescanbefoundinthepaperofMartinellietal.[18]).Thisprovidesanexceptional play-groundtostudythedifferentmodificationsoftheelectronicstructureandtheirconsequencesonthetransportproperties. Albeitlessstudied,allthesesubstitutionsarealsopossibleintheSrFe2As2 familyanddisplayalotofsimilaritieswiththe behaviorobservedintheBaFe2As2 family.

However substitution effects in the CaFe2As2 family appear quite different, probably related to the existence of the collapsed tetragonalphase observed inthe pure CaFe2As2 underpressure. Althoughonsets ofsuperconducting transition temperatures ashighas47 K, themaximumso far amongthe122 family,were observed byaliovalent substitution into thealcalineearthsiteofCaFe2As2singlecrystals[17],thereissomedoubtaboutthebulknatureofthissuperconductivity. Moreover the morphology of these crystals appear to be strongly dependent on the annealing conditions and not very reproducible[19]

2.1. Parentcompoundsandelectrondopingonironsitebytransitionmetalsubstitution

Iron substitutionsbyatomssituatedattherightofiron intheperiodictableareexpectedtoelectrondopethesystem. This wasclearly evidencedby ARPESmeasurements [22,24]whichshowedthat theareasoftheholebandsdecreaseand those oftheelectronbandsincreaseupon CoorNisubstitution, contraryto sometheoreticalproposals [25].Moreoveras shown inFig. 2, thephase diagramsforthese twosubstitutions matchwitheach other ifthey are plottedasa function of electron doping, showing unambiguously that each Co (Ni) atom adds one (two) electron(s) to the bands. The same observationwasfoundforRhandPdsubstitutions[26].

2.1.1. Transportinthehigh-temperatureparamagneticphase

Resistivity Asalreadypointedout above,the effectofelectrondoping doesnotappearon theresistivitycurves straight-forwardly. First let us note that the iron pnictides were sometimes qualified as “bad metals” due to the fact that their

Fig. 2. (a) Resistivitycurvesofthe122-compoundBa(Fe1−xNix)2As2fordifferentNiconcentrations(from[20]).Theevolutionoftheρ(T)curveswithNi substitutionisverysimilartothatobtainedwithCosubstitutionseeFig. 1.(b)PhasediagramindicatingTmagandTcforthetwofamilies.Aclosematching isobtainedbyplottingthedataversusxNiandxCo/2.

Fig. 3. TemperatureresistivitycurvesofSr(Fe1−xCox)2As2forlowCodopings.Thehigh-T paramagneticpartsarewellfittedbyA+B T2(fulllines)withA decreasingwithCocontentsandB remainingnearlyconstant.From[31].

resistivitiesareratherhighanddonotsaturateathightemperature[27,28].However,theobservationofaDrudelike com-ponentatlow frequenciesintheoptical conductivityofiron pnictidesrevealsthepresenceofitinerantelectrons moreor lesscorrelateddependingonthesystem.Moreover,inthecaseofBaFe2As2,thefactthatthe

ρ

(

T

)

curvecanbewellfitted by A

+

B T2 _{inthehigh-T paramagneticphase,asnoticedrecentlyinRef.[30],indicatesconventionalFermiliquidbehavior} withconsiderableelasticscattering, A beingmuchlargerthanB T2_{.Howeveritisworth mentioningherethatARPES} mea-surementshaveevidenced a strongincrease ofthenumberofelectrons withtemperatureinthistemperaturerange [29] (seeFig. 6below),whichindicates thatsomecareshould betakentoextractthegenuine T dependenceofthescattering ratesofthecarriersfromresistivitymeasurements.

In anycase, it isvery puzzling to see that theeffect oftiny substitution by Co(see Fig. 1a)or Ni (see Fig. 2a) isto decrease A while maintaining B T2 nearly constant. Thesame behavior isexemplifiedin thecaseof Sr

(

Fe1−xCox

)

2As2 as reportedinFig. 3 [31].TheseobservationsseemtoindicatethattheinitialintroductionofCoorNi intheFeAsslabs does notchangethenumberofcarriersbutdecreasetheresidualimpurityscattering.Thisisquiteoppositetowhatisexpected, since theseimpurities locatedin theFe planeswill be strongscatterersespecially forelectrons innarrow bands.Clearly moretheoreticalworkisneededtoexplainthisfirstevolutionofthetransportproperties.

Upon furthersubstitutionsby Co orNian increase inthe slopeofthe paramagneticpart of

ρ

(

T

)

isobserved athigh temperatureforallthecompounds.As seeninFig. 1orFig. 2,thischangeofbehaviorisconcomitantwiththeapparition ofsuperconductivity.Moreoverthisisalsoassociatedwitha drasticmodificationoftheelectronic structureinthe recon-structedmagneticphaseasevidencedbyHalleffect,thermoelectricpowerandARPESmeasurements.Thesedifferenteffects willbedescribedinthenextparagraphs.

Halleffect Hall effectmeasurements allow one to getmore insightinto the evolutionof thetransport properties inthe paramagnetic high-T phase. The Hall resistivity is always linear withmagnetic field allowing one to determine the Hall coefficient RH unambiguously. This is no longer true in the magnetic phase where a saturation with magnetic field is observedupondecreasingthetemperature(seebelow)[6,32].ThedatafortheHallcoefficient RHarepresentedinFig. 4a forasetofCodopingsinBaFe2As2.The strongincrease inthemagnitudeof RHiscorrelatedtothereconstruction ofthe

Fig. 4. (a)Temperaturedependenceofthe HallcoefficientforaseriesofBa(Fe1−xCox)2As2 crystals.ThedropofRH signalsthereconstructionofthe Fermi surfaceat TN.Tosee moreclearlythe evolutioninthe paramagneticphase,theHallnumber|nH|isplottedin(b)versus temperature.Here, nH(e/Fe) =0.32/RHx(10−9m3/C).From[6].

Fig. 5. Numberofholes(openbluecircles)andelectrons(blacksquares)extractedfromARPESmeasurementsonBa(Fe1−xCox)2As2singlecrystalsfromthe samebatchesasusedforresistivitymeasurements.Solidbluecirclesindicatethenumberofholesaftercorrectiontakingintoaccountthethreedimensional geometryoftheholepockets.BlackstarsarethelowT datafor|nH|reportedinFig. 4b.Hatchedareasindicatelikelyvaluesforthenumberofholesand electrons,includingpossibleexperimentalerrors.ThickblackandbluesolidlinesarepredictionofLDAcalculationsfortheevolutionofnumberofholes andelectrons[32]reproducedfromRef.[25].

Fermisurface atthemagnetictransitions.Inordertobetter visualizethebehaviorof RH intheparamagnetic phasesand forlargex,wehaveplottedinFig. 4bthevariationsoftheHallnumbernH

=

1

/(

e RH

)

.

The strongvariation of

|

nH

|

with temperatureindicates that several bandscontribute to the transport. Moreover the negative signof RH pointsout thatelectrons give thedominantcontributiontothecharge transportatall T whatever x. Assumingasimpletwobandmodelasastartingpoint,onecouldwrite:

σ

=

1

/

ρ

=

σ

h

+

σ

e (2) e RH

=

1 nH

=

σ

2 h nh

(

σ

e

+

σ

h

)

2

−

σ

2 e ne

(

σ

e

+

σ

h

)

2 (3) wherene(nh)aretheconcentrationofelectrons(holes)usuallytakenasT independentinametallicstate.Oneshouldnote thatchargeconservationimplies:

ne

=

nh

+

x (4)

withtheusualassumptionthatCogivesoneelectrontothesebands.Aswehaveonlythreerelationsforne

,

nh

,

σ

e

,

σ

h,this problemcannotbereadilysolvedwithoutfurtherelementsbasedonphysicalargumentsorotherexperiments.

