Antiferromagnetic order and domains in Sr3Ir2O7 probed by x-ray resonant scattering

4 MB·English

by  S. Boseggia

Antiferromagnetic order and domains in Sr Ir O probed by x-ray resonant scattering
3 2 7
S. Boseggia,1,2,∗ R. Springell,1 H. C. Walker,3 A. T. Boothroyd,4 D. Prabhakaran,4
D. Wermeille,5,6 L. Bouchenoire,5,6 S. P. Collins,2 and D. F. McMorrow1
1London Centre for Nanotechnology and Department of Physics and Astronomy,
University College London, London WC1E 6BT, United Kingdom
2Diamond Light Source Ltd., Oxfordshire OX11 0DE, United Kingdom
3European Synchrotron Radiation Facility, BP220, F-38043 Grenoble Cedex 9, France
4Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
5XMaS, UK-CRG, European Synchrotron Radiation Facility, BP220, F-38043 Grenoble Cedex, France
6Oliver Lodge Laboratory, Department of Physics,
University of Liverpool, Oxford Street, Liverpool, L69 7ZE, UK
(Dated: January 9, 2012)
2
This article reports a detailed x-ray resonant scattering study of the bilayer iridate compound,
1
Sr Ir O , at the Ir L and L edges. Resonant scattering at the Ir L edge has been used to
0 3 2 7 2 3 3
determinethatSr Ir O isalong-rangeorderedantiferromagnetbelowT ≈230Kwithanordering
2 3 2 7 N
wavevector,q=(1,1,0). TheenergyresonanceattheL edgewasfoundtobeafactorof∼30times
2 2 3
n largerthanthatattheL . ThisremarkableeffecthasbeenseeninthesinglelayercompoundSr IrO
2 2 4
a and has been linked to the observation of a J = 1 spin-orbit insulator. Our result shows that
J despitethemodifiedelectronicstructureoftheebffilaye2rcompound, causedbythelargerbandwidth,

6 the effect of strong spin-orbit coupling on the resonant magnetic scattering persists. Using the
programme SARAh, we have determined that the magnetic order consists of two domains with

] propagation vectors k =(1,1,0) and k =(1,−1,0), respectively. A raster measurement of a
l 1 2 2 2 2 2
e focussedx-raybeamacrossthesurfaceofthesampleyieldedimagesofdomainsoftheorderof100µm
- size, with odd and even l components, respectively. Fully relativistic, monoelectronic calculations
r
t (FDMNES), using the Green’s function technique for a muffin-tin potential have been employed
s to calculate the relative intensities of the L edge resonances, comparing the effects of including
. 2,3
t spin-orbitcouplingandtheHubbard,U,term. AlargeL toL edgeintensityratio(∼5)wasfound
a 3 2
for calculations including spin-orbit coupling. Adding the Hubbard, U, term resulted in changes to
m
the intensity ratio <5%.
-
d
PACSnumbers: numbers
n
o
c I. INTRODUCTION and Na IrO 11, insulating or poor metallic behavior has
[ 2 3
been observed. The traditional origin of the Mott in-

1 sulator, namely that U is similar in magnitude to the
Transitionmetaloxides(TMOs)areresponsibleforan
v band width, W, is not applicable in these cases, since U
enormous range of phenomena in solid state physics1,
2
is greatly reduced. The most likely culprit is then the
5 largely dominated by materials containing ions of the 3d
spin-orbit (SO) coupling, and in fact recently, the first
4 series. Studies into these compounds have not only en-
example of a spin-orbit Mott insulator was proposed to
1 riched our fundamental understanding of materials, but
1. haveresultedintherealizationofapplicationsinthereal explain the experimental data observed from the layered
iridate compound, Sr IrO 12.
