letters to nature................................................................. considered in the spin-1/2 Kondo problem, the spin triplet consists
Kondo effect in an integer-spin
quantum dot

S. Sasaki*, S. De Franceschi², J. M. Elzerman², W. G. van der Wiel²,
M. Eto²³, S. Tarucha*§ & L. P. Kouwenhoven²* NTT Basic Research Laboratories, Atsugi-shi, Kanagawa 243-0129, Japan² Department of Applied Physics, DIMES, and ERATO Mesoscopic Correlation
Project, Delft University of Technology, PO Box 5046, 2600 GA Delft,
The Netherlands³ Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku,
Yokohama 223-8522, Japan§ ERATO Mesoscopic Correlation Project, University of Tokyo, Bunkyo-ku,
Tokyo 113-0033, Japan..............................................................................................................................................

The Kondo effectÐa many-body phenomenon in condensedmatter physics involving the interaction between a localized
spin and free electronsÐwas discovered in metals containing
small amounts of magnetic impurities, although it is now recognized to be of fundamental importance in a wide class ofcorrelated electron systems1,2. In fabricated structures, the controlof single, localized spins is of technological relevance for nanoscale electronics3,4. Experiments have already demonstrated arti®cial realizations of isolated magnetic impurities at metallic
surfaces5,6, nanoscale magnets7, controlled transitions between
two-electron singlet and triplet states8, and a tunable Kondo effectin semiconductor quantum dots9±12. Here we report an unexpected Kondo effect in a few-electron quantum dot containing
singlet and triplet spin states, whose energy difference can betuned with a magnetic ®eld. We observe the effect for an evennumber of electrons, when the singlet and triplet states aredegenerate. The characteristic energy scale is much larger thanin the ordinary spin-1/2 case.
Quantum dots are small electronic devices13, which con®ne awell-de®ned number of electrons, N. The total spin is zero or an
integer for even N, and half-integer for odd N. The latter case is the
canonical example of the Kondo effect14,15 when all electrons can beignored, except for the one with the highest energy; that is, the caseof a single, isolated spin, S = 1/2 (Fig. 1a). Although the energy levelof the electron eo is well below the Fermi energies of the two leads,
Heisenberg uncertainty allows the electron on the dot to tunnel toone of the leads whereupon it is replaced quickly by anotherelectron. The timescale for such a co-tunnelling process16 is,~/U, where h = 2p~ is Planck's constant and U is the on-site
Coulomb energy. Figure 1a illustrates that particle exchange by cotunnelling can effectively ¯ip the spin on the dot. At low temperature, the coherent superposition of all possible co-tunnelling
processes involving spin ¯ip can result in a time-averaged spinequal to zero. The whole systemÐthat is, quantum dot plus
electrodesÐforms a spin singlet. The energy scale for this singlet
state is the Kondo temperature, TK. In terms of density of states, anarrow peak with a width ,kBTK develops at the Fermi energy (kB is
Boltzmann's constant). Note that for even N and S = 0, cotunnelling gives rise to a lifetime broadening of the con®ned state,
without producing any Kondo resonance. Such even/odd behaviour
corresponding to no-Kondo/Kondo has been observed in recent
experiments9,10.
It is also possible that a quantum dot with even N has a total spin
S = 1; for example, when the last two electrons have parallel spins. If
the remaining N - 2 electrons can be ignored, this corresponds to a
triplet state. Parallel spin ®lling is a consequence of Hund's ruleoccurring when the gain in exchange energy exceeds the spacing
between single-particle states8. The spin of the triplet state can also
be screened by co-tunnelling events. These are illustrated in thecentre-left side of Fig. 1b. In contrast to single-particle states that are764

of three degenerate two-particle states. Co-tunnelling exchanges
only one of the two electrons with an electron from the leads. The
total spin of the many-body Kondo state depends on how many
modes in the leads couple effectively to the dot17,18. If there is only
one mode, the screening is not complete and the whole system does
not reach a singlet state. In this case the Kondo effect is called``underscreened''. Calculations show that also for S = 1 a narrow
Kondo resonance arises at the Fermi energy, but the corresponding
TK is typically lower than in the case of S  12 (refs 19, 20). Someexperiments have reported the absence of even/odd behaviour21,22,
which may be related to the formation of higher spin states.
Here we investigate a quantum dot with even N, where the last
two electrons occupy a degenerate state consisting of a spin singlet
and a spin triplet. Figure 1b illustrates the different co-tunnelling
processes occurring in this special circumstance. Starting from
|S = 1, Sz = 1i, where Sz is the z-component of the total spin on thedot, co-tunnelling via a virtual state |1/2,1/2i can lead either to thetriplet state |1,0i or to the singlet state j0,0i. Via a second cotunnelling event, the state |1, -1i can be reached. As for the S = 1
case, the local spin can ¯uctuate by co-tunnelling events. By
a