In particular,itis instructivetolookatthelow T extrapolation ofnH andcompareitto ARPESdeterminations ofthe carriernumbers,asillustratedinFig. 5.Theverygoodagreement foundbetweennH

(

T

=

0

)

andthe numberofelectrons determinedbyARPESstronglysuggeststhatthelowT valueof

|

nH

|

correspondstotheactualvalueofne downto x



4%. This impliesthatonly electronscontribute to thetransport atlow T inthismulti-bandcompound andthatholes are so stronglyscatteredthattheyarenotdirectlyapparentinthetransportproperties.

Fig. 6. NumberofelectronsextractedfromARPESmeasurements[29]asafunctionoftheCocontentfordifferenttemperatures(left)andasafunctionofT

fordifferentCocontent(right).Thankstotheknowledgeofthe3Dshapeoftheelectronpockets[22],thenumberofelectronscanbereliablydetermined. ThesolidorangelineindicatesthenumberofelectronsexpectedfromLDAcalculation.

Thislargeasymmetrybetweenelectronandholescatteringrateshasbeenalsodeducedfromtheanalysisofelectronic Raman measurements,in whichdifferent partsofthe Brillouinzone canbe probed by usingdifferentpolarizations [34]. On thesame wayTHz optical measurements in Ba

(

Fe0.9Co0.1

)

2As2 clearly show that, in the normalstate, the electronic contribution to theinfrared anddc conductivitydominates over the holecontribution [35]. It hasbeen shownthat this disparity between electrons and holes could result from a large anisotropy of the one-particle scattering rates by spin and charge fluctuations on each Fermi surface sheet [36]. This is due both to the momentum dependence of the spin susceptibilityandthemulti-orbitalcompositionofeachFermipocket.Moreover,itisfoundthatthelongerlifetimeoccurs forthedxystatesoftheelectronFermisurfacesheets,wheretheFermivelocityismaximum.Howeverifforwardscattering

correctionsduetoanisotropicinterbandscatteringoffspinfluctuationsareincluded[37],theeffectivetransportrelaxation timesarefoundtobemuchmoreisotropicandtoshownospecialfeaturesaroundtheFermipockets.

ForlargeCodoping,ARPESexperimentsshowthattheholeFermisurfacepocketsbecomeverysmallwhiletheelectron pocketssignificantlyexpand[22,23].Inthiscasenh



ne (and

σ

h



σ

e)sothatEq.(3)writes:

|

nH

| 

ne

(

1

+

2σh

/

σ

)

(5)

tofirstorderin

σ

h

/

σ

.Thissimplelimitevidencesthat,whatevertheexactvalueofne,thedatafor

ρ

(

T

)

and

|

nH

(

T

)

|

would onlybeexplainedbyahighT increaseof

σ

hwithaweakminimumbelow100 K.Thisbehavior,oppositetothatexpected forametallicsystem,ledustoconcludethatneandnhareT dependent.Thisassumptionhasbeenconfirmedqualitatively afterwards byARPES measurements whichreveal astrong T dependence oftheelectronic structure inBa

(

Fe1−xCox

)

2As2. A similarevolutionoftheelectronicstructurewithtemperaturehasalsobeenobservedbyARPESinBa

(

Fe1−xRux

)

2As2 [33] (seebelow).

AsshowninFig. 6,theT dependenceofthenumberofelectronsdeducedfromARPESisstrikinglysimilartothatof

|

nH

|

reportedinFig. 4a,albeitabitsmallerquantitatively.ThisT variationofthecarriercontentcanbepartlyassignedtothe factthat EFisonly20–40 meVbelowandabovetheholeandelectronbandsintheBaFe2As2 parent.Thermalpopulation of the hole andelectron bandsyields then a shift of the chemical potential

μ

(

T

)

to fulfill Eq. (4). A rough calculation withintheFermiliquidtheoryandbasedonasimplesketchoftheCo8%–BaFe2As2band structuregivestherightorderof magnitudeforthe observedshiftof thechemical potential,supporting the ideathat thiseffectplays a leading role [29]. Consequently,partoftheT dependentbandshiftobservedbyARPEScouldbeasimpleconsequenceofthermalpopulation factorswhenthebottomortopofabandliesclosetotheFermienergy.Neverthelessonecannotexcludethatthiscanalso be dueto a weakeningof thecoupling betweenquasiparticles andinterbandspin fluctuationswith increasing T , asthe strengthofthespinfluctuationsisexpectedtodecreaseathighT [38].

Letuspoint out thatan attemptto explain thesign andthetemperatureanddoping variation oftheHall coefficient hasbeenproposedbyFanfarilloetal.[42].Theseauthorsshowthat,inamulti-bandsystemwithpredominantlyinterband interactionsbetweenelectronsandholes,currentvertexcorrectionsduetotheexchangeofspinfluctuationsinduceamixing oftheelectronandholecurrent,whichcouldresultinarenormalizedcurrentdominatedbythecharacterofmajoritycarrier. Howeverthistheoreticalapproachdoesnotconsiderthepossibilityofa T variationofthenumberofcarriers.

Scatteringratesofthecarriersandtemperaturedependenceoftheresistivity This temperaturedependence ofthe numberof carriershasimportantconsequences onthedetermination oftheir scatteringrates fromresistivity measurements.Indeed in a simple metal with only one single band, the T dependence of the resistivity can be directly assimilated to the T

dependenceofthescatteringrateofthecarriersfromEq.(1).InparticularithasbeenclaimedthatthelinearT dependence

oftheresistivityobservedupto

∼

120 K in Ba

(

Fe0.93Co0.07

)

2As2 (seeFig. 1a)supports theexistenceofa quantumcritical pointon thevergeoftheantiferromagneticorder[39,40].As shownabove, thefactthat thenumberofcarriersincreases withtemperatureindicatesthatthiscannotbeconcludeddirectlyfromresistivitymeasurements.Inthesameway,quantum criticalpoints havebeenclaimedin thecaseofBa

(

Fe1−xNix

)

2As2 forx

=

0

.

05 andx

=

0

.

07 on the observationofnearly linearresistivitydependences[44].AsfoundforCo-doped BaFe2As2 [43],theconcomitantobservationofanupturninthe

Fig. 7. (a) T variationofCot(H) =ρ/|RH|at1 T.(b)Thisquantity,whichreducesto

(

me/m0/)/τ ifσhσe,isplottedversusT2 intheparamagnetic phaseforx4%.ThisevidencesaFermiliquidbehaviorforT≤150 K.Insetof(a):CoefficientB oftheT2variationversusneinlogarithmicscales.The linecorrespondstoB∝1/ne.

spinlatticeNMRrelaxationrateweretakenasthesignatureofquantumcriticality.Suchlinearresistivitydependencescan alsobeobservedinFig. 2aforx

=

0

.

06.Howevertheanalysisinasinglebandapproachperformedbytheseauthors[44]is highly questionable;inparticular,wehaveclearlyshownthatbothholes andelectronscontributetothetransportbeyond theoptimaldoping[20].

