Supplementary Online Material
Further structural characterization of the samples
The samples on which this manuscript is based were investigated in detail by X-ray
diffractometry (XRD), atomic force microscopy (AFM), transmission electron
microscopy (TEM), high resolution transmission electron microscopy (HRTEM) and
high angle annular dark field scanning transmission electron microscopy (HAADFSTEM).
AFM investigations performed at randomly chosen sites of the samples and in several
such spots indicated that the layers of the superlattices, although not monitored by
RHEED during growth, were grown in the step flow growth regime which assures their
pseudomorphic growth and single crystalline-like quality. We comment here that
RHEED monitoring is not required for growing high quality superlattices in the step flow
growth regime. It is by now a well established fact that the RHEED oscillations
characteristic for layer-by-layer growth are not present when step flow growth takes place
(see for instance G. Rijnders et al., Appl. Phys. Lett. 84, 505, (2004)). A typical example
is shown in Fig. 1(a) which is an AFM micrograph (6 m  6 m) taken on the top
surface of the 1.6/5 nm SL. For comparison, in Fig. 1(b) we show the image of an AFM
micrograph (4 m  4 m area) taken on the top surface of a LSMO/SRO bilayer, whose
two layers were also grown in the step flow growth regime without RHEED monitoring.
These are much larger areas than what the STEM investigations summarized briefly in
Fig. 1 of the manuscript allow for and give us confidence that such STEM pictures taken
randomly are typical for the entire surface of the SLs.
Figure 1. Typical AFM micrographs taken on the top surface of (a) a 1.6/5 nm SL and of (b) a LSMO/SRO
bilayer.
Figure 2. Cross section HAADF-STEM micrographs of the (a) SL 1.6/3.0 and (b) SL 1.6/5.0.
Figure 3. Upper panel: Z-STEM micrograph of sample SL1.6/5.0 showing the interfaces between a 1.6 nm
LSMO layer and two adjacent 5 nm thin SRO layers. Lower panel: Intensity scan along the line indicated in
the upper panel. The monotonic dependence of intensity on atomic number allows for the identification of
the chemical elements.
Concerning the non-equivalent interfaces between LSMO and SRO, it is a known fact
that SrRuO3 layers grown by PLD on TiO2-terminated SrTiO3 (such as we employed for
the growth of our SLs) terminate always with SrO, due to the high volatility of RuO2 at
the high temperature (i.e. 650°C) (see Appl. Phys. Lett. 84, 505, (2004)). Thus, in the
growth direction (i.e. from the right to left in the STEM micrograph shown in Fig 1), the
SRO layers terminate as SrO and this forces the adjacent next LSMO to start growing
with MnO2 surfaces. The same applies for the LSMO layers: MnO2 is more volatile than
LaO and thus the LSMO layers will terminate with LaO. It usually takes at least 45-60
seconds from the end of the growth of one layer and the start of the growth of the next
one, long enough for this termination conversion to occur at elevated temperatures at
which the growth takes place (see Appl. Phys. Lett. 84, 505, (2004)).
In Fig. 2 we show additional HAADF-STEM micrographs taken on the SL 1.6/5.0 and on
the SL 1.6/3.0.
In Fig. 3 we show another Z-STEM image of sample SL1.6/5.0 with the corresponding
intensity scan along the line indicated in the upper panel of Fig. 3. This image shows the
symmetry between the two interfaces much more clearly. Moreover, one should have in
mind that the electron beam probes atom columns with a finite number of atoms, as the
TEM specimen has a finite thickness and is not perfectly flat. The columns are made of a
random mixture of La and Sr in the case of the A-site columns of the LSMO layers and
not only La atoms, which makes slight intensity variations expectable from one La/Sr
column to the next. Such slight intensity variations are always seen by STEM, see for
instance the papers by D. A. Mueller et al., Science 319, 1073 (2008) and L. Fitting
Kourkoutis et al., Appl. Phys. Lett. 91, 163101 (2007).
Figure 4. Cross section TEM micrographs of the (a) 1.6/5 nm SL, (b) 1.6/8 nm SL and (c) the
LSMO/STO/SRO/STO SL.
Supplementary conventional TEM investigations allowed us to image at lower
magnification and get overview cross section TEM micrographs of the Sls. In Fig. 4(a)
the TEM micrograph of the 1.6/5 nm SL is shown, the inset being a selected area electron
diffraction (SAED) pattern of the SL, showing satellite reflections around the main
reflections, indicating sharp coherent LSMO/SRO interfaces. In Fig. 4(b) the cross
section TEM micrograph of the 1.6/8 SL is shown and Fig. 4(c) shows the cross section
TEM micrograph of a LSMO/STO/SRO/STO SL with 10 repeat units.
XRD  -2 spectra of LSMO /SRO SLs
1.6 / 3 nm
1.6 / 5 nm
1.6 /8 nm
1000000
Intensity [a.u]
100000
10000
1000
100
15
20
25
30
35
40
45
50
55
2 [deg]
Figure 5. XRD (-2) scans of the LSMO/SRO SLs around the STO(100) and STO(200) substrate
reflections.
The -2 XRD graphs of the LSMO/SRO SLs with three different periodicities to which
we refer in the manuscript are given in Fig 5. All the SLs showed satellite reflections
around the main STO (100) and STO (200) reflections of the STO substrate, arising from
the periodicity of the LSMO/SRO repeat units.
