Anisotropic softening of magnetic excitations in lightly electron doped Sr$_2$IrO$_4$

1.2 MB·

by  Xuerong Liu

AnisotropicsofteningofmagneticexcitationsinlightlyelectrondopedSr IrO
2 4
X. Liu,1,2,3,∗ M. P. M. Dean,3 Z. Y. Meng,1 M. H. Upton,4 T. Qi,5 T.
Gog,4 Y. Cao,3 J. Q. Lin,1 D. Meyers,3 H. Ding,1,2 G. Cao,5 and J. P. Hill3
1BeijingNationalLaboratoryforCondensedMatterPhysicsandInstituteofPhysics,ChineseAcademyofSciences,Beijing100190,China
2Collaborative Innovation Center of Quantum Matter, Beijing, China
3Condensed Matter Physics and Materials Science Department,
Brookhaven National Laboratory, Upton, New York 11973, USA
4Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
5Center for Advanced Materials, Department of Physics and Astronomy,
University of Kentucky, Lexington, Kentucky 40506, USA
6 (Dated:May30,2016)
1
Themagneticexcitationsinelectrondoped(Sr La ) IrO withx = 0.03weremeasuredusingresonant
0 1−x x 2 4
inelasticX-rayscatteringattheIrL -edge. Althoughmuchbroadened,welldefineddispersivemagneticex-
2 3
citationswereobserved. Comparingwiththemagneticdispersionfromtheundopedcompound,theevolution

y ofthemagneticexcitationsupondopingishighlyanisotropic. Alongtheanti-nodaldirection,thedispersionis
a almostintact. Ontheotherhand,themagneticexcitationsalongthenodaldirectionshowsignificantsoftening.
M
Theseresultsestablishthepresenceofstrongmagneticcorrelationsinelectrondoped(Sr La ) IrO with
1−x x 2 4
closeanalogiestotheholedopedcuprates,furthermotivatingthesearchforhightemperaturesuperconductivity

