Table Of ContentIntrinsic and extrinsic x-ray absorption effects in soft x-ray diffraction from the
superstructure in magnetite
C. F. Chang,1 J. Schlappa,1 M. Buchholz,1 A. Tanaka,2 E. Schierle,3 D. Schmitz,3 H. Ott,1
R. Sutarto,1 T. Willers,1 P. Metcalf,4 L. H. Tjeng,1,5 and C. Schu¨ßler-Langeheine1
1II. Physikalisches Institut, Universita¨t zu K¨oln, Zu¨lpicher Str. 77, 50937 Ko¨ln, Germany
2Department of Quantum Matter, ADSM, Hiroshima University, Higashi-Hiroshima 739-8530, Japan
3Helmholtz-Zentrum Berlin, Albert-Einstein-Str. 15, 12489 Berlin, Germany
4Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
5Max Planck Institute for Chemical Physics of Solids, No¨thnitzerstr. 40, 01187 Dresden, Germany
(Dated: January 14, 2011)
We studied the (001) diffraction peak in the low-temperature phase of magnetite (Fe O ) us-
2 3 4
1 ing resonant soft x-ray diffraction (RSXD) at the Fe-L and O-K resonance. We studied both
2,3
1 molecular-beam-epitaxy(MBE)grownthinfilmsandin-situ cleavedsinglecrystals. Fromthecom-
0 parisonwehavebeenabletodeterminequantitativelythecontributionofintrinsicabsorptioneffects,
2 therebyarrivingataconsistentresultforthe(001)diffractionpeakspectrum. Ourdataalsoallow
2
n fortheidentificationofextrinsiceffects,e.g. foradetailedmodelingofthespectraincasea”dead”
a surface layer is present that is only absorbing photons but does not contribute to the scattering
J signal.
3
1 PACSnumbers: 71.30.+h,61.05.cp
]
l Magnetite, Fe O , shows a first order anomaly in the both Wilkins et al. and Schlappa et al.. In both recent
e 3 4
- temperature dependence of the electrical conductivity at publications8,9theshapeoftherespectiveFe-L2,3spectra
r T ∼120K,thefamousVerweytransition.1 Itisaccom- are explained by absorption effects. Presently, hence, at
t V
s panied by a structural phase transition from the cubic least three different Fe-L RSXD spectra for the (001)
. 2,3 2
t inverse spinel to a distorted structure. One usually con- peakofmagnetitehavebeenpublishedandverydifferent
a
m nectsthistransitionwithchargeorderingoftheFe2+ and conclusions have been drawn about the electronic origin
Fe3+ ions on the octahedrally coordinated, so-called B- of the peak.
-
d sites. In a recent diffraction study, Wright, Attfield and Here we report our efforts to resolve the confusion
n Radaelli found long-range charge order from the pattern about the RXSD data on magnetite. Our strategy is
o of shorter and longer bond lengths between B-site iron to carry out the experiments using a magnetite bulk sin-
[c and oxygen ions below TV.2,3 Subsequently, using this glecrystalwhichwascarefullycleavedin-situ inorderto
structure as input, local density approximation + Hub- obtain the best possible surface quality, and to compare
1 bardU (LDA+U)bandstructurestudieshavecalculated theresultswiththemeasurementsonhighqualityMBE-
v thecorrespondingorbitalordering,whichinvolvesmainly grown magnetite thin films. In this manner we are able
8
the minority spin electron in the t2g state of the 2+ B- to distinguish intrinsic absorption effects from extrinsic
4
sites.4,5 effects. Takingintrinsiceffectsproperlyintoaccount, we
5
2 Recently this t2g orbital order has been studied using find consistent results for in-situ cleaved bulk samples
1. RSXD at the O 1s → 2p (K)6 and Fe 2p → 3d (L2,3)7 and thin films. Furthermore, taking a so-called ”dead”
resonance. The O-K edge resonance enhancement of the surfaceintoaccount,whichleadstoextrinsicabsorption,
0
(001)diffractionpeak(notationreferstothecubicroom- we are able to provide a quantitative explanation for the
1 2
1 temperature unit cell) on an ex-situ polished bulk single varying RSXD spectra reported in the literature so far.