0 world; from high temperature superconductivity in the 2 4
2 cuprates2 to colossal magnetoresistance (CMR) in per- Supported by density functional theory calculations
1 ovskite manganites3 and more recently, multiferroicity4. with local density approximation (LDA) +U + SO, an-
v: It was inevitable that further advances would be made gular resolved photoemission spectroscopy (ARPES), x-
i and new physics would be discovered in the heavier 4d ray absorption (XAS), optical conductivity data12 and
X and 5d series. As the transition metal ion species be- later, x-ray resonant scattering (XRS)5, a convincing ar-
ar comes heavier, relativistic effects start to play a more gument was made for the role of the SO energy ζSO, in
important role and the competing energy scales of the the observed insulating behavior and a novel, Jeff = 21
crystalfieldandspin-orbitcouplingpresentahostofnew Mottgroundstate. TheIr5d levelsaresplitbythecrys-
possibilities5–8. tal field (CF) into t2g and eg orbitals. The CF energies
are large which results in a low spin state, t5 . In the
Conventional wisdom concerning TMOs describes the 2g
limit of strong SO coupling the t band is split into a
3d compoundsashavingalocalized, stronglycorrelated, 2g
J = 1 doublet and a J = 3 quartet, which is lower
narrow d band with a large value for the Coulomb re- eff 2 eff 2
pulsion, U. 5d TMOs by contrast were thought to have in energy. The Jeff = 32 band is filled by four of the Ir
weakly-correlated,wided bandswithareducedCoulomb 5d5 electrons, leaving a half-filled Jeff = 12 band. The
term. One might then expect the 5d TMOs to have a Coulomb repulsion, U, splits the J = 1 band, giving
eff 2
greater tendency to be metallic. However, in a num- risetoaMottinsulator; thefirstexampleofa‘spin-orbit
ber of notable cases, for example Sr IrO 9, Sr Ir O 10 integrated narrow band system’12.
2 4 3 2 7
2
Sr Ir O is the next compound along the Ruddles- Sr Ir O . Theaimistodeterminethemagneticstructure
3 2 7 3 2 7
den Popper series, Sr Ir O from Sr IrO . It can ofthiscompoundandtoinvestigatetheunusualbehavior
n+1 n 3n+1 2 4
be described as a bilayered iridate, which displays bulk oftheL edgeresonances, attributedtoaneffectofthe
2,3
properties10,13 with some similarities to its single lay- J = 1 state5, and to determine if this effect persists in
eff 2
ered cousin14,15. It is a weakly insulating magnetic a larger bandwidth, less insulating system.
compound with a tetragonal I4/mmm crystal structure The article is organized as follows: Section IIA de-
at room temperature10. A weak ferromagnetic compo- scribes the crystal structure determination and section
nent is observed to appear in the magnetization data at IIB, the bulk susceptibility data, comparing with pre-
T ∼280K and a second transition, resulting in a fur- vious reports. Section IIC is an x-ray resonant scat-
A
ther increase in magnetization occurs at T ∼250K10, tering (XRS) investigation of the magnetic order, which
B
attributed to spin-canting of an antiferromagnetically includes a study of the energy, polarization and tem-
ordered state. The magnetic moment reported at 2K perature dependences of the resonant magnetic peaks, a
in an applied field of 7T is only 0.037µ /Ir, more Group Theory treatment of the magnetic structure and
B
than 25 times lower than the expected 1µ /Ir for an a domain imaging measurement. Section III reports cal-
B
S= 1 system. The effective moment, deduced from culations of the energy resonances and compares with
2
a high-temperature Curie-Weiss (CW) fit to the mag- experimentaldata. Weconcludethatthemagneticstruc-
netic susceptibility, χ, in a field of 7T was reported tureisatwo-domaincommensurateantiferromagnetwith
to be 0.69µ /Ir, compared to the theoretical value of propagation vectors, k =(1,1,0) and k =(1,−1,0)
B 1 2 2 2 2 2
1.73µ /Ir for an S= 1 system. These results are con- andaN´eeltemperature,T =230±5K. Theexception-
B 2 N
sistent with a picture of a canted antiferromagnetic, ally large ratio of Ir L to L edge magnetic scattering
3 2
J = 1 insulator, similar to the single layered Sr IrO intensitythatwasseeninSr IrO 5 isalsopresentinthis
eff 2 2 4 2 4
compound. Despite these similarities, Sr Ir O is much compound, suggesting that the J = 1 state may still
3 2 7 eff 2
more metallic than Sr IrO , reflecting the general ten- be realized in this much wider bandwidth compound.
2 4
dency towards greater metallicity with increasing n in
the Sr Ir O series16. A question then remains as
n+1 n 3n+1
to the robustness of the properties driven by the strong II. EXPERIMENTAL RESULTS
spin-orbit coupling, as the electron correlation strength
is changed. A. Crystal structure determination
In order to investigate the nature of the antiferromag-
neticorderingoftheIrmagneticmoments,thetechnique
ofneutrondiffractionwouldnormallybethefirstportof
call. However,duetothestrongabsorptioncross-section
for thermal neutrons of both naturally occurring iridium
isotopes, 191Ir (954barn) 193Ir (111barn) and the small
magneticmoment,x-rayresonantscattering(XRS)isthe
most suitable tool to investigate the magnetic structure
ofSr Ir O . Itisbothanelementselectiveandshellspe-
3 2 7
cific technique and can be used to measure systems with
small magnetic moments17. The origin of the magnetic
scattering is due to electric multipole transitions from
core levels to spin-polarized, empty states in the valence
band. The intensity of the scattering is determined by O
c
the SO splitting of the initial and intermediate states O’
and the overlap integral of the intermediate levels with Sr
the initial and final electronic orbitals. For the case of a Ir
Sr Ir O this effect is large at the Ir L , which probe
3 2 7 2,3
dipole transitions from 2p , 2p core levels, respec-
1/2 3/2 a
tively, to 5d states.