7 inthissystem.
2
PACSnumbers:71.27.+a,74.25.Ha,78.70.Dm
]
l
e
- Together with the tremendous research activity on the su- energy electron evolution as observed in the cuprates. An
r
t perconductingcuprates[1,2],effortstocomparethecuprates anisotropic pseudo gap opens on the Fermi surface, with the
s
. with other related systems have also been on-going for samesymmetryasthatofthecuprates. However, therelated
t
a decades. Such comparison serves as a natural approach to question of whether the magnetic correlations that are often
m clarifytherolesofmultipleemergentphenomenainthephase implicated in HTS [13, 14, 18] are also analogous remains
- diagramofthecuprates, includingmagneticfluctuations, su- largelyunexplored.
d
perconductivity, pseudo gap and charge density waves etc. Here we measure the magnetic excitations in electron
n
The5doxideSr IrO isanexcellentcandidateforsuchstudy. doped(Sr La ) IrO withx = 0.03usingIrL edgeres-
o 2 4 1−x x 2 4 3
c This so called spin-orbit-coupling driven Mott insulator [3] onant inelastic X-ray scattering (RIXS). The samples at this
[ is in close proximity to the single layered cuprate La CuO , dopingshowweaklymetallicbehaviorandastronglyreduced
2 4
both structure-wise [4] and electronically [5–8]. Sr IrO magnetic moment induced by field [15, 19]. In the ARPES
2 2 4
v hosts a single hole in the t2g manifold where a Mott gap measurements,asizableFermisurface[7,17]wasobserved.
2 is opened, assisted by strong spin-orbit coupling [3, 9, 10], The phase diagram summarized by X. Chen et al. [16] sug-
7 and its magnetic excitation spectrum can be well described geststhatthisdopingsitsattheborderofthemetal-insulator
1 using a Heisenberg model of effective spin-1 moments on a transition. Weobservethatdopinginducesdampedmagnetic
2 2
square lattice [11, 12]. With a minimum single band model, excitationswithastronglyanisotropicsofteningcomparedto
0
. Sr2IrO4 and La2CuO4 are strikingly similar [13], leading to the undoped compound. Along the anti-nodal direction, the
1
the proposal that this compound could also host unconven- dispersionisalmostintactwithdoping.Alongthenodaldirec-
0
6 tional high temperature superconductivity (HTS) upon dop- tion, however, themagneticexcitationsarestronglysoftened
1 ing[13,14]. Moreover,duetotheoppositesignsofthenext- byabout 27%. Thisphenomenologyiscloselyanaologousto
: nearest-neighborhoppingintegralinthesetwosystems,theo- theholedopedcupratesandsupportstheoreticalnotionsthat
v
i reticalworkfurthersuggeststhattheelectrondopedSr2IrO4 electron-dopingiridatesmayinduceHTS[13,14].
X
mightbemorecloselyanalogoustothoseofhole(ratherthan Thehighqualitysinglecrystalsusedweresynthesizedus-
r electron)dopedcuprates[13,14]. ingaself-fluxtechnique[15].IrL -edgeRIXSmeasurements
a 3
AlthoughthephasediagramofdopedSr IrO hasnotbeen were carried out at 27ID and 30ID of the Advanced Photon
2 4
fully explored, a large amount of experimental work sup- Source. The incident X-ray energy was set to 11.215 keV
ports the hypothesis that the Fermiology of the doped iri- basedonaresonantconditionsurvey. Theoverallexperimen-
datesiscloselyanalogoustothecuprates. Upondopingwith tal resolution was about 37 meV (FWHM) estimated from a
La up to 6%, Sr IrO evolves from an antiferromagnetically Lorentzianfittingofthequasi-elasticline. Alldatapresented
2 4
ordered insulator to a paramagnetic [15] or percolative [16] werecollectedatlowtemperatureof20K.Forconvenience,
metal.AT-linearresistivitywasobservedwithpotassiumsub- the reciprocal space here is indexed using I4/mmm nota-
stitution [15]. Further, angle-resolved photoemission spec- tion,wherethe[1,0,0]directionisparalleltothenearestIr-Ir
troscopy (ARPES) data from several groups [5–7, 17] has bond directions and, in analogy to the notation used in elec-
shown convincingly that doping indeed drives a similar low tronic structure measurements [5–7, 20] we refer to this as
2
theanti-nodaldirection, whereastheBrillouinzonediagonal whose width was pre-determined as 37 meV FWHM from
[1,1,0] is referred to as the nodal direction. The insensitiv- an off-resonant spectrum and kept fixed during the fitting.
ityoftheRIXSspectratotheout-of-planedirectionwascon- The upturn on the high energy loss side was accounted
firmed at multiple Q points with different out-of-plane mo- for with a Gaussian tail. For the magnetic excitation, we
mentumtransfervalues,consistentwiththe2Dnatureofthis model the imaginary part of the magnetic susceptibility with
material. a Lorentzian and note that the measured RIXS intensity,
Figure 1 summarizes the RIXS spectra taken at different I(Q,ω), is proportional to this multiplied by the Bose-
Q points along several cuts in reciprocal space. In addition Einsteinfactor,
tothequasi-elasticlinescenteredatzeroenergyloss,twodis-
Γ 1
persivefeaturescanbeobservedbelow1eV.Suchanobserva- I(Q,ω)∝ Q · , (1)
tionissimilartothatontheundopedcompound[11,21]. The (ω−ωQ)2+Γ2Q 1−e−ω/kBT
higherenergydispersivefeature(centeredaround0.7eV)was
whereω andΓ aretheenergyandFWHMofthemagnetic
Q Q
suggested to originate from the so called spin-orbit exciton,
excitation at Q respectively, and k is the Boltzmann con-
B
andthelowerenergydispersionwasassignedasmagneticin
stant.ThisformwasnumericallyconvolvedwithaLorentzian
nature. The magnetic dispersion maximum reaches approx-
in order to account for the experimental resolution. Simi-
imately 200 meV at the (π,0) point, similar to the magnon
larformalismwassuccessfullyappliedtothedopedcuprates
bandwidth obtained on the undoped sample. The relative
[22,23,25].
strength of the magnetic excitations to the spin-orbit exciton
excitationsobservedhereissimilartothatobservedintheun-
dopedcompoundwiththesameexperimentalgeometry.Since
thecreationoftheexcitonisexpectedtoscalewiththeunoc-
cupiedt states,thedopingcouldresultinnomorethan6%
2g
reduction of its spectral weight. Based on this argument, we
concludethatthespectralweightofthemagneticexcitations
arenotsignificantlysuppressedupondoping.
(π,0)
)
t
ni (0,0)
u