IntheassumptionthatonlyoneelectronbandcontributestothetransportofBa

(

Fe1−xCox

)

2As2,thequantityCot

(

H

)

=

ρ

/

|

RH

|

equals me

/

e

τ

andgives a direct determination of the electron scatteringrate 1

/

τ

(

T

)

.The datafor Cot

(

H

)

are reported in Fig. 7a for all the superconducting samples.The very similar behavior displayed by Cot

(

H

)

above TAF for all x doesnot showup anydirect incidenceonthe transportof thespin fluctuationsdetectedin thenuclear spinlattice relaxationrates[21].ThismightleadustoanticipatethatthevariationofnHisalwaysgovernedbyaT variationofne,even forthelowerCocontents.Asshownbelow,theinterplaybetweencharge transportandspinfluctuationscanbeevidenced bylongitudinalmagnetoresistivitymeasurements.

As shownin Fig. 7b forx



4%, thisyields 1

/

τ

(

T

)

data whichsplit, asusual, ina T -dependent 1

/

τ

e

(

T

)

anda resid-ual 1

/

τ

0.Theformerisverywellfittedbelow150 KbyaFermiliquidlike T2 lawhighly dependentonx,whichexcludes anelectron–phononscatteringcontribution.Suchelectron–electronscatteringprocessesaregivenby:

¯

h

/

τ

e

(

T

)

=

A

(

kBT

)

2

/

EF (6)

where A isadimensionlessconstant[41].Theyareoverwhelmedby phononprocessesinusual metals,butareenhanced heresincekBT



EF.Forx

=

14%,withEF

=

25 meV andme

/

m0

=

2 takenfromARPES,weestimateatypicalvalue A



4, whichcorroboratesthevalidityofouranalysis.WefurthermorefindthattheT2 _{coefficientdisplaysasimple1}

_/

_n

evariation (inset ofFig. 7a), whichagrees with EF

∝

nαe forasimpleparabolic band,with

α

=

1 inthe 2D case.As forthedisorder inducedresidualscatteringrate

τ

−1

0 ,wecanseeinFig. 7b,thatitremainsunchangedintheparamagneticstateforallx,so thatnativedisorderdominatesovertheeffectofCosubstitutionintheFeplanes.

It is worth mentioninghere thatsuch a T2 dependenceforthe scatteringrateof themajority carriershasbeen also deduced fromoptical conductivity measurements [45]. Indeedthe frequency-dependentconductivitycan be decomposed intoabroadtemperatureindependentbackgroundandanarrowDrude-likecomponentwhichsolelydeterminesthe trans-port propertiesanddisplays a T2 _{behaviour within anextended temperaturerange.The plasmafrequency deducedfrom} thisanalysisisfoundtobe independentoftemperature,whichindicates thatthenumberofcarriersremains constant,in contrasttowhatfoundfromHalleffectandARPESmeasurements.

Spinfluctuationsinthetransportproperties Surprisingly,aspointedout above,there isnoidentified signaturesofthespin fluctuationsintheresistivityandHalleffectofCo-doped122compoundsintheparamagneticstateforT

>

TAF.Conversely asshallbeillustratedbelow,wehaveshownthatthecouplingbetweenthechargecarriersandthespindegreesoffreedom can berevealedby highresolutionmeasurementsofthelongitudinalmagnetoresistivity(LMR)[46].Whilealargepositive LMRcomponentisfoundintheAFphaseofBaFe2As2,anegativeandmuchsmallercomponentismeasuredinthe param-agneticstateofCo-substitutedBaFe2As2asreportedinFig. 8.ThenaturalexplanationforthisnegativeLMRisthatitresults fromthesuppressionofspinfluctuationsbythemagneticfield,whichresultsinthedecreaseofthemagneticcontribution totheresistivity.ThesmallvalueoftheLMRmeasuredhere(lessthan0.2%at45 Kand14 T)comfortstheobservationthat thismagnetictermplaysaminorroleinthevalueofthetotalresistivity.

Moreover,weobservedthatthedependenceoftheLMRcoefficient

γ

(

T

)

,definedas



ρ

(

T

,

H

)

= −

γ

(

T

)

H2_{,withT and} CocontentreportedinFig. 9amimicsthebehavioroftheNMRrelaxationratesdisplayedinFig. 9b.Thisstronglysupports therelationbetweenthenegativeLMRandtheAFspinfluctuations.

The T dependenceoftheLMRcoefficient canbeexplainedinanitinerantnearlyantiferromagneticFermiliquidmodel with

Fig. 8. Magneticfielddependenceoftheresistivityofthenon-AFBa(Fe0.925Co0.075)2As2forT rangingfrom30to120 KforHab-planeandI .Linesare fitswithaquadraticfielddependence.From[46].Inset:Thelongitudinal

δ

ρ/ρ0valuesplottedversusH2forHI (fullsymbols)orH⊥I (emptysymbols) showthattheLMRisisotropicinthis7.5%Co-dopedsample.

Fig. 9. (a)TemperaturedependenceofthelongitudinalMRcoefficientsγ(T) = −ρ/H2_fortheBa(Fe

1−xCox)2As2sampleswhoserespectivepositionsin thephasediagramareindicatedbyarrowsintheinset.Theshapeofthecurvesresemblethosefoundforthe75_AsNMR1

/T1T relaxationratesdisplayed in(b).(b)75_AsNMR1

/T1T relaxationratesforasimilarseriesofBa(Fe1−xCox)2As2samples.From[43].Theupgoingarrowsin(a)indicatetheonsetsof theupturnsin1/T1T observedin(b)forthesameCocontents.

where

ρ

sf isthemagneticpartoftheresistivityandisfoundtobeproportional toT when thespinfluctuationspectrum istwo-dimensional[47]anda

(

T

)

measures thecouplingeffectivenessbetweentheuniformmodeatq

=

0 andthemodes withq

≈

QAF[48].Goodfitsofourdatacanbeobtainedwith

a

(

T

)

=

1

T

− θ

for x

<

0

.

075 (8)

with

θ

∼

TNforx

=

0

.

047 and 0

.

06 and

a

(

T

)

=

1

(

T

− θ)

2 for x

≥

0

.

075 (9)

where

θ

decreases slightly from 0 in the optimally dopedsample to

∼ −

50 K in the most doped 15.4%Co one. These negative values of

θ

that reveal theexistence ofshort-range AFspin fluctuationsare in relatively good agreement with thoseextractedfromINSorNMRexperiments,albeitalittlesmaller[49,43].

These results uncover a subtle modification of the interaction betweenthe conduction electrons and the fluctuating magneticmoments intheparamagnetic state,which occurssimultaneously withthelossoflong rangeantiferromagnetic orderat lowertemperatures when Tc is optimal. Thiswouldbe relatedto themulti-orbital natureof theiron pnictides. Inunderdoped compounds, strongorbital differentiationbetweenthe3d Feorbitals[28,50,51] resultsina description in termsofcoexistingitinerantandlocalizedelectrons.Thesituationappearsthenreminiscentofthatencounteredins–dAF metalswheretheelectronsintheconductionsband arethechargecarrierswhilethoseinthenarrowdband contribute to the spin fluctuations [47]. Beyond optimal doping, the weakening of the orbital differentiation withelectron doping

Fig. 10. (a) TemperaturedependenceoftheSeebeckcoefficientS dividedbyT inaseriesofsuperconductingBa(Fe1−xCox)2As2samples.Thedottedlines emphasizelinearityonalogT scale.(b) Plotoftheslopen ofthelogarithmictemperaturedependenceofS/T asafunctionofCosubstitutionx which

showsanincreaseclosetox0.05.From[54].

predicted theoretically [51,52],might resultin a stronghybridization betweenlocalmoment anditinerant electrons and in amodificationofthe couplingbetweenchargecarriers andmagnetic fluctuations.A morepreciseconsideration ofthe characteristicsandnesting propertiesofthedifferentFermisheetsisnecessarytoexplainthequantitativeevolutionofthe LMRinthesemulti-orbitalcompounds.