Comparison sample: superlattice [LSMO/STO/SRO/STO]10
In order to unravel the origin of the strong interlayer coupling exhibited by our
LSMO/SRO SLs we fabricated SLs in which STO layers of 1 nm or 2 nm thickness were
introduced in between each adjacent LSMO and SRO, so that LSMO and SRO do not
have intimate interfaces. The cross section TEM micrograph of a SLs with 4 unit cell
thick STO spacers is shown in the Fig. 6(a) and a zoom in of the microstructure was
allowed by HAADF-STEM imaging (Fig. 6(b)). The EDX investigations (Fig. 6(b))
demonstrated that the STO layers prevented not only the intimate interfacing of LSMO
and SRO layers, but also the diffusion of Ru inside the LSMO layers.
LSMO
SrRuO3
SrRuO3
SrTiO3
Ti
SrTiO3
Mn
Ti
Ru
(a)
2 nm
(b)
Figure 6. (a) Cross section TEM micrograph of a LSMO/STO/SRO/STO SL and (b) a zoom in of the
microstructure of the same SL obtained by HAADF-STEM.
[LSMO/STO/SRO/STO]10
4
µ0H = 0.1 T FC
-4
magnetic moment m (10 emu)
5
in-plane
out-of-plane
3
2
1
0
0
50
100
150
200
250
300
350
Temperature T (K)
Figure 7. Magnetization vs. temperature measured for a LSMO/STO/SRO/STO SL.
The magnetic properties of the SLs with 4 unit cell thick STO spacing layers showed
very different behavior with respect to the LSMO/SRO SLs. Below 140 K the overall
magnetic moment, both in-plane and perpendicular-to-plane, of the SLs continued to
increase with decreasing temperature, indicating that the magnetic moments of the LSMO
and SRO do not orient antiparallel any longer (Fig. 7).
Influence of lattice defects
Possible imperfections at the LSMO/SRO interface were studied in additional
calculations; both defects and lattice relaxation were simulated.
Since Ru or Sr vacancies were not seen in the Z-STEM micrographs we focused on the
investigation of O vacancies which would not be visible in Z-STEM. Vacancy
concentrations up to 10% at both interfaces were treated within the coherent potential
approximation, with an O vacancy described by an empty sphere. The results indicated an
insignificant decrease of the total magnetic moment by -0.04 µB/Mn for 10%
concentration of O vacancies (see Fig. 8). It turned out that the magnetic moments of the
Ru atoms at the interfaces were mostly affected, which could be understood in terms of
the strong coupling of the Ru d states with the O p states. This coupling was decreased
upon the formation of O vacancies, and, as a consequence, the Ru moments were
increased.
Figure 8. Magnetic moments at the SRO/LSMO interfaces with RuO2 (left) and SrO (right) termination.
The local moments are given for 10% concentration of O vacancies (‘vacancies’) and vertical lattice strains
of 10% (‘expansion’ and ‘compression’).
It could not be safely assumed that the ultrathin layers grew with bulk structure. However,
the structural relaxation of such big a unit cell is hardly manageable on an ab initio level
at present. In this respect we had to make an assumption for the structure and motivated
our assumption by the Curie temperatures. Further we inspected effects of lattice
deformation at the interface. We investigated the change of the magnetic moments under
the influence of 10% expansion or 10% compression of the spacing between the LSMO
and SRO subsystems. The magnetic-moment profiles are as well shown in Fig. 8. Note
that the magnetic moments behaved differently for the two interfaces. In case of the
RuO2-terminated interface the total magnetic moment was marginally affected (0.05
µB/Mn). At the SrO-terminated interface, however, it increased (decreased) by 0.25
µB/Mn upon expansion (compression). These findings were related to the change of the
Mn valency due to coupling with Sr.
Non-collinear magnetization states
Concerning the explanation of the anisotropy of the hysteresis loops, we investigated
non-collinear magnetic structures for both the in-plane and the out-of-plane geometry by
means of a relativistic KKR code. By fixing the local magnetic moments in SRO but
rotating all LSMO moments, we addressed the antiferromagnetic structure (SRO and
LSMO moments oriented oppositely), a perpendicular configuration (SRO and LSMO
moments at 90°), and a ferromagnetic configuration (all moments oriented parallel). We
found that the local moments depended negligibly on the relative orientation and on the
orientation with respect to the surface normal. According to the total energy the
antiferromagnetic state was preferred, whereas both the perpendicular and the
ferromagnetic configuration were clearly ruled out at this LSMO/SRO thickness ratio.
However, a canted magnetic configuration in which the moments deviated slightly from
the main orientation (i.e. a few degrees off the easy axis) would require extensive
calculations and, thus, could not be excluded at the moment. Such a magnetic order could
be induced by tetragonal distortions at the interfaces.
A canted magnetic configuration with antiferromagnetic coupling of the in-plane
component and ferromagnetic coupling of the out-of-plane component would explain the
anisotropy of the hysteresis loops, but not the exchange bias effect. At present we are not
able to treat the exchange bias effect within our ab initio calculations. But following the
recommendations of the referee we are working on the understanding of the exchange
bias. We assume that the multilayer probably consists of two exchange-bias systems with
opposite exchange bias, which are related to the interface between multilayer and
substrate and the free surface of the sample. A simulation of hysteresis loops including
exchange constants from our ab initio calculations is computationally difficult and is
beyond the scope of this paper.