ΓL
•

ΓR
•

U

•

•

• ε0
1
|S,Sz〉 = | , + 1 〉2 2•
1| ,– 1 〉
2 2

b
•

••

•

•
•

•

••

•

•

•

|1,+1〉
•

•
•

|1,0〉

|0,0〉

•

•

••

|1,–1〉

••

•
•

•

•
•

•

•

••

•
•

Figure 1 Spin-¯ip processes leading to ordinary and singlet±triplet Kondo effect in aquantum dot. a, Co-tunnelling event in a spin-1/2 quantum dot for odd N. Only thehighest-energy electron is shown, occupying a single spin-degenerate level, eo. (The caseof two, or more, closely spaced levels has also been considered theoretically within thecontext of the spin-1/2 Kondo effect30.) The green panels refer to S z = 1/2 and -1/2
ground states, which are coupled by a co-tunnelling event. The two tunnel barriers havetunnelling rates ¡ R and ¡ L. In the Coulomb blockade regime (|eo| , U ), adding or
subtracting an electron from the dot implies an energy cost ,U. Hence the intermediatestep (orange panel) is a high-energy, virtual state. The spin-¯ip event depicted here isrepresentative of a large number of higher-order processes which add up coherently suchthat the local spin is screened. This Kondo effect leads to an enhanced linear-response
conductance at temperatures T ( T K . b, Co-tunnelling in an integer-spin quantum dot
for even N at a singlet±triplet degeneracy. Two electrons can share the same orbital with
opposite spins (singlet state in the blue panel) or occupy two distinct orbitals in one of thethree spin-triplet con®gurations (green panels). The different spin states are coupled byvirtual states (orange panels). As in the spin-1/2 case, spin-¯ip events can screen thelocal magnetic moment. Note that an S = 1 Kondo effect only involves |1,+1i, |1,0i and|1, -1i.

© 2000 Macmillan Magazines Ltd

NATURE | VOL 405 | 15 JUNE 2000 | www.nature.com

letters to nature
coupling to all triplet states, the singlet state enhances the spin
exchange interaction between the dot and the leads, resulting in ahigher rate for spin ¯uctuations. This particular situation yields astrong Kondo effect, which is characterized by an enhanced TK. This
type of Kondo effect has not been considered before, probably
because a singlet±triplet degeneracy does not occur in magnetic
elements. Recent scaling calculations by Eto and Nazarov indeed
indicate a strong enhancement of TK at the singlet±triplet
degeneracy23; these workers also argue23 that the total spin of the
many-body Kondo state behaves as in the case of S = 1.
Our quantum dot has the external shape of a rectangular pillar(Fig. 2a, b) and an internal con®nement potential close to a twodimensional ellipse24. The tunnel barriers between the quantum dot
and the source and drain electrodes are thinner than in our previous
devices8,24 such that co-tunnelling processes are enhanced. Figure 2dshows the linear response conductance (d.c. bias voltage Vsd = 0)versus gate voltage, Vg, and magnetic ®eld, B. Regions shown dark
blue have low conductance, and correspond to the regimes of
Coulomb blockade for N = 3 to 10. In contrast to previous
experiments9±12 on the Kondo effect, all performed on lateral

10
9
8

–0.4

SOURCE7c

N =6Energy∆↑ ↑B0Gate voltage (V)