3/2,5/2
Recent work by Kim et al.5 proposed that there may FIG. 1: (Color online) The Sr Ir O I4/mmm crystal struc-
3 2 7
be an even greater potential behind the XRS technique, ture (left) with two bilayer molecules per unit cell. A 50%
interpretingtherelativestrengthofthemagneticscatter- occupancyoftheO’sitesresultsinanoctahedraloxygenen-
ing at the L and L edges to suggest a possible J = 1 vironment of the Ir ions, rotated from one layer to the next.
2 3 eff 2
ground state. However, the interpretation of these data ApolyhedralrepresentationoftheIroctahedralenvironment
hasbeendisputed18. Amajorquestionremainsastothe is shown on the right-hand-side.
robustness of the potential J = 1 state for such dra-
eff 2
matic changes in the electronic properties. This article Single crystals of Sr Ir O were grown at the Claren-
3 2 7
presentsadetailedaccountofaresonantx-rayscattering donLaboratory,OxfordUniversity,UK.Theseweresyn-
investigation into the barely insulating bilayered iridate, thesizedinPtcruciblesusingtheself-fluxtechniquefrom
3
off-stoichiometric IrO , SrCO and SrCl compounds. intense x-ray sources, for the purpose of determining the
2 3 2
The mixture was heated to 1440◦C, fired for 20h and magnetic structure, using the I4/mmm space group is
slowly cooled at 3◦/h. The resulting samples were plate- reasonable.
like with the c-axis along the shortest dimension of
∼2×2×0.1mm size crystals.
Sr3Ir2O7 is the n=2 compound of the Srn+1IrnO3n+1 B. Magnetization measurements
Ruddlesden-Popper series, whose synthesis was first re-
ported in 199419. However, the exact crystal struc-
ture remains a contentious issue. Previous articles have
reported the tetragonal I4/mmm19, the orthorhombic 4
Bbca10, Bbcb20 and Pban21 space groups. It is clear )
-3 ( a )
that the structure contains strongly coupled double Ir- 0 0 .5 T
1
O layers, separated by layers of Sr-O and off-set along * 3 0 .1 T

the c-axis, which result in a double-layered framework /Ir 0 .0 5 T
B
of Ir atoms centered inside oxygen octahedra. It is the m 0 .0 0 5 T
(
rotation of these octahedra and the correlation between 2
n
therotationsthatleadtothesubtledifferencesincrystal io
t
structure reported thus far. a
tiz 1
X-ray diffraction data were collected with a Super- e
n
nova x-ray diffractometer equipped with a microfocused g
monochromatic Mo source at the Research Complex at a
M 0
Harwell (RCaH), Chilton, UK. A Sr3Ir2O7 single crystal
of dimensions 0.108×0.134×0.072mm was mounted. )
s
1369 reflections (204 unique) were measured at room it ( b )
n 2 3 0 K
temperature in an ω-scan mode within a 2θ range of u

7.84◦ to 64.6◦. The data were corrected for Lorentz, .
b
r
polarization and absorption effects. The 1369 reflec- a
(
tions were used to obtain the cell parameter: a =
3.897(5) and c=20.892(5)˚A and the calculated density ion 2 7 5 K
t
was 7.947g/cm3. a M
iz
Initially, the diffraction data were modeled with an et d 2M /d T 2
I4/mmm space group and a full occupancy of the atom n
g
sites. As a consequence we obtained a large R factor a
(>0.7) and the thermal parameter of O(3) (equivalent M 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0
to O atomic positions, labelled O’ in Fig. 1 (a)) became T e m p e r a t u r e ( K )
very large compared to the other atoms and strongly
anisotropic with an ellipse highly elongated along the a-
FIG.2: (Coloronline)SQUIDmagnetizationdata,asafunc-
axis. A further step was then to remove the O(3) atom
tionoftemperatureforfieldcooled(FC)measurementsinthe
fromitspositiononthemirrorplaneandshiftitby0.4˚A
basal plane, ranging from 0.005T to 0.5T applied magnetic
assigning it an occupancy of 0.5. Subsequent refinement
field,panel(a). Twotransitionscanbeobservedathightem-
of several parameters (isotropic extinction, anisotropic peratureandadownturninthemagnetizationat50K,which
thermal parameter for Ir and Sr, isotropic thermal pa- becomesapositiveupturnasthefieldisincreased. Panel(b)
rametersforO(3))byfull-matrixleast-squarestechniques shows the 0.005T data, together with the second derivative
convergedatR=0.039. ThecrystalstructureofSr Ir O of the magnetization; the peaks at 230K and 275K indicate
3 2 7
is shown in Fig. 1 (left panel), the oxygen atoms high- the two transition temperatures.