Thermopowerandquantumcriticalpoint It hasalsobeenproposed that thermoelectricpower (TEP)measurements canbe usedtoprobespinfluctuationsinproximitytoaquantumcriticalpointinFe-basedsuperconductors.Whenthelow-energy spin fluctuationsare quasi-two-dimensional, withatypical two-dimensional ordering wave vector andthree-dimensional Fermi surface,theelectrons are stronglyscatteredin the“hot”regionson theFermisurface.This resultsinalogarithmic temperature dependenceforthe Seebeckcoefficient S [53], asobservedin differentheavy-fermioncompounds. TEP data in Ba

(

Fe1−xCox

)

2As2 havebeen analysedundertheselines [54]. Asreportedin Fig. 10,a logarithmic dependenceof S

/

T canbeobservedinasmalltemperaturerange.Moreovertheincreaseof

|

S

|/

T andtheslopeofitslogarithmictemperature dependencenearx



0

.

05 wasinterpretedasduetoanincreaseofscatteringonnearlycriticalspinfluctuations.

However,themaximumofn peaksnearx

=

0

.

05 whereamagnetictransitionisstillobservedaround60 K(seeFig. 1). Surprisinglythistransitionisnot visibleonthe TEPdataandone canwonder aboutthe meaningofa temperature loga-rithmicdependencebetween30and100 Kinthis5%Co-dopedsamplewherescatteringprocessesareexpectedtobevery differentinthemagneticandparamagneticphases.

2.1.2. Transportinthelowtemperatureantiferromagneticphase

Parentcompounds Thedropoftheresistivityintheparentcompoundsofthe122systems,asseeninFig. 1aforBaFe2As2, signalsthereconstruction oftheFermisurface belowthemagneto-structuraltransitionwiththeappearanceoftiny Fermi surfaces.Thishasbeenvery wellevidencedbyARPES[55–59] andquantumoscillations[60–62]measurements. Transport propertiesin thelow-T magneticphase wereanalysed withina multi-bandapproachwithdifferenttypesofcarriersand differentmobilities[63–65].Contrarytowhatisobservedintheparamagneticstate,theresidualresistivity

ρ

s inthe mag-netic stateisvery sensitivetothermalannealings[66,65],

ρ

s ofas-grownsamplesbeingdecreasedby upto oneorderof magnitude byappropriate treatment asseen inFig. 11a [65].Moreimportantly, thetemperaturedependence oftheHall coefficient inFig. 11bis strongly affectedby thermal annealing,which evidences the contributionof differentelectronic bandsinthetransportproperties.

Concomitantdataofresistivity,Hall effectandmagnetoresistancewere analysedwithin amulti-carriersmodel[63,65]. InRef. [65],threedifferentcarriers–twoelectron bandsandoneholeband–arenecessarytoaccountfortheresults,in agreement withquantumoscillationsresultsobtainedonannealed BaFe2As2 [62].Onetype oftheelectron carriershasa lowerdensityandahighermobilitythanthetwootheroneswhichdisplaysimilarfeatures.Onecannoticethatthe evolu-tionoftheHallcoefficientwithannealingsuggeststhattheholemobilityshouldbemoresensitivetoimpurities,washing outthecontributionofholestotheHalleffectatlow T inas-grownsamples.Adifferentanalysisofthemagneto-transport inthemagneticphaseofBaFe2As2wasproposedin[63,64]basedontheobservationoflinearfielddependenceofthe mag-netoresistance above1 Tinas-grownsamples.Howevermeasurements atmuchhigherfields(upto50 T)showquadratic magnetoresistance[67].

Inalltheseanalyses,thenumberofcarriersinthedifferentbandswereconsideredtobeindependentofT .Asunusual temperature effects on the electronic bands were observed by ARPES experiments in the paramagnetic phase of Ba-122 [29,33],one can expect that such temperaturedependent band shifts haveenhanced effects on the reconstructed Fermi surfaceduetothestronglyreducedsizeoftheFermipocketsintheSDWstate.InfactchangeintheFermisurfacetopology withtemperaturehasbeenproposedtoexplainelectronicRamanscatteringinthespin-densitywavephaseofSrFe2As2[68]. The temperaturedependenceoftheSDWgapsrevealsan unusualevolutionofthereconstructedelectronic structurewith

Fig. 11. (a)Effectofannealingunderthevariousconditionsshowninthefigureonthein-planeresistivitycurvesoftwinnedBaFe2As2samples.(b) Effect ofannealingonthemagneticfielddependenceoftheHallresistivity(from[65]).

Fig. 12. (a)ThermoelectricpowerasafunctionoftemperatureforBa(Fe1−xCox)2As2(from[69]).(b) SchematicphasediagramofBa(Fe1−xCox)2As2based ontransportandARPESmeasurements.GreendashedlineshowsthedopinglocationofthesuddenchangeinS.Thebluearearepresentsthedopingregion wherethereconstructionoftheFermisurfaceoccurs(from[70]).

atleastonegapbeingactivatedonlywell belowthemagneticSDWtransitionTN.Thisisassociatedwithasignchangeof thelowfieldHallcoefficient RH,frompositiveathighT tonegativeatlowerT whentheotherSDWgappeakemergesin theRamandata.Theseobservationshavebeenascribedtoatemperatureinduceddisappearanceofaholepocket,indicating achangeinFermisurfacetopologydeepintheSDWphase[68].

Transportinthemagneticphaseofelectrondoped122compounds Asseenabove,thetopologyoftheFermisurfaceintheSDW phase makesit particularlysensitiveto externalperturbations. It wasfound very earlythat atiny electron dopingofthe 122compoundshasanimportanteffectintheirtransportpropertiesinthemagneticphase.InBa

(

Fe1−xCox

)

2As2,Halleffect andthermopowermeasurements [6,69]evidenceadrasticchangeintheelectronic structureforx



0

.

02,asillustratedin Fig. 12afortheSeebeckcoefficient S.

Asthethermoelectricpower(S)isconnectedtothederivativeofthedensityofelectronicstates,itisparticularlysensitive to anymodification oftheFermi surfacetopology.Moreover, itis foundthat the suddenchangein S occursneartheCo dopingwheresuperconductivity emergesinthephasediagram.SubsequentARPESmeasurementsevidencethat theFermi surface reconstructionvanishes atthisdopinglevel,thetop oftheholebandsinthereconstructed Fermisurface moving belowthe Fermienergy,which signalsthe occurrenceofa Lifshitztransition[56].Superconductivity andmagnetismcan

Fig. 13. (a)Temperaturedependenceofthein-planeresistivityρ(T)ofBa(Fe1−xRux)2As2singlecrystals.Thearrowssignaltheoccurrenceofthe magne-tostructuraltransitions.(b) TemperaturedependenceoftheHallcoefficientRH(T)inthevicinityofRH=0[76].

coexist only when these holepockets are suppressed. This shows that the topology of the Fermi surface has important consequencesonthesuperconductingandmagneticpropertiesofthesecompounds(seeFig. 12b).

2.2. Isovalentsubstitution

Anotherpossibilitytoinducesuperconductivity intheiron-pnictidesisuponsubstitutionby isovalentatoms, eitheron the FesitebyRuatomsorontheAssitebyPatoms. Thistypeofsubstitution doesnot changethebalancebetweenthe electronandholebands.Themodificationsoftheelectronicstructuremustbedrivenherebystructuralmodificationssuch astheheightofAswithrespecttotheFeplanesorthevalueoftheAs–Fe–Asbondingtetrahedralangle.