b

1/2
6

S=0

S=1
1/2

5
0.75

0

4

↑↓
↑↓
↑↓

–1.2

S=1/2

dl/dVsd (e 2/h)Vgd
Vsd –0.2

DRAIN

N=3

–0.2

0.2

Figure 2 Sample description, energy spectrum and magnetic-®eld evolution of theground state. a, Cross-section of our rectangular quantum dot. The semiconductormaterial consists of an undoped AlGaAs(7 nm)/InGaAs(12 nm)/AlGaAs(7 nm) double
barrier structure sandwiched between n-doped GaAs source and drain electrodes. A gateelectrode surrounds the pillar and is used to control the electrostatic con®nement in thequantum dot. A d.c. bias voltage, Vsd, is applied between source and drain, and current, I,¯ows vertically through the pillar. In addition to Vsd, we apply a modulation with r.m.s.
amplitude Vac = 3 mV at 17.7 Hz for lock-in detection. The gate voltage, Vg, can change
the number of con®ned electrons, N, one-by-one from ,10 at Vg = 0 to 0 at Vg = -1.8 V.
A magnetic ®eld, B, is applied along the vertical axis. Temperature, T, is varied between
14 mK and 1 K. Our lowest effective electron temperature is 25 6 5 mK. b, Scanningelectron micrograph of a quantum dot with dimensions 0.45 ´ 0.6 mm2 and height of,0.5 mm. c, Schematic energy spectrum. Solid lines represent the B-evolution of the ®rst
four orbital levels in a single-particle model. The dashed line is obtained by subtracting thetwo-electron exchange coupling from the fourth level. At the crossing between thisdashed line and the third orbital level at B = B0 the ground state for N = 6 undergoes a
triplet-to-singlet transition. B0 < 0.22 T with a slight dependence on Vg. We de®ne ¢ as
the energy difference between the triplet and the singlet states. d, Colour-scale
representation of the linear conductance versus Vg and B. Red stripes denote conductancepeaks of height ,e 2/h. Blue regions of low conductance indicate Coulomb blockade. The
Vg-position of the stripes re¯ects the ground-state evolution with B, for N = 3 to 10. The
N = 6 ground state undergoes a triplet-to-singlet transition at B0 < 0.22 T, which results
in a conductance anomaly inside the corresponding Coulomb gap.

0.75

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Magnetic field (T)Concuctance (e 2/h)

0

0

0

N=7

0
–0.2

0.2

N=6

N=5

1.0

N=7

0.5
T

–1.4
0.9

Magnetic field

0.25 0.25

N=5

N=6

a
–0.5

0
0.5
Bias voltage (mV)Concuctance (e 2/h)Iaquantum dots with unknown electron number, here the numberof con®ned electrons is precisely known. Red stripes in Fig 2d
represent Coulomb peaks as high as ,e2/h. The B-dependence of the®rst two lower stripes re¯ects the ground-state evolution for N = 3
and 4. Their similar B-evolution indicates that the third and fourthelectron occupy the same orbital state with opposite spin, which isobserved also for N = 1 and 2 (not shown). This is not the case for N= 5 and 6. The N = 5 state has S = 1/2, and the corresponding stripe
shows a smooth evolution with B. Instead, the stripe for N = 6 has akink at B < 0.22 T. From earlier analyses24 and from measurementsof the excitation spectrum at ®nite Vsd (discussed below), we canidentify this kink with a transition in the ground state from a spin
triplet to a spin singlet. At the triplet±singlet transition (at B = B0 in
Fig. 2c) we observe a strong enhancement of the conductance. In
fact, over a narrow range around 0.22 T, the Coulomb gap for N = 6
disappears completely.
To explore this conductance anomaly, we show in Fig. 3a
differential conductance measurements, dI/dVsd versus Vsd,
taken at B = B0 and Vg corresponding to the dotted line in Fig. 2d.
At temperature T = 14 mK, the narrow resonance around zero
bias has a full-width at half-maximum, FWHM, of ,30 mV.
This is several times smaller than the lifetime broadening,¡  ¡ R  ¡ L < 150 mV, estimated from the FWHM of the
Coulomb peaks. The height of the zero-bias resonance decreases
logarithmically with T (Fig. 3b). These are typical `®ngerprints' of
the Kondo effect. From FWHM < kBTK, we estimate TK < 350 mK.
We note that we can safely neglect the Zeeman spin splitting because
gmBB0 < 5 mV p kBTK, implying that the spin triplet is in fact threefold degenerate at B = B0. This condition is essential to the Kondo
effect illustrated in Fig. 1b. Alternative schemes have recently been
proposed for a Kondo effect where the degeneracy of the triplet stateis lifted by a large magnetic ®eld25,26.
For N = 6, we ®nd markedly anomalous T-dependence only at the

0.0
1.0

0.5
T

0.0
1.0

0.5
T

b

0.1 1
10

c
102
Temperature (mK)