lightedingreenrepresentthosewithonly50%occupancy.
Thisrefinementofthelatticeparametersandatomicpo- The bulk magnetization data were collected, using a
sitionsisincloseagreementwiththeinitialreportonthe QuantumDesignMPMS-7superconductingquantumin-
crystal structure of Sr3Ir2O7 by Subramanian et al.19. terferencedevice(SQUID)magnetometer,attheLondon
The disorder of O atoms is associated with the alter- Centre for Nanotechnology, UCL, London, UK. Figure 2
nate rotation of the IrO octahedra about the c-axis. showsthemagnetization,M(µ /Ir)asafunctionoftem-
6 B
From our data this rotation is about 11.91◦. An octa- perature, T, measured in the basal plane. Field cooled
hedral representation of the structure is shown in Fig. 1 (FC) measurements were made on cooling in an applied
(rightpanel). Noadditionalsuperlatticereflectionscould magnetic field, ranging from 0.05−0.5T. On inspection
be discerned in the data suggesting that the octahedral of the FC data, it is clear that there are two transitions
rotationsarenotcorrelated,neitherintheplanenorper- at high temperature, T and T , with a downturn in
A B
pendiculartoit. Althoughitispossiblethatmoresubtle the magnetization at low temperature, beginning at ap-
crystallographic effects might be elucidated using more prox. 50K. This downturn becomes an upturn in M at
4
higherfields. Panel(b)ofFig. 2showsthesecondderiva-
(cid:2)(cid:1) (cid:1)(cid:8)(cid:3)(cid:3)(cid:2)(cid:7)(cid:9)
tiveofthe0.005TFCdata, whichgivesT =275Kand (cid:6)
A ( a ) e ¢
TB =230K. p k f
These data are qualitatively similar to those reported
e ¢
previously on single crystals. A study by Cao et al. s
reported transitions TA =285K, TB =260K14, for FC e
magnetization measurements in the ab-plane. The lower p e (cid:1)(cid:4)(cid:1)(cid:8)(cid:4)(cid:4)(cid:3)(cid:9)
transition temperatures in our case may be due to varia- s
tionsinthesamplequalityorsmalldifferencesinoxygen k
i
stoichiometry between the two studies.
(cid:1) (cid:1)(cid:8)(cid:2)(cid:4)(cid:4)(cid:3)(cid:9)
C. X-ray resonant scattering (cid:5)
The x-ray resonant scattering experiments were con-
3 0 0 0
ductedattheI16beamlineoftheDiamondLightSource, T = 4 0 K
( b )
Didcot, UK and at the BM28 (XMaS) beamline22 at 2 5 0 0 ( (cid:10) (cid:1)(cid:10) L )
the European Synchrotron Radiation Facility (ESRF), )
c
Grenoble, France. Measurements were performed at the /se 2 0 0 0
IrL2 (12.831keV)andL3 (11.217keV)absorptionedges, ts
probingtransitionsfromthe2p1 tothe5d3 andfromthe (c 1 5 0 0 s - p
2p3 to the 5d3,5, states, respec2tively. 2 sity s - s
2 2 2 n 1 0 0 0
te
In
5 0 0
1. Ordering wavevector
0
On I16 the x-rays were provided by means of a U27- 2 2 .9 2 3 .0 2 3 .1 2 3 .9 2 4 .0 2 4 .1
type undulator insertion device, focussed to a beam size
L ( r .l.u )
of20×200µmatthesampleposition, usingasetofpar-
allel double focussing mirrors. A Newport 6-axis N-6050
FIG.3: (Coloronline)(a)Schematicoftheexperimentalcon-
Kappa diffractometer was used to maneuver the sample
figurationusedformeasuringXRS.Thesampleorientationis
orientationandanavalanchephotodiode(APD)wasused
labelled with respect to the incoming and outgoing wavevec-
to detect the scattered photons. tors. (b) L scan across the magnetic (1 123) and (1 124)
2 2 2 2
At the BM28 bending magnet beamline the energy reflections at the L edge, T=40K, measured on I16. Both
3
was selected using a double-bounce Si (111) monochro- theσ−σandσ−πpolarizationchannelsareshown;theblue
mator, and higher order harmonics were rejected by open circles and black filled spheres, respectively. The solid
rhodium coated mirrors, providing a beam footprint of lineisafittoaLorentzianpeakshapeforeachreflectioninthe
∼300×800µm at the sample. The diffractometer was σ−π channel. FWHM’s of 0.031(4) and 0.024(3) r.l.u were
found for the (1 123) and (1 124) reflections, respectively.