: crystal was interpreted by Huang et al. as a signature The soft x-ray scattering experiments were performed
v
of a particular charge/orbital order at the oxygen-sites.6 at the HZB beam line UE46-1 at BESSY using the two-
i
X At the Fe L2,3-edges, using MBE-grown thin films, the circle UHV diffractometer designed at the Freie Univer-
r (001) maximum energy coincides with the resonance of sit¨atBerlin. Weused40nmthickmagnetitefilmsepitax-
a 2
the 2+ B-site ions and was assigned by Schlappa et al. ially grown on an epi-polished MgO(001) substrates and
to Fe t2g-orbital order on these sites.7 several magnetite bulk single crystals. The samples were
Very recently these results have been challenged. oriented such that two base vectors of the cubic room-
Wilkins and coauthors have presented RSXD data from temperature unit cell (a = 8.396 ˚A) were parallel to the
the (001) peak [(001) in the orthorhombic notation used scattering plane. The polarization of incoming light was
2
in Ref. 8] of bulk magnetite at the O-K and Fe-L either parallel or perpendicular to the scattering plane
2,3
resonance.8. Their O-K spectrum is similar to that of (π- or σ-polarization, respectively). A silicon-diode pho-
Huang et al.6 but their Fe-L data are very differ- tondetectorwithoutpolarizationanalysiswasusedwith
2,3
ent from those of Schlappa et al.7 Almost at the same the angular acceptance set to 1◦ in the scattering plane
time Garc´ıa et al.9 reported a Fe-L RSXD spectrum and 5◦ perpendicular to it. The energy dependence of
2,3
from a bulk sample, which is very different from those of the diffraction-peak intensities (diffraction spectra) from
2
7 0 0 7 1 0 7 2 0 7 3 0 7 0 0 7 1 0 7 2 0 7 3 0
(a )
F e -L 2,3 (0 ,0 ,1 /2 ) p (a ) F e -L 2,3 (0 ,0 ,1 /2 ) p
w ith
F ilm
w ith o u t
B u lk
a b s o rp tio n c o rr.
(w /o a b s o rp tio n c o rr.)
) )
its its X A S
n n
. u . u
rb rb
(a (a
tensity (b ) O -K (0 ,0 ,1 /2 ) p tensity (b ) O -K (0 ,0 ,1 /2 ) p
In In
F ilm
B u lk
(w /o a b s o rp tio n c o rr.) X A S
5 2 6 5 2 8 5 3 0 5 3 2 5 3 4 5 2 6 5 2 8 5 3 0 5 3 2 5 3 4
P h o to n E n e rg y (e V ) P h o to n E n e rg y (e V )
FIG. 1: (color online) RSXD spectra of the (001) peak of FIG. 2: (color online) RSXD spectra of the (001) peak of
2 2
bulkmagnetite(opensymbols)andmagnetitethinfilm(filled bulk magnetite without (open symbols) and with absorption
symbols) at (a) Fe L -edges and at (b) O K-edge. The correction (filled symbols) at (a) Fe L -edges and at (b) O
2,3 2,3
spectra are scaled to equal height. K-edge. Thespectraarescaledtoequalheight. XASspectra
are shown as solid lines.
the film sample were recorded by varying the photon en-
ergy and keeping the momentum transfer constant. For tures, while in the O-spectrum, the main peak, which is
bulk samples this method leads to distorted spectra be- justontheslopeoftheabsorptionsignal,becomesshifted
cause of the much narrower peaks and refraction effects. in energy.
We therefore performed longitudinal (L) scans at every For a film of thickness D the factor to correct for ab-
photon energy and integrated the (001)-peak intensity. sorption effects is µ/(1−exp(−2µd)). d = D/sinθ de-
2
Fig. 1 displays the (001) resonance spectra at the Fe scribestheeffectivephotonpathlengthatincidentangle
2
L andatOK-edgesforbulkmagnetiteandmagnetite θ. To perform this correction requires to know µ in ab-
2,3
thin film. One can observe very distinct differences be- solute units. Because of the thinness of the films, the
tween the bulk and the thin film. At the Fe edge, for correction should be smaller than for the bulk.