103

0.0

–0.8

–0.7
Gate voltage (V)–0.6

Figure 3 Zero-bias resonance and T-dependence of the conductance at the singlet±
triplet degeneracy. a, Kondo resonance at the singlet±triplet transition. The dI/dVsd versus
Vsd curves are taken at Vg = -0.72 V, B = 0.21 T and for T = 14, 65, 100, 200, 350, 520
and 810 mK. Insets to a: Kondo resonances for N = 5 (left inset) and N = 7 (right inset),measured at Vg = -0.835 V and Vg = -0.625 V, respectively, and for B = 0.11 T and
T = 14 mK. b, Peak height of zero-bias Kondo resonance versus T as obtained from a(®lled diamonds). The line demonstrates a logarithmic T-dependence, which ischaracteristic of the Kondo effect. The saturation at low T is probably due to electronicnoise. c, T-dependence of the linear conductance versus Vg for B = 0.12 T (spin-triplet
ground state), B = 0.22 T (singlet±triplet degeneracy), and B = 0.32 T (spin-singlet
ground state). Each panel shows 7 traces at T = 20 (dot-dashed line), 35, 70, 120, 260,490 (solid lines) and 1,050 (dashed line) mK. The arrows emphasize the temperaturedependence in the valley for N = 6.

© 2000 Macmillan Magazines Ltd

765

letters to naturesinglet±triplet degeneracy. Figure 3c shows the conductance versus
Vg for different T. The upper panel shows data for B = 0.12 T. The
two Coulomb peaks correspond to the transition from N = 5 to 6
and from N = 6 to 7. The small, short-period modulations superimposed on the Coulomb peaks are due to a weak charging effect in
the upper part of the GaAs pillar above the dot27. We will ignore this®ne structure and focus on the general T-dependence. Upon
increasing T, the valley conductance for N = 6 goes up due tothermally activated transport. A similar behaviour is seen in thelower graph for B = 0.32 T. In contrast, at the singlet±triplet
transition for B = 0.22 T we ®nd an opposite T-dependence, again
indicating the formation of a Kondo resonance. At the lowest T, thevalley conductance is as high as 0.7e2/h, which is close to the heightof the Coulomb peaks.
The T-dependence for N = 5 and 7 is visibly different from that in
the non-Kondo valley for N = 6 (lower panel of Fig. 3c). Such a
difference is a manifestation of the ordinary spin-1/2 Kondo effectexpected for odd N. Indeed the corresponding zero-bias resonances
are clearly observed (see insets to Fig. 3a). Their height, however, ismuch smaller than for the singlet±triplet Kondo effect. There is also
some indication for a triplet Kondo effect in the T-dependence for N= 6 at B = 0.12 T, although the associated zero-bias anomaly is not asapparent.
We now investigate the effect of lifting the singlet±triplet degeneracy by changing B at a ®xed Vg corresponding to the dotted line in
Fig. 2d. Near the edges of this line, that is, away from B0, theCoulomb gap is well developed, as denoted by the dark colours in
Fig. 2d. The dI/dVsd versus Vsd traces still exhibit anomalies,
however, now at ®nite Vsd (see Fig. 4a). For B = 0.21 T we observe3b

Vsd (mV)

0.2

0.11 T–0.2
0.1

0.21 T2–0.7

Magnetic field (T)0.4

Magnetic field (T)

0.9

c

–0.9
0.1

1

d
0.39 T
0
–0.3

0
0.3
Bias voltage (mV)

Figure 4 Singlet±triplet energy separation tuned by a magnetic ®eld. a, dI/ dVsd versus Vsd
characteristics taken along the dotted line in Fig. 2d (Vg = -0.72 V) at equally spaced
magnetic ®elds B = 0.11,0.13,...,0.39 T. Curves are offset by 0.25 e 2/h. b, Extracted
peak positions from dI/dVsd curves in a versus B. Each symbol refers to a gate
voltage taken between ±0.72 and ±0.70 V. c, Colour-scale plot of dI/ dVsd measured at
Vsd = 0.67 mV as a function of B and Vg. The solid line identi®es the ground state, whereas
the dashed line indicates the ®rst excited state8 for N = 6. From their difference we extract
the singlet±triplet energy splitting, ¢(B ), using a proportionality factor a = 6.7 meV V-1 toconvert gate voltage into energy. The two solid lines in b represent 6¢(B ) with ahorizontal shift of 0.08 T to compensate for the shift of the singlet±triplet transition to ahigher magnetic ®eld in a high-bias measurement. d, Energy diagrams for two different
transport regimes, both with eVsd = ¢. Left: both ground and excited states lie between
the two Fermi energies, so two channels are available for direct tunnelling. The excitation
spectrum in c is measured in this regime. Right: both ground and excited states lie below
the Fermi levels of the leads (Coulomb blockade regime). Inelastic co-tunnelling is
illustrated, where one electron tunnels out of the lower-energy state and another tunnels
into the higher-energy state.
766

Received 3 February; accepted 28 April 2000.
1.
2.
3.
4.