a vertical scattering Eulerian cradle-type with a Vortex 2 2 2 2
detector mounted on the 2θ (detector) arm. The degree
oflinearpolarizationintheplaneofthestoragering(re-
ferredtoasσ-polarizedlight)iscloseto100%atI16and
BM28. measure the polarization state of the scattered photons
In both cases the samples were mounted in Displex isthatfluorescentphotons,thatareemittedisotropically
cryostats with the [110] and [001] directions in the verti- several hundred eV below the absorption edge, are dis-
calscatteringplane, the[001]beingperpendiculartothe criminated out, this may reduce overall signal strength,
sample surface. A schematic of the sample orientation but dramatically improves the signal to noise ratio. For
canbeseeninFig. 3(a). Apolarimeterwasmountedon the Ir L edges a Au (333) reflection was used.
2,3
thedetectorarm;thisconsistsofananalyzercrystalwith
a Bragg angle close to 45◦ at the selected energies and The crystal mosaic, determined from the full-width
a suitable detector. By rotating the polarimeter set-up at half-maximum (FWHM) of the specular reflection
by 90◦ it is possible to detect π-polarized light. In this (0024) in the unrotated σ−σ channel, was 0.044◦. In
way it is possible to discriminate between the two po- theσ−πrotatedchannel,peakswerefoundatthe(11L)
22
larization channels of σ−π and σ−σ scattering, which positions. Examples of these peaks at the (1123) and
22
means that different scattering mechanisms can be dis- (1124) reflections are shown in Fig. 3, as measured on
22
tinguished. For example, an incident x-ray beam of lin- I16 at 40K at the L edge, in reciprocal lattice units
3
early polarized light is rotated by 90◦ when scattered by (r.l.u). σ−π intensity is shown as the full black circles
magnetic dipoles23. A side-effect of using an analyzer to and σ−σ as the open blue circles.
5
2. Energy dependence and branching ratio et al. the L edge resonance appears to present a similar
3
two-component shape.
Theresonantenhancementofthe(1 124)reflectionat
2 2
60K was measured as a function of energy at the Ir L
2,3
edges, from ∼50eV below the edge to ∼50eV above. 3. Order parameter
The fluorescence was measured simultaneously in order
to compare the energy dependence of the magnetic re-
In order to determine the transition temperature of
flection intensity with the absorption white line.
the magnetic ordering and the type of phase transition
occurring in Sr Ir O , we measured the intensity of the
3 2 7
1 0 (1 124)and(1 123)reflectionsatthepeakoftheL edge
2 2 2 2 3
2 .0 T = 6 0 K L (2 p 5 d ) 9 resonance in both the unrotated σ−σ and the rotated
2 1/2
) L 3 (2 p 3/2 5 d ) 8 σ−π channels.
. units1 .5 7 Inte
Intensity (arb01 ..50 Xss --A psN E S F lu o re s c e n c e 23456 nsity (arb. units) alized)001 ...680 qoFWHM (2)0000....11220505 50 T1e0m0 p e ra1t5u0re (K 2)00
* 1 0 1 rm
0 .0 1 1 2 0 0 1 1 2 5 0 1 2 7 5 0 1 2 8 0 0 1 2 8 5 0 1 2 9 0 0 0 ity (no0 .4 2 3 0 K
s
n
P h o to n E n e rg y (e V ) Inte0 .2 M ab S Q U ID (n o rm a liz e d )
(1 /2 1 /2 2 4 ) L e d g e
FIG.4: (Coloronline)Measurementoftheresonantenhance- 3
ment of the (12 1224) reflection across the L2 and L3 edges at 0 .0 (1 /2 1 /2 2 3 )
60K, well below T . The solid black line shows the x-ray 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0
N
absorption near edge spectra (XANES), measured in fluores- T e m p e ra tu re (K )
cence mode, normalized to the number of initial states. The
blue solid points show the intensity of the (1 124) peak in
2 2 FIG. 5: (Color online) The temperature dependence of the
the rotated σ−π channel and the red open triangles result (1 124) and (1 123) peaks, measured at the L edge on the
from the unrotated σ−σ intensity. 2 2 2 2 3
BM28 beamline is compared to the SQUID magnetization
data. The transition temperature of the observed magnetic
Figure 4 shows the energy dependence of the (1 124) reflections, determined by XRS, coincides with the second
2 2
magnetic reflection at the L2,3 edges. The XANES spec- transition, TB =230K in the bulk magnetization data.