2.2.1. Isovalentsubstitutionontheironsite:Ru

RusubstitutionattheFesiteexpandsthelatticeinthe

(

a

,

b

)

-planebutshrinksitalongthec direction[76,77],resulting inweakerlatticeanisotropyandstrongmodificationoftheelectronicstructure.Thisisdifferentfromtheeffectofexternal pressureorPsubstitutionattheAssitewhichbothinduceadecreaseinallthelatticeparameters.Significantmodifications of the electronic structure were indeedobserved by ARPES studies [74,75].The evolution of the temperature resistivity curves as a function of Ru content is reported in Fig. 13 for Ba

(

Fe1−xRux

)

2As2 single crystals [76].Similar resultswere reportedin[77,80].Theevolutionofthe

ρ

(

T

)

curveslooklikethoseobservedforthedopedsamplesasreportedinFigs.1a and2a.AsinelectrondopedBaFe2As2,thesharpdropsignallingthemagnetostructuraltransitionintheparentcompound evolvestowards a step-likeincrease inresistivitywhen Ruis introduced.Thisis incontrasttowhat isobserved in poly-crystallinesampleswheretheresistivityalwaysdecreasesatthetransition[11,12].ExceptforthesamplewithaRucontent of 0.15,it isnot possibleto distinguishthestructuralandmagnetic transitions TS and TN fromresistivitymeasurements (seealsoRef.[77]).Superconductivityappearsforx

=

0

.

15 andamaximumTc of

∼

19

.

5 K isfoundforx

=

0

.

35.Asinthe electrondopedcompounds,coexistencebetweenmagnetismandsuperconductivityisclearlyevidencedwiththeoptimalTc occurringwhen long-rangemagneticorderisfullysuppressed.HoweverNMR studiesclearly show thatsuperconductivity coexistswithAForderonlyintheregionswheremomentsaresmallerthan

∼

0

.

3

μ

B,incontrasttotheobservationdone

inCo-dopedsamples[78,79].

The evolutionoftheHallcoefficientwithRusubstitutionreportedinFig. 13bdiffersfromtheobservationdone inthe othercompounds.Indeed,achangeofsignofRH isseenatlowtemperatureforintermediatedoping,between0.24to0.55 asreportedin[80].Itisalsofoundthatthethermopowerexhibitsaverycomplicatedbehaviorasafunctionoftemperature and Ru substitution and becomes also positive atlow T for intermediate doping [81]. In a multi-band framework, this indicatesthatholesandelectronscontributesimilarlytothetransportinalargetemperaturerange.ARPESdataoncrystals with35%Rushowedthatthenumberofholesandelectronsaresimilar,i.e.,n

=

ne

=

nh



0

.

11 carriers

/

Fe[74].Itisworth pointingout thatthisvalueissignificantlylarger thanthatdeterminedby ARPESintheparamagneticphaseofBaFe2As2:

n

=

0

.

06

(

2

)

carriers

/

Fe[22],confirmingthatimportantmodificationsoftheelectronicstructureoccuruponRusubstitution. Moreover,FermivelocitiesincreasesignificantlywithrespecttoBaFe2As2,suggestingareductionofcorrelationeffects.

LetuspointoutthatEometal.claimedthatthechangeofsigninRHobservedinBa

(

Fe1−xRux

)

2As2cannotbeexplained inamulti-bandapproachbutrathercomesfromanon-Fermi-liquid-likebehaviorinthevicinityoftheAFMphase.However some oftheir argumentsresultfrommiscalculations.In particular,usingacarrierdensityof0.15electrons/Fe,theyfound 1

/

ne

=

0

.

98

·

10−3_cm3

_/

_{C whilearightcalculationwouldgive2}

_.

₁₂

_·

₁₀−3_cm3

_/

_C.1_{Consequently,contrarytowhatisasserted}

inthispaper[80],themobilitiesofholesandelectronsarecomparableathighT whilethatoftheholesslightlyovercomes thatoftheelectronsatlow T .Moreovertheseauthorsspeculatedthattheirmagnetoresistancedata,alwayslower than1%

1 _{KnowingthatthecellvolumeofBaFe}

2As2(V=0.204 nm3)containstwoFe2As2,anumberofcarriersofn=0.15 carriers/Fe correspondsto2.94· 1027_carriers/m3_{,resultinginaHallcoefficientequaltoR}

Fig. 14. (a)Transversemagnetoresistanceρ/ρ0foraBa(Fe1−xRux)2As2singlecrystalswith35%Ruatdifferenttemperatures.Solidlinesarequadraticfitsof thedata.(b) Temperaturedependenceofthenumberofcarriersandoftheholeandelectronscatteringratesdeterminedfromresistivity,Hallcoefficient andmagnetoresistancedataasexplainedinthetext.DottedlinesarequadraticfitsofthedatashowingthatboththeelectronsandholesexhibitaFermi liquidbehavior[82].

at14 T, are much smaller thanthose predictedby a two-band modelforwhich “a large MRis expectedaslong asthe electron andhole carrierscoexist andtheirmobilities are comparable”.However, we donot understandhowtheselatter valueswereestimatedbyEometal.[80].Solvingtheproblemintheoppositeway,itispossibletodeterminedirectlythe holeandelectronconductivities

σ

h and

σ

e andthenumberofcarriersn

=

nh

=

ne frommeasurements ofresistivity,Hall effectandmagnetoresistanceusingthefollowingequations:

σ

=

1

ρ

=

σ

h

+

σ

e RH

=

Re

σ

h

−

σ

e

σ

h

+

σ

e with Re

=

1

/

n

|

e

|



ρ

0

ρ

=

R 2 e

σ

e

σ

hH2 (10)

Combiningtheseequationsonefindsthatthemagnetoresistancewritesas:



ρ

ρ

0

=

1 4

(

R 2 e

−

R2H

)



H

ρ

0



2 (11) This equation isimportant asthe proportionalitybetween themagnetoresistance and

(

H

/

ρ

0

)

2 has oftenbe taken asan indication that theso-called Kohlerlawis obeyedornot. Inmulti-band systems withne

=

nh,Eq.(11)tells usthat this proportionality can be observed if R2e

−

R2H is weakly T dependent, that is for Re



RH or RH nearly constant with T . Consequentlytheobservationornotofthe“Kohlerlaw”mustbe consideredwithcautionandnorapidconclusion canbe drawn.

We displayed inFig. 14a ourown dataof theorbital magnetoresistance fora single crystalofBa

(

Fe1−xRux

)

2As2 with 35%Ru[82].ThesedataareverysimilartothosereportedbyEometal.[80]foranoptimallydopedcrystal.Usingresistivity, Hall coefficientandmagnetoresistance data,Eqs.(10)make itpossible todeterminethe temperaturedependencesofthe numberof carriersandthescatteringrates forholes andelectrons thatare reportedin Fig. 14b.The numberofcarriers

∼

0

.

12

(

1

)

electrons/Febetween50 and150 K is invery good agreementwith that foundby ARPES measurements (n

=

0

.

11 carriers

/

Fe) at20 K on similar crystals[74].This givessome confidence to thisanalysisin termsof two electronic bands.Letusalsonoticethatthesmallincreaseinn forT

>

120 K iscompatibletomodificationsoftheelectronicstructure with T asobservedby ARPESmeasurements [33].Moreover thescatteringratesofbothelectrons andholesexhibit a T2 dependenceasalsofoundforBa

(

Fe1−xCox

)

2As2,demonstratingonceagainthatdirectconclusionfromtheT dependenceof resistivitymustbeconsideredwithcautioninthesemulti-bandsystems.