Vg (V)

Differential conductance (e 2/h)athe singlet±triplet Kondo resonance at Vsd = 0. At higher B, thisresonance splits apart showing two peaks at ®nite Vsd. It is
important to note that these peaks occur inside the Coulomb gap.
They result from ``inelastic'' co-tunnelling events16,28, where``inelastic'' refers to energy exchanging between quantum dot andelectrodes (see right drawing in Fig. 4d). The upper traces in Fig. 4a,for B , 0.21 T, also show peak structures, although less pronounced.
In Fig. 4b we plot the positions of the dI/dVsd peaks in the plane of
Vsd and B. The different symbols refer to different gate voltages, andit can be seen that these positions do not depend on Vg. The solidlines are obtained from the excitation spectrum measured (seeFig. 4c) in direct tunnelling (see left-hand drawing in Fig. 4d).
They represent the measured B-dependence of the singlet±triplet
energy difference, ¢. The fact that these independent measurements coincide implies that inelastic co-tunnelling occurs wheneVsd = 6¢. Note that this condition is independent of Vg, consistent
with our observations. We believe that for small ¢ ( ( kBTK), thesplit resonance re¯ects the singlet±triplet Kondo anomaly shifted to®nite bias. This resembles the splitting of the Kondo resonance by
the Zeeman effect9,10,29, although on a very different B-scale. In thepresent case, the splitting occurs between two different multiparticle states and originates from the B-dependence of the orbital
motion. For increasing ¢, the shift to larger Vsd induces spindecoherence processes, which broaden and suppress the ®nite-bias
peaks29. For B < 0.39 T the peaks have evolved into steps28, which
may indicate that the spin-coherence associated with the Kondo
effect has completely vanished.
M

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letters to nature

Acknowledgements
We thank Yu. V. Nazarov, K. Maijala, S. M. Cronenwett, J. E. Mooij and Y. Tokura for
discussions. We acknowledge ®nancial support from the Specially Promoted Research,
Grant-in-Aid for Scienti®c Research, from the Ministry of Education, Science and Culture
in Japan, from the Dutch Organisation for Fundamental Research on Matter (FOM), fromthe NEDO joint research program, and from the EU via a TMR network.
Correspondence and requests for materials should be addressed to S.D.F.
(e-mail: silvano@qt.tn.tudelft.nl).

.................................................................
Direct observation of the alignmentof ferromagnetic spinsby antiferromagnetic spins

F. Nolting*, A. Scholl*, J. StoÈhr², J. W. Seo³§, J. Fompeyrine§,
H. Siegwart§, J.-P. Locquet§, S. Anders*, J. LuÈning², E. E. Fullerton²,
M. F. Toney², M. R. Scheinfeink & H. A. Padmore** Advanced Light Source, 1 Cyclotron Road, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, USA² IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose,
California 95120, USA³ Institute de Physique, University of NeuchaÃtel, CH-2000 NeuchaÃtel, Switzerland§ IBM Research Division, ZuÈrich Research Laboratory, CH-8803 RuÈschlikon,
Switzerlandk Department of Physics and Astronomy, Arizona State University, Tempe,
Arizona 85287-1504, USA