tra (solid black line) has been included to reference the
energyoftheabsorptionedges. Thecontrastinintensity
Fig. 5 presents an integration of θ−2θ scans at the
betweenthetwoedgesisstriking;similartothatreported
l=23,24 peaks and is compared to FC, SQUID magneti-
for Sr IrO 5, the integrated intensity of the magnetic
2 4 zationdata,measuredin0.005T.Thetransitionappears
scattering at the L edge is almost 30 times larger than
3 second order with a N´eel transition to a commensurate
that at the L (note that the signal at the L edge has
2 2 antiferromagnet, T ≈230K. This is very close to the
N
been magnified by a factor of 10 for clarity). The excep-
transition, T , observed in the bulk magnetization data
B
tionallylargeratiooftheL /L edgeresonantintensities
3 2 shown in Fig. 5 and described in section IIB.
ispeculiartotheiridatesthusfar. Other5d compounds,
A question then remains as to the origin of the higher
such as the conventional band insulator K ReCl 24, ex-
2 6 temperature transition, T , observed in the bulk mag-
A
hibit rather more modest ratios (∼2).
netization. It is possible that this indicates a transition
The widths of the L edge resonances are
2,3 to an incommensurate antiferromagnetic structure. Fu-
FWHM =5.29(5)eV and FWHM =8.25(5)eV, re-
L2 L3 ture measurements are planned to investigate the reso-
spectively, similar to those found for Sr IrO 5 and other
2 4 nant magnetic scattering in this phase.
5d materials24. At the L edge the peak magnetic in-
2
tensity is at the peak of the absorption edge white line,
whereas at the L edge the resonance consists of two
3
components, the most intense of which is centered on 4. Magnetic structure
the inflection point of the absorption edge and the other
at the peak of the white line. Energy scans at various FromtheXRSinvestigationdescribedpreviously,ase-
temperatures about the ordering temperature indicated ries of peaks were found at (hkl) positions, which result
22
thatbothcomponentssharethesamedipolarorigin. On from a commensurate, ordered magnetic structure. Us-
close inspection of the recent report on Sr IrO 5 by Kim ing the SARAh computer program25, we have used the
2 4
6
approach of representational analysis, i.e. the applica- Fig. 6andaregeneratedbytwoarmsofthepropagation
tion of Group Theory to solve the magnetic structure of vector k=(1,1,0): k =(1,1,0) and k =(1,−1,0).
2 2 1 2 2 2 2 2
Sr Ir O . Theresultingmagneticstructuremaythenconsistoftwo
3 2 7
domains,whichhaveintensityforodd(even)l peaks,re-
spectively.
5. Magnetic domain imaging
In order to investigate the possibility that domains of
odd (even) l may exist in our samples we compared the
intensitiesofseveralmagneticreflections. Thesimilarin-
tensities of the (1 124) and (1 123) peaks measured on
2 2 2 2
the XMaS beamline, suggest that if the two-domain pic-
ture is correct then the domains are significantly smaller
than the 300×800µm beam size, utilized on BM28. An
approximatelyequivalentnumberofthesedomainswould
thenbeilluminatedateachofthepeakpositions. Onthe
c
I16beamlinehowever,thex-raysarefocussedatthesam-
ple position. The beam spot is reduced, using a pair of
a
parallel double focussing mirrors and slits, which results
inafootprintonthesamplesurfaceof(18×100µm). In
a this case we observed large differences in the intensities
of odd (even) l magnetic reflections.
In order to image the intensity of these magnetic re-
flections over a selected sample volume we performed a
1
raster in x and y sample position at the l=23,24 mag-
netic reflections, at the L edge peak resonance energy
3
at 40K.