Itisworthnoticingherethatthescatteringrates(

∼

5

·

1013 _s−1_{)ofbothelectrons andholesareofthesameorderas} thatofelectronsinBa

(

Fe1−xCox

)

2As2 (seeFig. 7).MoreovertheholemobilityovercomesthatofelectronsatlowT ,which impliesthatsomescatteringprocessesresponsibleforthelowmobilityofholesinBaFe2As2areconsiderablyreducedbythe introductionofRu.ThisisquitesurprisingaprioriasRusubstitutionwouldhavebeenexpectedtoresultinstrongdisorder scattering. However ARPES measurements reveal a homogeneous electronic structure andno strong disorder associated with Ru substitutions. Moreover, it appears that Ru substitution also strongly weakens theelectron correlationsboth in electron andholebands, whichcan explain the increasedmobilityofholes in BaFeRuAs comparedto BaFeCoAs[74].By takingintoaccountdisordereffectsinfirst-principlescalculation,itwas shownthat,whilelargescatteringisfoundonthe entireFebands,thestatesnearthechemicalpotentialremainverysharpandcoherent[83].Thisexoticbehaviororiginates froma coherent interference ofon-site and off-site disorderpotentials. Thisinsensitivity to impurity scatteringprovides

Fig. 15. (a) Temperaturedependenceofin-planeresistivityρ(T)ofBaFe2(As1−xPx)2forx rangingfrom0.33to0.71.Theredlinesarethefitofnormal-state resistivity topower-lawdependenceρ0=ATα.Inset:Temperaturedependenceof−RH(T)forx=0.33.(b) Magnetoresistance



ρxx/ρxx plottedasa

functionof

(

μ0H/ρxx)2forx=0.33.Theinsetshows



ρxx/ρxxversustan2θH.From[16].

a natural explanation of the unusual resilience of transport and superconductivity against a high impurity level in this Ba

(

Fe1−xRux

)

2As2 system.

2.2.2. SubstitutionontheAssite:P

The structuralmodifications inducedby Psubstitution attheAs siteare verysimilar tothose ofhydrostaticpressure. P substitutionreduces allthe axislengthsandthepnictogenheight zPn relativeto theFeAs layers [14–16].According to densityfunctionaltheory(DFT),theholepocketsarequitesensitivetothispnictogenposition.Indeedastrongincreasein thewarpingofoneholesheetwas evidencedbyARPESmeasurements,whichwouldleadtoweakenthenesting between theelectron andholeFermisurfaces[86].Amongthe122compounds,BaFe2

(

As1−xPx

)

2 was particularlystudiedasitwas consideredastheidealsystemtostudythequantumcriticality inironpnictides(forareview,see[85]).Sincesubstitution takesplaceoutsidetheFeAslayers,thescatteringrateofthedefectsintroducedbyPsubstitutionwas showntobe partic-ularlylow,asdemonstratedbytheobservationofquantumoscillationsinawiderangeofPconcentrations[84].Thisgave risetoalotofdifferentstudiesoftransport,magnetic,specificheat,. . . properties.

Thefirstassertionofquantumcriticalitywasclaimedfromresistivitymeasurements[14–16].AsshowninFig. 15a,the in-planeresistivity

ρ

displaysalineartemperaturedependenceforx

=

0

.

30 correspondingtothemaximumvalueofTc [16]. TheauthorsalsonotethattheHallcoefficientisremarkablyenhanced atlowtemperature(seefigureinFig. 15b)andthat themagnetoresistancereportedinFig. 15cviolatesKohlerlaw.Alltheseresultsweretakenasindicativeofnon-Fermiliquid behaviorandtheproximityofaquantumcriticalpoint.

Besides, recentmeasurements usinghighmagneticfield tosuppresssuperconductivity haverevealeda T2 _behaviorat lowtemperatureforallcompositions(x

≥

0

.

32)andacrossovertowardsalineartemperaturedependenceasT isincreased, consistent withaFermi-liquidgroundstate atlow T [87].Asoptimaldopingisapproachedfromtheoverdoped side,the range of T overwhich T2 behavior is observeddecreases. Goodfits ofthe resistivity curvesare done withapower law expression

ρ

(

T

)

=

ρ

0

+

ATn,withthecoefficient A beingstronglypeakedatTcmax,whichwasinterpretedbytheauthorsas theproximitytoaquantumcriticalpoint.

However alltheseconclusions weredrawnwhileconsideringasingleband picturetodescribethetransportproperties ofBaFe2

(

As1−xPx

)

2.Itisworth notingherethatthesamemiscalculationintheestimateof Re

=

1

/

ne asdone inRef.[80] for BaFeRuAs ledthe authors to concludethat the simplemulti-band picture cannot be applied. The actual value of Re, equalto2

.

05

·

10−9 m3

/

C isinfactveryclosetothemeasuredvalueof RH (seefootnotep. 11).Moreover,aspointedout above inthecaseofBaFeRuAs,the apparentviolationofKohler’slawfora two-bandsystemcanvery simplyderivefrom Eq.(11)if

(

R2

e

−

R2H

)

isdependenton T .Consequently,rulingout multi-bandeffectstoexplain thetransportpropertiesof BaFe2

(

As1−xPx

)

2appearsnotreallylegitimatehere.

As in Ba

(

Fe1−xCox

)

2As2, the Hall coefficient isnegative, indicating that the electron scattering ratesmust be smaller than thatofholes.Asa matteroffact,onlytwoelectronsheetscanbe revealedbyquantumoscillationmeasurements in overdoped BaFe2

(

As1−xPx

)

2.UsingthesameapproachasdoneaboveforBaFeRuAs,itispossibletodeterminethenumber ofcarriersandthescatteringratesofelectronsandholesfromthedataofresistivity,Hallcoefficientandmagnetoresistance reportedinFig. 15.Thenumberofcarriersfoundfromsuchadecompositionis

∼

0

.

06 carriers

/

Fe,inaverygoodagreement withthatdeterminedbyquantumoscillationmeasurements[84].

Eveniftheexistenceofaquantumcriticalpointdeducedfromtheanalysisofthetransportpropertiesinasingleband approach mustbe considered with caution asshown above, it is importantto point out that the presence of a QCP in

The only possibility to induce superconductivity by hole doping in the 122 system is by alkali metal substitution in the insulating blocking layers. Indeed substitution at the Fe site by elements at the left of Fe, as Mn or Cr, which wouldformally leadto holedoping, failstoinduce superconductivity[95,96]. InthecaseofMn substitution, ithasbeen demonstratedthat theadditionalholes givenbyMn donot delocalizebutactaslocalmoments onMn siteswithstrong stabilization ofthe antiferromagnetic order [97,98].However Hall effect measurements clearly show a changeof signin

RH fromnegative topositive uponCr andMnsubstitution, indicatingthat holes areactually added[95,99].Forthe elec-tron doped122 family,such asBa

(

Fe1−xCox

)

2As2,experimental and theoretical worksillustrate the systematicevolution ofthe transportproperties andelectronic structure;they all highlightthe importance ofmulti-band effects.The detailed investigations andanalyses suggestasymmetric quasiparticlescatteringinthe holeandelectronbands,withstill a much larger mobility in the electron band. Detailed studies of the Hall resistivities in Mn-substituted BaFe2As2 aswell as si-multaneousanalyses ofbothlongitudinalandtransversemagnetoconductivitiesdemonstratedthat minornumberofholes withhighmobilityweregeneratedbytheMndoping,whilethemajorityelectronandholeFermisurfacesintheelectronic structure of the parent BaFe2As2 were almost preserved [100]. Where are located the minority holes is not yet clearly elucidated.