example, the first peak at 707 eV is much more pro- In Fig. 3 we now compare again the corrected spec-
nounced in the bulk than in the thin film. At the O tra from the bulk (filled symbols) with the uncorrected
edge,theenergypositionofthepeakofthebulkisclearly film spectra as presented in Ref. 7 (open symbols). For
shifted with respect to that of the thin film. We ascribe the O-K spectra the agreement between bulk and film
thesedifferencestoachangeofthescatteringvolumedue data is now close to perfect. Also for the Fe resonance
to variations of the penetration depth of the light as a the overall agreement between the spectra is very good,
function of its energy. This effect is quite severe for en- all spectral features agree. The main discrepancy here is
ergyvariationsacrossresonancesinthesoftx-rayregime in the relative intensities of the L and L part of the
3 2
due to the very high photo-absorption coefficients. For Fe-resonance spectra. The application of an absorption
a bulk sample, the scattered intensity in specular geom- correction on also the thin film data would probably re-
etry is proportional to 1/µ, with µ being the absorption solve much of this discrepancy. Thus, apart for this, we
coefficient.10 This absorption effect can be accounted for find very similar spectra from the film and the bulk at
by multiplying the resonance spectra by µ; µ can be re- both resonances. We can, hence, safely conclude that
liably obtained from the x-ray absorption spectroscopy the resonant diffraction data recorded from the thin film
(XAS) signal recorded in the total electron yield mode. sample are representative for the material magnetite as
The effect of this correction is shown for bulk mag- such and that the conclusions derived from the data of
netiteinFig.2forboththeFe-L andO-K resonances. magnetite thin films in our former Letter7 stand for the
2,3
The open symbols are the raw data and the filled sym- intrinsic properties of magnetite.
bolsarethoseaftercorrection. Theabsorptionsignalsare We now compare our experimental data with those
shown as solid lines. The correction for the Fe-spectrum from Huang et al.6, Wilkins et al.8, and Garc´ıa et al.9
affects mainly the relative intensities of the spectral fea- frombulkmagnetite. WefirstfocusontheFeL -edges
2,3
3
because our raw data are already very different. In fact,
7 0 0 7 1 0 7 2 0 7 3 0
itisquiteunlikelythatabsorptioninanotherwiseintact
(a ) samplecansuppressthescatteredintensitycompletely.11
F e -L 2,3 (0 ,0 ,1 /2 ) p What could cause such strong distortions, however, is
a layer on top of the sample, which does absorb photons
F ilm
B u lk but does not contribute to the scattered signal. This
could be either a polycrystalline layer or a crystalline
)
its layer with different surface orientation as the bulk or a
n
rb. u llaayyeerrsocfedniaffreiroeinstlcikheelmyiicsadlecmomonpsotsriattieodn.inTFhiagt.t4h.isT”hdeedaida”-
(a mondsymbolsaretheexperimentaldatafromWilkinset
sity (b ) al.8 andthegreenthicksolidlineisasimulationinwhich
ten O -K (0 ,0 ,1 /2 ) p we describe the presence of an absorbing layer of thick-
In
F ilm ness D by multiplying our experimental RSXD spec-
a
B u lk trum by e−2daµ(hv) with da =Da/sinθ.
We find the best agreement between data and simula-
tion for d ×µ ≈ 18 at the absorption maximum. The
a
resulting spectrum reproduces not only the peak posi-
5 2 6 5 2 8 5 3 0 5 3 2 5 3 4 tion but also the shape of the data from Wilkins et al.8
P h o to n E n e rg y (e V ) verywell. Wenotethatascomparedtoourexperimental
spectrum the green line has been multiplied by a factor
FIG. 3: (color online) RSXD spectra of the (001) peak from 500; more than 99 percent of the intensity of the diffrac-
2
magnetitethinfilmandbulkcrystalat(a)FeL -edgesand tionspectrumistakenawaybytheabsorbingdeadlayer.