2 50
(1/2 1/2 24) (1/2 1/2 23)
45
0.75
40
3 35
0.7
m) 30
m
on (0.65 25
siti
4 o
p 20
y
0.6
15
A B
10
0.55
FIG. 6: (Color online) The upper panel shows the unit
5
cell structure for the domain with ordering wavevector,
k1 =(12,12,0), as determined by Group Theory calcula- 0.5− 0.28 −0.26 −0.24 −0.22 −0.2− 0.28 −0.26 −0.24 −0.22 −0.2 0
tions performed using the program, SARAh25 and the XRS x position (mm) x position (mm)
data, presented in section IIC. The lower panel shows a
schematicrepresentationofthetwomagneticdomains,Aand
FIG.7: (Coloronline)Intensityofthe(1 124)reflection,left
B, defined by the ordering wavevectors, k =(1,1,0) and 2 2
1 2 2 panel and (1 123), right, as a function of x and y sample
k =(1,−1,0). 2 2
2 2 2 position. ThesemeasurementsweremadeattheL edgeres-
3
onanceatatemperatureof40K,wellbelowtheN´eeltemper-
In order to calculate the symmetry allowed relations ature, TN =230K. The beam size projected on the sample
surface is highlighted by the black rectangle in the left-hand
between the moments, the only inputs required were the
panel.
space group of the crystal structure, the atomic coordi-
nates of the magnetic atoms and the propagation vec-
tor, k. The possible magnetic structures are shown in Figure 7 presents contour plots of the (1 124) and
2 2
7
(1 123) reflections over a 100×300µm area of the sam- ativistic monoelectronic calculation (DFT-LSDA) with
2 2
ple. Theresultsareclear; inregionsofthesamplewhere spin-orbit coupling on the basis of the Green’s-function
there is little to no intensity of the l=24 peak there is technique (multiple scattering) for a muffin-tin poten-
a maximum in the intensity of the l=23 peak and vice tial. In order to take account of the effect of the inter-
versa. Domains of odd and even l persist through the site Coulomb repulsion U, not negligible in many theo-
sample. This is not difficult to imagine, since the only riesof5d Mott-insulators, weincludedtheHubbardcor-
difference between the two ordering wavevectors k and rection (LSDA+U). The value of U=0.25eV was chosen
1
k , is the respective orientation of one magnetic bilayer according to the optical conductivity measurements pre-
2
toanotherandtheseareofequivalentenergycost. These sented by Moon et. al16. The simulated spectra derive
images indicate a domain size of approx. 100×100µm entirely from the E1−E1 dipole interaction (we previ-
andconfirmthecalculationsandresultspresentedinsec- ously checked that there were no effects due to higher
tion IIC, supporting the determination of the magnetic order terms). For the calculation we used a magnetic
structure. unit cell of size 2a×2b×c, containing 128 atoms with
a cluster radius 3.8˚A and an average of 19 atoms per
cluster.
III. RESULTS OF FDMNES CALCULATIONS
)
e
c
n
e 2 .5
6 c
s
e X A N E S flu o re s c e n c e
r
N O S O N O U o 2 .0 F D M N E S + S O + U (0 .2 5 e V )
5 S O flu
S O + U = 0 .2 5 e V ed 1 .5
) S O + U = 0 .5 e V liz
s a L
it 4 rm 1 .0 2
n o
. u (n 0 .5 L
b S 3
r 3 E

a N
( A 0 .0
ity X 1 .0
s 2 ) T = 6 0 K
ten nits 0 .8 (1 /2 1 /2 2 4 p e a k )
In 1 rb. u 0 .6 F D M N E S + S O + U (0 .2 5 e V )
a
ity ( 0 .4 ss -- ps
0 s
n
1 1 1 9 0 1 1 2 2 0 1 2 8 1 0 1 2 8 4 0 te
In 0 .2
E n e r g y ( e V )
* 1 0
0 .0
1 1 1 5 0 1 1 2 0 0 1 1 2 5 0 1 2 7 5 0 1 2 8 0 0 1 2 8 5 0 1 2 9 0 0
FIG. 8: (Color online) FDMNES (finite difference method
for solving the Schro¨dinger equation) calculations performed E n e r g y ( e V )
at the Ir L edges for the Sr Ir O compound are shown
2,3 3 2 7
for various initial parameters: assuming negligible SO and U FIG.9: (Coloronline)FDMNEScalculationsfortheXANES
(solid black line), including SO, but with no U (red line), in- spectra and the (1 124) magnetic reflection, including spin-
cludingSOandU=0.25eV16 (blueline),andSO+U=0.5eV orbit (SO) coupli2ng2 and including both SO coupling and
(green line). Spectra have been separated for clarity. U=0.25eV are represented by solid black lines. The cal-
culations are compared to the experimental XANES data at
the L edges (blue solid points) and the (1 124) magnetic
One of the most striking aspects of the x-ray reso- 2,3 2 2
reflection (green solid points).