.
b
ar (π/2,π/2)
(

y
t
si
n (π,π)
e
t
n
I
(π,0)
(π/2,π/2) FIG.2:Acomparisonofthedispersionofthemagneticexcitationsin
(Sr La ) IrO withx = 0.03withtheundopedcompound. Top
1−x x 2 4
−0.2 0 0.2 0.4 0.6 0.8 1
pannel:thesolidsquaresanddiamondsarefromthecurrentworkon
Energy loss (eV) thedoped andundoped samples, and theopen circlesare fromthe
undoped compound extracted from Ref. [11]. Bottom pannel: the
energy-momentumintensitymapofthemeasuredRIXSspectrawith
FIG.1: RIXSenergylossspectrarecordedalongseveralcutsinre-
thequasi-elasticlinesubtracted; thewhitedots(Ref.[11])andblack
ciprocal space. A damped magnon excitation is observed dispers-
diamonds(oursample)arefortheundopedcompound.
ingfromlowenergyat(0,0)and(π,π)tohigherenergiesaround
thezoneboundaryat(π,0)and(π/2,π/2). Thespin-orbitexciton
modeisseenaround0.7eV. The obtained dispersion relation is shown in the top panel
of Fig .2 (solid red squares), together with that from the un-
The dispersion of the observed magnetic excitations was dopedcompound.Theopencirclesarethedataextractedfrom
extracted by fitting the RIXS spectra up to 0.45 eV energy Ref. [11], and the black diamonds are the magnon energies
loss. The quasi-elastic line was fitted with a Lorentzian, measuredonourownundopedsample[19].Upon3%doping,
3
the magnetic excitations in (Sr La ) IrO are modified in thecenterofthemagneticexcitationat(π,0)agreeswellwith
1−x x 2 4
astronglyanisotropicmanner.Alongthe(0,0)→(π,0)anti- thatoftheundopedcompound.For(π/2,π/2),thelargesoft-
nodaldirection,themagneticdispersioninthedopedsample ening is clearly observable from the raw experimental data.
followsthatoftheundopedcompoundclosely.Themaximum Our fitting gave a peak center of 77(±6) meV, compared to
at (π,0) zone boundary determines a dispersion bandwidth 110meVfromRef. [11]and105meVfromourownundoped
of ∼ 200 meV. In contrast, there is a significant “softening” sample. Suchanisotropicimpactfromdopingalsoappearsin
along the (0,0) → (π,π) nodal direction with doping. At thebroadeningofthemagneticexcitations. Thefittedwidths
the (π/2,π/2) zone boundary point, the magnetic excitation (FWHM)are155and214meVfor(π,0)and(π/2,π/2)re-
is softened by about 27%. Such anisotropic response can be spectively. Themorebroadenedmagneticexcitationssuggest
seenmoredirectlyintheenergy-momentumintensitymapin strongerscatteringalongthenodaldirection.
the bottom panel of Fig .2 where the measured RIXS spec- The anisotropic response to doping implies that our ob-
trawithonlythequasi-elasticlinesubtractedareshown. The served magnetic excitations are not from macroscopic phase
comparisonpresentedinFig.2leadstoourtwomajorobser- separation, which might be a general concern in doped sys-
vations. Firstly, the magnetic excitations from the isospin-1 tems. Rather,theintroducedcarriersmusteitherco-existwith
2
square lattice in the undoped compound evolve, but clearly orresideinnano-scaleproximitytotheobservedmagnetism.
survive upon 3% doping where a sizable Fermi-surface has On the other hand, we do not rule out microscopic inhomo-
well developed [7, 17]. Secondly, the response of the mag- geneity, whichhasbeencommonlyobservedinelectroncor-
neticexcitationstodopingishighlyanisotropic. relatedsystemsupondoping[26]. Indeed,withscanningtun-
Moredetailsofsuchanisotropicimpactfromdopingcanbe nelingmicroscopymeasurementsontheir5%dopedsample,
seen in Fig. 3 where the RIXS spectra for two characteristic X.Chenetal. [16]observednano-scaleinhomogeneousdis-