2,3
(b) O K-edge using π polarized light. Concerning the Fe L data from Garc´ıa et al.9 we note
2,3
that their (raw) data are closer to ours, although there
are appreciable quantitative differences. It therefore ap-
7 0 0 7 1 0 7 2 0 7 3 0 pears likely that the effect of an absorbing dead layer is
present also in their data, although of a much thinner
B u lk F e O one than in the work of Wilkins et al.8
3 4
its) F e -L 2,3 (0 ,0 ,1 /2 ) p Wenowaddresstheoxygenresonancespectra. Experi-
n R S X D th is w o rk mentallybothinthepapersbyWilkinsetal.8andHuang
rb. u XR AS SX Dth Wis iwlkoinrks etal.6 asingleresonancepeakisobserved,whileourdata
ity (a X"DAeSa dW lailkyienrs" m o d e l sehtoawl.colbeaserlryveaasdadtietliloitneal1l.y3aeVbrohaigdhheruminpeanteragbyo.uHtu4aenVg
s
n
Inte x 5 0 0 h1.i3g-heeVr psahtoetlolinteenoecrcguyr,swahticehneirsgmiesisswinhgerientohueradbastoar.ptTiohne
cross section is high and the filter effect discussed above
for the Fe resonance may suppress this feature. Since no
7 0 0 7 1 0 7 2 0 7 3 0
absorptiondataforenergyreferencearegivenbyWilkins
P h o to n E n e rg y (e V ) et al.8 we focus on those from Huang et al.,6. In Fig. 5
(a) we reproduce the O-K RSXD data from Huang et
FIG. 4: (color online) Fe L -edges RSXD spectra of the
2,3 al.6. Again, we aligned the energy scales using the O-K
(001) peak and XAS spectra taken from our magnetite bulk
2 XAS spectra (thin/dotted lines). Since our experiment
crystal (red) and from Wilkins et al.,8 (black). The green
was performed with higher energy resolution, we broad-
thick line is the result of a simulation multiplied by a fac-
ened our experimental XAS data slightly to obtain the
tor 500 (see text). The XAS spectra are included as energy
reference. same energy resolution as in the experiment of Huang et
al.6. On such a calibrated energy scale we find the res-
onance peak at a by 230 meV higher photon energy, i.e.
data. InFig.4wepresentourdataandthosereproduced much closer to the absorption maximum than Huang et
fromthepaperofWilkinset al.8. Theenergyscaleswere al. did.
aligned using the XAS data to account for small energy- We have carried out the same simulation as in the Fe
scale offsets between different soft x-ray monochroma- L -edgesanalysisaboveforOK-resonanceasshownin
2,3
tors. TheenergyscalegivenatthetopofFig.4refersto Fig. 5 (a). The triangle symbols are the experimental
the one used by Wilkins et al.8, and the bottom scale is data from Huang et al.6 and the green thick solid line is
the one of our experiment. It was claimed by Wilkins et thesimulationresult. Theresultingspectrumreproduces
al. that their data were strongly distorted by absorption the main peak position and shape, and also contains the
effects,whichsuppressedallscatteredintensitywhenthe weak and broad hump at 4 eV above the main peak, i.e.
absorption increases. However, this cannot be the case astructurewhichisnotpresentintherealspectrumand
4
how much intensity of the diffraction spectrum is taken
5 2 7 5 2 9 5 3 1 5 3 3 5 3 5
away by the absorbing dead layer: more than 95 percent
(a ) ofthesignalisgone. TheshapeofthespectrumofHuang
etal.6 iscompletelydestroyed,the1.3-eVsatelliteissup-
B u lk F e O
3 4 pressed, and the 4-eV feature is artificially generated by
O -K (0 ,0 ,1 /2 ) p
the dead surface layer.
Wenotethatassumingaphotonmeanfreepath(1/µ)
) x 2 3
its of about 1300 ˚A (a value proposed by Huang et al.6)
n
. u at the energy between 528 and 531 eV, and considering
rb thedetectiongeometrywithphotonincidenceanddetec-
ity (a (b ) tion angle around 45 degrees, we find a thickness of the
ns R S X D th is w o rk ”dead” surface layer of about a quarter of a micrometer.
te X A S th is w o rk A similar thickness comes out for the data of Wilkins et
In R S X D H u a n g al.8 attheFe-L whenweestimatethephotonmeanfree
X A S H u a n g 3
"D e a d la y e r" m o d e l path at the Fe-L3 maximum based on our XAS data.