nant scattering investigations of both single and bilay-
ered iridate compounds is the very large ratio of L and
3
L edge magnetic scattering intensities. In order to bet- Figure8showsacomparisonofseveraldifferentcalcu-
2
ter understand the origin of this remarkable effect we lationsinordertoobservethepotentialeffectsoftheSO
have performed calculations with the FDMNES code26. couplingandtheHubbardU termontherelativeintensi-
FDMNES is an ab initio cluster-based, monoelectronic ties of the L edge resonances. It is clear that the spin-
2,3
code that calculates x-ray absorption spectra and x- orbitcouplingtermplaysthegreatestroleintherelative
ray resonant scattering spectra. We used the fully rel- strengths of the L and L edge resonances. Including
3 2
8
the Hubbard U term dampens the L edge signal still indicate a two-domain commensurate antiferromagnetic
2
further, but there is relatively little difference between (AF) structure with wavevectors k =(1,1,0) and
1 2 2
0.25eV and 0.5eV; the values calculated for Sr3Ir2O7 k2 =(12,−12,0), although further azimuthal measure-
and Sr2IrO4, respectively. ments are planned to determine the precise direction of
Figure 9 compares the experimental data for the themagneticmoments. Theorderingtemperatureofthis
XANES spectra and x-ray resonances of magnetic reflec- commensuratephasewasfoundtocoincidewiththelower
tionstoFDMNEScalculations. Theupperpanelpresents oftwotransitions,T =230K,observedinthebulkmag-
B
theXANESdataforL3 andL2 edges(bluesolidpoints), netization data. The higher transition temperature may
whose edge jumps are normalized to the number of ini- be due to an incommensurate AF phase.
tialstates,respectively. TheFDMNEScalculationssolid TheLorenzianprofileoftheenergydependenceistyp-
black line) closely resemble the data; the intensity of the ical of a dipolar magnetic origin and only has intensity
white line compared to the edge and the fine structure in the rotated, σ−π channel. FDMNES calculations,
featuresintheXANESspectraarewell-reproduced. The including spin-orbit coupling and the Hubbard term, U,
lower panel of Fig. 9 shows the magnetic resonances of have reproduced many features of the XANES and XRS
theL2,3edgesintheσ−πchannel,measuredatT=60K data, although the L2 edge damping is more extreme in
at the (1 124) magnetic reflection (solid green points). theexperimentaldata. TheintensityoftheL edgereso-
2 2 3
Some features are well modeled by the FDMNES and nanceisafactorof30timeslargerthanthenearnegligi-
others are not; the ratio of L3 to L2 edge intensity is ble L2 edge, which mirrors results reported on the single
large(∼5),butthedampingofthesignalattheL2 edge layer cousin, Sr2IrO45; an effect which is robust enough
isnotasextremeasthatfoundintheexperimentaldata. toovercometheincreasedbandwidth,W,inthebilayered
Allofthescatteredintensityappearsintheσ−πchannel. iridate. This could be explained by the J = 1 model
However, the energy position of the maximum L3 edge proposed by Kim et al.5 or that the obseerffved 2moment
resonance coincides with the peak in the white line ab-
is the 5d orbital angular momentum and not the total
sorptionspectrum,nottheinflectionpoint,asisthecase moment18.
for the experimental data. These discrepancies may be
duetotheextremespin-orbitcouplingregimeofSr Ir O
3 2 7
and the possible realization of a J = 1 insulator.
eff 2
V. ACKNOWLEDGEMENTS
IV. DISCUSSION AND CONCLUSIONS We thank the Impact studentship programme,
awarded jointly by UCL and Diamond Plc. for fund-
This articlepresentsa study of x-rayresonantscatter- ing the thesis work of S. Boseggia. G. Nisbet and P.
ingattheiridiumL2 andL3 edgesinbilayeredSr3Ir2O7. Thompson provided excellent instrument support at the
The principal aims were to investigate the magnetic I16andBM28beamlines,respectively. WealsothankN.
structure and energy dependence of the magnetic reflec- Casati for his support in the measurements and refine-
tions, in order to probe the robustness of the L2 edge ment process of the crystal structure determination. We
damping observed in Sr2IrO4, reported to be caused by thankA.S.Willsforusefuldiscussionsconcerningtheap-
a Jeff = 21 state5. plication of the SARAh code to modelling the magnetic
Calculations performed with the SARAh25 pro- structure. We also acknowledge fruitful correspondence
gramme, combined with the results from XRS data, with Y. Joly, concerning the FDMNES calculations.
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