Holedoping isthen achievedby substitution ofKor Naatthealkaline earth site, themoststudied compoundbeing Ba1−xKxFe2As2.Comparedtoits counterpart electrondoped Ba

(

Fe1−xCox

)

2As2, thereare relativelyfew systematicstudies oftransportpropertiesallalongthephasediagram,duetothelargerdifficultytogrowgoodsingle crystalswithanarrow compositionaldistributionespeciallyforheavilyKdopedcrystals

The evolution ofthe resistivitycurves reportedinFig. 16a showsup some differencesfromthe observationsdone in electrondopedcompounds[101].First,thedropofresistivitywhichsignalsthemagneto-structuraltransitionat138 K in the parent compound is shifted to lower temperature upon K substitution but without strong modification of the

ρ

(

T

)

curves: the derivativesof the resistivity always display a unique peak, showing that the magnetic andstructural transi-tions takeplace atthe sametemperatureasevidenced byX-rays andneutrondiffraction measurements [102].The shape oftheresistivitycurvesisalsoverydifferent:inKsubstitutedBaFe2As2,resistivitycurvesexhibitacrossoverfromalow-T positive to a high-T negative curvature contrary to the case for the other types of substitution. Moreover, one can see that the

ρ

(

T

)

curves remain almost unchanged once the superconductivity sets in. Resistivity measurements performed for a large rangeof hole doping show that the room-temperature resistivity

ρ

(

300 K

)

remains constant, within statisti-cal error,over thewhole composition rangefromheavily underdoped sampleswith x

=

0

.

22 toheavily overdoped x

=

1 [103,104]. This is very different fromwhat is observed in the other types ofsubstitution (see Figs. 1, 2, 13 or 15), for which

ρ

(

300 K

)

decreases notably withdoping. By contrast,one observes that theHall coefficient RH exhibitsa signifi-cant modificationwith K content,as seen is Fig. 16b. In particular, a change ofsign in RH is observed assoon as Kis introduced, indicating that the contribution of holes rapidly overcomes that of electrons. Moreover one can notice that the crossover temperature, where RH turns to a decrease upon cooling israther close to the crossoverseen in resistiv-ity.

These results were usually discussed in a two-band approach. However, to our knowledge, there were no attempts to analyse resistivity and Hall coefficient data simultaneously as a function of x and T in order to get the rough evo-lution trends of the different parameters defined in Eq. (3). In particular, the saturation of the

ρ

(

T

)

curves at high

T was interpreted by an effect of “shunting”, with the conductivity of one band being strongly T dependent, while the other is nearly T independent [106,101]. One can notice that optical conductivitydata have been often interpreted along theselines[105,45,107].TwoDrudeterms,representing twogroups ofcarrierswithdifferentscatteringrateshave been used to describe the real partof the optical conductivity witha “broad” Drude component witha T -independent

scattering rate, and a “narrow” Drude T dependent component. In the case of the optimally doped Ba0.6K0.4Fe2As2, the scattering rate of the “narrow” Drude peak was found to increase linearly with T from 50 to 300 K, suggesting the presence of a quantum critical point into the superconducting dome [107]. However, direct fits of the

ρ

(

T

)

curves using a power-law dependence

ρ

(

T

)

=

ρ

0

+

ATn as done in P-substituted BaFe2As2 [61] did not give conclusive re-sults. Although the exponent n is found to be minimum (

∼

1

.

1–1

.

5) for x

=

0

.

39 with maximum Tc, negative values are obtained forthe residual resistivity

ρ

0, which indicates that this fittingprocedure must be considered withcaution [101,103,104].

Fig. 16. (a) TemperaturedependenceofresistivityofBa1−xKxFe2As2 (x=0 to 0.37)singlecrystals.Themagneto-structuraltransitionisshiftedtolower temperaturesandbecomesroundedwithfurtherpotassiumdoping.Theresistivityanomalyinthenormalstatecannotbeexplicitlyresolvedwhenthe dopinglevelis0.25withTc=29 K andbeyond,from[102].(b) TemperaturedependenceoftheHallcoefficientRHfor0≤x≤0.55.Thetrianglesindicate thecrossovertemperature,whereRHturnstoadecreaseuponcooling.From[103].

Fig. 17. Phase diagram of Ba1−xKx(Fe0.93Co0.07)2As2 (dark blue/orange) compared to the phase diagrams of Ba1−xKxFe2As2 and Ba(Fe1−xCox)2As2 (light blue/yellow).From[109].

2.4. Comparisonbetweenthedifferenttypesofsubstitution 2.4.1. Roleofdisorder

ValueofTc IthasbeenoftensuggestedthatTc ishigherinthehole-dopedthanintheelectron-dopedBa-122compounds dueto moredisordereffectsinthelattercase,wherethe dopantsarelocated intheFeAslayers (seeforinstance[18] in thisvolume).ItwasindeedshownthatthechemicalnatureofthesubstitutionintheFeAslayerhasanimportantinfluence onthesuperconductivityandthetransportproperties.ForinstanceNi(Pd)substitutionintheBaorSr-122systemsresults inlowermaximumTc thanCo(Rh)substitution[20,26].ThishasbeeninterpretedasastrongerpairbreakingeffectforNi orPdsubstitutionthanforCo[108].

However itis not so straightforward to assert that lower Tc in Co-substituted samplesas compared to K-substituted samples isexclusivelydueto disordereffectssincethe electronicstructuresare verydifferentinthesetwo cases.Indeed thephasediagramsareasymmetricforelectronandholedopings,whichmayindicatethattheexcesspositiveandnegative chargesactdifferently.Averyinterestingexperimentofco-dopingusingthecombinationofbothKandCosubstitutionsin Ba1−xKx

(

Fe0.93Co0.07

)

2As2 [109] haveclearly evidencedthatthecharge intheFeAs layersplaysamajorrole incontrolling the shapeofthephasediagram oftheBa-122 compound.As reportedinFig. 17,the emergenceofsuperconductivityand thedisappearanceofthemagneticphaseareonlydependentontheeffectivechargegiventotheFeAslayer.However,one cannoticethatthemaximumTc inthehole-dopedpartofthephasediagramishigherthanintheCosamples,whichhas beeninterpretedastheeffectofdisorderintroducedbytheCosubstitutionintheironlayer.

Neverthelessone canpointoutthat,inouranalysisoftransportdatainBa

(

Fe1−xCox

)

2As2,thescatteringratesof elec-trons atlow T do not dependon the Cocontent from4% to 20%Co (see Fig. 7b), whichled usto concludethat native disorder dominatesover theeffect ofCo substitution[6].Moreover, Katase etal.[110] showedthat the superconducting

Fig. 18. Temperaturedependenceofthein-planeresistivityρa(green)andρb(red)ofBa(Fe1−xCoxx)2As2forCoconcentrationsfromx=0 to 0.085.Solid verticallinesmarkcriticaltemperaturesforthestructuralandmagneticphasetransitionsTSandTN,respectively.Thediagramsontherightillustrate howmeasurementsofρaandρbweremade.Darkarrowsindicatethedirectioninwhichuniaxialpressurewasapplied,andsmallerarrowsindicatethe

orientationofthea andb crystalaxes.From[71].

dome ofepitaxialfilms ofLa-dopedBaFe2As2 closelyoverlapswiththat ofCo-dopedBaFe2As2,leading themto conclude that Tc doesnotdependonwhetherornotimpuritydopantsarelocatedintheFeAslayerbutonlydependsontheexcess chargesprovidedby thedopants.ThisresultalsosuggeststhatthedifferencesobservedinFig. 17intheholedopedarea ofthephase diagrambetweenBa1−xKxFe2As2 andBa1−xKx

(

Fe0.93Co0.07

)

2As2 isnotdueto disordereffectsinduced byCo substitutionbutmustberelatedtodifferencesinthemagnitudesofsuperconductinginteractionsfortheholeandelectron dopedBaFe2As2.