In summary, we have recorded RSXD spectra of the
(001)peakatbothFeL -edgesandOK-edgefromin-
2 2,3
vacuocleavedmagnetitesinglecrystals,whichessentially
agreewiththosefrommagnetitethinfilmspublishedear-
5 2 6 5 2 8 5 3 0 5 3 2 5 3 4
P h o to n E n e rg y (e V ) lier. Wefoundthatourspectradifferstronglyfromthose
published by Huang et al.6 and Wilkins et al.8, and to
FIG. 5: (color online) (a) O K-edge RSXD spectra of the lesser extent, from Garc´ıa et al.9 We were able to as-
(001) peak and XAS spectra taken from our magnetite bulk cribe the distortions in their spectra to extrinsic effects,
2
crystal (red) and from Ref. 6 (black). The green thick line is namely the presence of a dead surface layer. Both our
a simulated result (see text). The XAS spectra are included bulk and thin film data can hence be used for a reliable
as energy reference. (b) Red line and symbols is our RSXD modeling of the charge and orbital ordering phenomena
spectrum,andgreenthicklineisthesamesimulatedresultas in magnetite.
in (a) but now both on the same vertical scale, showing that
morethan95percentofsignalistakenawaybytheabsorbing We acknowledge BESSY for excellent working condi-
layer. tions and Eugen Weschke for the making his soft x-ray
diffractometer available for the experiment. We thank
Lucie Hamdan and the mechanical workshop of the II.
which is artificially generated by the local minimum in Physikalische Institut for their skillful technical assis-
the absorption at that photon energy. In panel (b) we tance. The research in Cologne is supported by the
plot our original spectrum (red line and symbols) and Deutsche Forschungsgemeinschaft through SFB 608 and
theonegeneratedbyassuminganabsorbinglayer(green by the BMBF through contract 05KS7PK1; work at
solid line) on the same vertical scale. One can also see BESSY by the BMBF through contract 05ES3XBA/5.
1 E. J. W. Verwey, Nature (London) 144, 327 (1939). V. A. M. Brabers, Phys. Rev. B 79, 201102(R) (2009).
2 J.P.Wright,J.P.Attfield,andP.G.Radaelli,Phys.Rev. 9 J. Garc´ıa, G. Sub´ıas, J. Herrero-Mart´ın, J. Blasco,
Lett. 87, 266401 (2001). V. Cuartero, M. C. Sa´nchez, C. Mazzoli, and F. Yakhou,
3 J.P.Wright,J.P.Attfield,andP.G.Radaelli,Phys.Rev. Phys. Rev. Lett. 102, 176405 (2009).
B 66, 214422 (2002). 10 J. Als-Nielsen and D. McMorrow, Elements of Modern X-
4 I. Leonov, A. N. Yaresko, V. N. Antonov, M. A. Korotin, ray Physics (Wiley, New York, 2001).
and V. I. Anisimov, Phys. Rev. Lett. 93, 146404 (2004). 11 P. Abbamonte, private communication: For a single res-
5 H.-T.Jeng,G.Y.Guo,andD.J.Huang,Phys.Rev.Lett. onance the scattered intensity I = |f(cid:48)+if(cid:48)(cid:48)|2 at the res-
93, 156403 (2004). onance maximum is proportional to µ2, because the real
6 D. J. Huang, H.-J. Lin, J. Okamoto, K. S. Chao, H.-T. partofthescatteringamplitude,f(cid:48)iszeroattheresonance
Jeng, G. Y. Guo, C.-H. Hsu, C.-M. Huang, D. C. Ling, maximum and f(cid:48)(cid:48) ∝ µ. The absorption effect, however, is
W. B. Wu, et al., Phys. Rev. Lett. 96, 096401 (2006). linear in µ, which means that the observed intensity will
7 J.Schlappa,C.Schu¨ßler-Langeheine,C.F.Chang,H.Ott, still be finite and proportional to µ. While the actually
A. Tanaka, Z. Hu, M. W. Haverkort, E. Schierle, probed linear combination of scattering amplitudes may
E.Weschke,G.Kaindl,etal.,Phys.Rev.Lett.100,026406 weaken this simple argument, it is still very unlikely that
(2008). absorptioncanreducethescatteredintensitytozerofora
8 S. B. Wilkins, S. Di Matteo, T. A. W. Beale, Y. Joly, wide range of photon energies.
C. Mazzoli, P. D. Hatton, P. Bencok, F. Yakhou, and