and conventional transmission electron microscopy (TEM) analysis
show that the epitaxial LaFeO3 ®lm consists of two microscopic
crystallographic domains characterized by orientations of the
LaFeO3 c-axis along the [100] and [010] directions in the SrTiO3
surface plane8. The Co ®lm, grown in the form of a stepped wedge,
was deposited in situ at room temperature and capped with a 1-nm
Pt layer to prevent its oxidation. X-ray diffraction analysis of asample with a Co thickness of 2.5 nm (and a 1-nm Pt cap layer)
revealed a polycrystalline Co structure. Kerr measurements showedthat the easy magnetization axis of the sample was in-plane withuniaxial symmetry about the surface normal. All measurements
reported here were performed on as-grown samples. Because thesamples were not set in a magnetic ®eld they did not exhibit amacroscopic exchange bias4,5. (For LaFeO3, chemical decomposition prevents the use of setting temperatures close to the NeÂel
temperature (740 K) to create large exchange bias. However, lowtemperature (390 K) annealing of Co/LaFeO3 in a 500-Oe applied®eld is suf®cient to produce a macroscopic bias of 0.007 erg cm-2 atroom temperature and 0.1 erg cm-2 at 4.2 K). Our ability to probe
the spatially resolved magnetic con®guration allowed us to observe
local bias effects, which average to zero macroscopically.
Spectro-microscopy studies were carried out using the PEEM2
facility at the Advanced Light Source in Berkeley9. The focused Xrays, whose polarization could be changed from linear to right orleft circular10, are incident on the sample at an angle of 308 from thesurface and form a 30-mm spot. The low-energy secondary photoelectrons from the sample are imaged by an all-electrostatic photoemission electron microscope (PEEM) with magni®cation onto aphosphor screen that is read by charge-coupled device (CCD)
camera. The spatial resolution of PEEM2 is limited by chromaticaberrations to 20 nm. For imaging we exploited several uniquespectroscopic capabilities associated with the variable energy andpolarization of the X-rays10. By tuning the photon energy to either
the Fe L-edge, near 710 eV, or the Co L-edge, near 780 eV, we canrecord separate images of the antiferromagnetic (AFM) LaFeO3
layer and the ferromagnetic (FM) Co layer. We use linear X-ray..............................................................................................................................................

NATURE | VOL 405 | 15 JUNE 2000 | www.nature.com

b Co layer

a LaFeO3 layer

2 µm
Normalized intensity (a.u.)

The arrangement of spins at interfaces in a layered magnetic
material often has an important effect on the properties of thematerial. One example of this is the directional coupling between
the spins in an antiferromagnet and those in an adjacent ferromagnet, an effect ®rst discovered1 in 1956 and referred to as
exchange bias. Because of its technological importance for thedevelopment of advanced devices such as magnetic read heads2
and magnetic memory cells3, this phenomenon has received muchattention4,5. Despite extensive studies, however, exchange bias isstill poorly understood, largely due to the lack of techniques
capable of providing detailed information about the arrangementof magnetic moments near interfaces. Here we present polarization-dependent X-ray magnetic dichroism spectro-microscopythat reveals the micromagnetic structure on both sides of aferromagnetic±antiferromagnetic interface. Images of thin ferromagnetic Co ®lms grown on antiferromagnetic LaFeO3 show adirect link between the arrangement of spins in each material.
Remanent hysteresis loops, recorded for individual ferromagnetic
domains, show a local exchange bias. Our results imply that thealignment of the ferromagnetic spins is determined, domain bydomain, by the spin directions in the underlying antiferromagnetic layer.
We investigated a thin Co ®lm on top of a 40 nm LaFeO3 ®lmgrown on SrTiO3(001). The sample was prepared in a molecularbeam epitaxy system with the LaFeO3 ®lm grown using a block-byblock growth method6 at 750 8C under a beam of atomic oxygen anda partial O2 pressure of 5 3 10 2 6 Torr. This method has been shownto yield high-quality epitaxial ®lms7. Plan-view electron-diffraction

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28. Funabashi, Y., Ohtsubo, K., Eto, M. & Kawamura, K. Phase relaxation and non-equilibrium transport
properties through multilevel quantum dot. Jpn J. Appl. Phys. 38, 388±391 (1999).
29. Wingreen, N. S. & Meir, Y. Anderson model out of equilibrium: Noncrossing-approximation
approach to transport through a quantum dot. Phys. Rev. B 49, 11040±11052 (1994).
30. Inoshita, T., Shimizu, A., Kuramoto, Y. & Sakaki, H. Correlated electron transport through a quantum
dot: The multiple-level effect. Phys. Rev. B 48, 14725±14728 (1993).

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Photon energy (eV)Figure 1 Images and local spectra from the antiferromagnetic and ferromagnetic layers
for 1.2-nm Co on LaFeO3/SrTiO3(001). a, Fe L-edge XMLD image; b, Co L-edge XMCD
image. The contrast in the images arises from antiferromagnetic domains in LaFeO3 (a)and ferromagnetic domains in Co (b) with in-plane orientations of the antiferromagnetic
axis and ferromagnetic spins as indicated below the images. The spectra shown
underneath were recorded in the indicated areas and illustrate the origin of the intensity
contrast in the PEEM images.

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