ImpurityscatteringandresistivityanisotropyaboveTNintheunderdopedareaofthephasediagram Aswe haveshownabove, theresistivitydropwhichsignalstheoccurrenceofthemagnetostructuraltransitionintheparentcompoundBa(Sr)Fe2As2 transformsintoa step-likeincreasein theresistivityassoonasCoorNi areinserted intheFeAs layers(see forinstance Fig. 1 [6]andFig. 2 [20]) orby PsubstitutionontheAssite[16].However,noincrease ofresistivitywasobservedinthe holedopedK-substitutedcompounds(seeFig. 16 [101,111]).

Resistivitymeasurementsinthepresenceofuniaxialstresshaveshowedthatthisincreaseinresistivityresults predom-inantlyfromtheresistivitycomponentalong theb-axiswhichisfound tobe largerthanalong thea-axis intheelectron dopedBa-122[71,64,73].Thisanisotropyofresistivityinthetetragonalphaseishowevermuchreducedintheholedoped Ba1−xKxFe2As2 andalso changessignforsufficiently highdopings[111,112].This in-planeresistivity anisotropy whichis observedabovethestructuraltransitionTShasbeentakenasthehallmarkofanematicstateiniron-pnictides(Fig. 18).

Inone hand,bycomparing CoandNi dopedsamples,ithasbeenargued [72] that theresistivityanisotropy doesnot depend on impurity concentration andis thus an intrinsicproperty determined by the Fermisurface anisotropy. Onthe otherhanditwasshownbyIshidaetal.thattheresistivityanisotropyisstronglydependentonthequalityofthesamples [73], which tends to suggest that it is more likely extrinsic in origin and comes from anisotropic scattering potentials inducedbyFevacanciesandCodefectsintheantiferromagneticphase.

Modelsbasedon spin-fluctuationscatteringinpresenceornotofstronglyanisotropicimpurity states[115,37,113,114] were proposed to explain thesedifferent types of behaviors. Within scenario which privileges the role of scattering off elongated(“nematogen”)defects,themuchlarger anisotropyinelectron-dopedBa-122 comparedtohole-dopedBa-122is explainedasaconsequenceofthepresenceofdopantswithintheironplanes.Inthelattercase,thesmallerandnegative anisotropymightarisefrompeculiarfeaturesintheelectronicbandstructure.

Theoriginofthisresistivityanisotropyisstillanongoingdebatewhosediscussionconstitutestheentiresubjectofother contributions inthisvolume [116,117].Thus we willnot detailthisissue hereandrecommendthe interested readersto lookatthesepapers.

Interplaneresistivity Alltheresistivitydatareporteduptonowhaveconcernedthein-plane

ρ

abresistivity,alongtheFeAs

Fig. 19. TemperaturedependenceoftheinterplaneresistivityρcforBa(Fe1−xCox)2As2(a)andBaFe2(As1−xPx)2(b)(from[118,121]).WhileTmax (arrows) decreaseswithCodopingin(a),itincreasesandrapidlydisappearsinthecaseofPsubstitution.

difficulty to extractgoodabsoluteresistivityvalues inthiscase[118].Asystematicstudyofthetemperaturedependence of

ρ

c indifferenthole andelectrondopedBa-122 was performedby Tanataret al.[118–120].In allcases,

ρ

c displays a shallowcrossovermaximumatTmax,followedbyabroadminimumathighertemperatureabovewhich

ρ

c increaseslinearly with temperature(see Fig. 19).None of thesefeatures are apparent in thein-plane resistivity. In BaFeCoAs[118],the T

dependenceoftheinterplaneresistivityshow somecorrelationwiththeNMRKnightshiftandspinlatticerelaxationrate, whichwasassignedtotheformationofapseudogap[43].ItwasthusconcludedthattheT dependenceof

ρ

c constitutesa goodprobetodetectthepresenceofapseudogapinironpnictides.However,whileinelectron-dopedcompounds[118,119], this“pseudogap”regionextendsfromparentcompoundtofarbeyondtheendofthesuperconductingdomewitharapid suppressionof Tmax withdoping[118],themaximumin

ρ

c shiftstohighertemperaturesinholedopedBa-122[120]and isoelectronicPorRusubstitutedsamples[121,122]inwhichitdisappearsveryrapidlywithdoping:attheoptimaldoping,

ρ

c showsT -lineartemperaturedependencewithoutanycrossoveranomalies.

Ontheotherhand,infraredstudiesofthea–b-planeresponseinCoandPsubstitutedBaFe2As2 [123]andofthec-axis response in optimally dopedBaFeCoAs [124] identify a suppression of the spectral weight at low frequencies, which is reminiscenttothespectroscopicmanifestationsofthepseudogapinthecuprates.Openingofapseudogapwasalsoreported viaopticalconductivityinunderdopedBa1−xKxFe2As2 [125].Howeveralltheanalysisoftheopticalresponsewasperformed thereinasinglebandapproach.ItwaspointedoutinRef.[124]thatthemulti-bandcharacteroftheironpnictidesislikely toalsoplayaroleinthesuppressionofthespectralweight.Inparticular,detailedcalculationsevidencearoleofmulti-band effectsinthespectralweightredistributioniniron-pnictides[38].

Inconclusion,theT dependenceoftheinterplaneresistivity

ρ

c

(

T

)

andtheinterlayerchargedynamicsinironpnictides appearstobefarfrombeingwellunderstoodandcallsforfurthertheoreticalanalysis.LetusmentionherethattheT

de-pendence of

ρ

c is verysimilar to that measuredin Sr2RuO4,anothermulti-band compound where“metallic”conduction is alsoobserved athigh T ina regimewith nocoherentband formation [126].This posesthe question ofthenature of thequasiparticlesthatcontributetothec-axistransportintheseanisotropiccompounds.Thisissueclearlydeservesfurther investigations.

3. 111compounds

3.1. LiFeAs

Among theiron pnictides, theLiFeAscompound occupiesaspecialplace invariousaspects. Firstit isnaturally super-conductingwitharelativelyhighTc

∼

18 K withoutanychemicaldoping.Cleavedsinglecrystalsdisplaynosurfacestates, whichmakes itveryappropriate forARPESmeasurements.It hasbeenshownthatthenesting betweenholeandelectron Fermipocketsisverypoor,whichhasraisedthequestionoftheroleofantiferromagneticfluctuationsforsuperconductivity inthiscompound[127,128].

Due toreduceddefectcontent,theresidualresistivity inLiFeAsisfound tobequite lowwithresidualresistivity ratio muchlargerthanfoundintheother pnictidecompounds[129–131].Thelowtemperatureresistivityfollowsaquadratic T

dependence,whichisaclearindicationofFermiliquidbehaviorwithelectron–electronscattering.TheHallcoefficient RHis negative indicatingthatthetransportpropertiesaredominatedbyelectronsinthisnearlycompensatedmaterial,asfound inthenon-magneticstate ofBaFe2As2 [6].Asafunctionoftemperature, RHexhibitsasignificanttemperaturedependence withaminimumaround100 Kandasaturationtowardszerowithincreasing T ,whichsignalsthatthemobilitiesofholes andelectronsbecomesimilar.