zoneboundarypoints,namely(π/2,π/2)and(π,0),areplot- tribution of the local density of states, which is further sup-
ted.Thedatawasfittedwiththeschemedescribedearlier.The portedbytheworkbyY.J.Yanetal. [27]. Similarly, nano-
fasterdownturnacrosszerotowardsthenegativeenergyloss scale inhomogeneity has also been observed in hole-doped
sideofthefittedmagneticexcitationpeaks(redsolidlines)is cuprates[26],andmightbeanintrinsicfeatureofthesedoped
duetotheBose-Einsteinfactor. Forcomparison,themagnon Mottinsulators.
energies of our undoped sample are indicated with vertical Thedopingevolutionofthemagneticexcitationswereport
dashedlines. here shares much in common with that has been observed
in the hole doped cuprates. It has been shown [22–25] that
400 the magnetic excitations survive into the heavily overdoped
( π, 0 )
region in many cuprate families with both dispersions and
350 (π/2, π/2)
spectralweightssimilartothoseofundopedcompounds. For
300 Sr IrO , theARPESmeasurements[7,17]showthatdoping
) 2 4
counts250 msigenVifircaanngtely. rAetfotrhmesdothpeinJgeflfev=el s21tubdaienddhinerae,ftehwe Jheufnfd=red21s
y (200 bandhasalreadyextendedacrosstheFermienergy,resulting
sit inasizableFermisurface[17].Theindirectchargegapseems
n150
e tobeclosedwiththeappearanceoftheelectron-likepockets
nt
I100 around (π/2,π/2) and hole-like pockets around (π,0). To
explainsuchadrasticresponse,A.delaTorreetal. [7]sug-
50 geststhatdopingstronglyweakenstheonsiteCoulombrepul-
sion,leaving(Sr La ) IrO tobeintheweaklyinteracting
0 1−x x 2 4
−0.1 0 0.1 0.2 0.3 0.4 region. Such strong doping dependence of the Coulomb U
Energy loss(eV)
was also discussed for cuprates [28], which was challenged
bymanyothers[29]. Ourresultsshowthat,althoughthedop-
FIG. 3: RIXS spectra for (π/2,π/2) (open diamonds) and (π,0)
ing significantly renormalizes the electron band structure in
(open circles) respectively. Dashed lines through the data points
(Sr La ) IrO , thesystemstillsupportsmagneticcorrela-
showourfittingresults. Thetwopeaksdepictedbysolidredlines 1−x x 2 4
arethefittedmagneticexcitationpeaks,withhorizontalbarsshowing tionswithsimilardispersionandspectralintensity,indicating
theirFWHMoftheLorentzianmodelinEq.1. Theverticaldashed thatithasasimilardegreeofelectron-electroncorrelationas
linesindicatethemagnonenergiesatthesetwoQpointsinourun- theundopedcompound.
dopedsample[19]. The observation of anisotropic modification to the mag-
netic excitations is particularly interesting. We notice that
At both Q points, the magnetic excitations are much such anisotropic softening of magnetic excitations along the
broader than the instrumental resolution. This is in contrast nodal direction has been also observed with RIXS in hole-
to the case of the undoped compound [11, 12, 19, 21], for doped superconducting cuprates as well [30, 31], where in
whichthemagnonsareresolutionlimited. Thus,themagnetic doped Bi-based cuprates, the magnons collapse along the
excitation is highly damped upon doping. From our fitting, nodal direction but persist along the anti-nodal direction in
4
the momentum space. Such behavior is captured in random
phase approximation (RPA) calculations of the magnetic re-
sponse in the cuprates based on itinerant quasiparticles [30–
∗ Electronicaddress:[email protected]
34]. Hence, such anisotropic softening of the magnetic ex-
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