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1
Elect
CoF
e
mag
n
Carolin Sc
h
Anne Warl
a
Heiko Wen
1
Fakultät für
P
Duisburg, Ge
Germany.
3
P
r
USA.
4
Inorga
n
Suppleme
n
BTO/CFO
s
Suppleme
n
mosaicity o
f
peak of CF
O
ric in

e
2
O
4
/
B
n
etic
f
h
mitzAnto
n
a
nd
1
, Bern
h
de
1
P
hysik and C
e
rman
y
.
2
Hel
m
r
esent addres
s
n
ic Chemistr
y
n
tary Figure
S
s
urface. The c
o
n
tary Figure
S
f
the sample.
b
O
, respectivel
y

plan
e
B
aTi
O
f
ields
n
iak
1
, Detle
f
h
ard Krum
m
e
nter for Nan
o
m
holtzZentru
m
s:
Departmen
y
and Catalysi
s
S
1

Largear
e
o
ntrast of the
S
2

Xray dif
f
b
d: scans
a
y
.
e
pol
a
O
3
na
n
: Su
p
f
Schmitz
2
,
m
e
1
, Ralf Fe
o
integration D
u
m
Berlin für M
a
t of Physics,
W
s
,
Universiteit
e
a SEM imag
e
image has b
e
f
raction rock
i
a
round the (0
3
a
rizat
n
oco
m
p
plem
Pavel Bori
s
yerherm
2
,
E
u
isbur
g
Esse
n
a
terialen und
E
W
est Virginia
U
Utrecht, Univ
e
e
. Largeare
a
e
en enhanced
i
ng curves.
a
3
1) Bragg pe
a
ion i
n
m
pos
enta
r
s
ov
1,3
, Fran
k
E
sther Dud
z
n
(CENIDE),
U
E
nergie, Albe
r
U
niversity, 1
3
e
rsiteitsweg
9
scanning el
e
afterwards.
: Schematic
m
a
ks for STO,
B
n
mul
t
ite tu
n
r
y inf
o
k
M.F. de
G
z
ik
2
, Wolfg
a
U
niversität Du
i
r
tEinsteinStr
.
3
5 Willey Stre
e
9
9, 3584 CG
U
e
ctron micros
c
m
easurement
B
TO and arou
n
t
iferr
o
n
ed
b
o
rmat
G
root
4
, Sve
n
a
ng Kleem
a
i
sbur
g
Essen,
r.
15, 12489 B
e
e
t, Morganto
w
U
trecht, Nethe
r
c
opy image of
geometry to
o
n
d the (062)
d
o
ic
b
y
i
on
n
Stienen
1
,
a
nn
1
, and
47048
e
rlin,
w
n 26506, WV
r
land
s
the
o
btain twist
d
iffraction
2
Supplemen
incident soft
parallel or p
e
Suppleme
n
a factor of
4
applied.
Suppleme
n
to a magne
t
along the (y
tary Figure
S
xrays. a: No
e
rpendicular t
n
tary Figure
S
4
) of Ti, O, Fe,
n
tary Figure
S
t
ic field applie
d
z) plane.
S
4

Measure
m
rmal incidenc
e
o the wave v
e
S
3

XANES a
n
Co, and Ba
m
S
5 Schemati
c
d
along the y
d
m
ent geometr
e
(
k
= 0). b:
G
e
ctor k of the
x
n
d XLD over
v
m
easured und
e
c
magnetic fi
d
irection is sc
ies for XLD.
T
G
razing incid
e
x
rays.
v
iew spectra.
e
r grazing xr
a
eld induced
d
hematically s
h
T
wo measure
e
nce (
k
= 60°
)
XANES (bla
c
a
y incidence
(
d
eformation
s
h
own for two
c
ment geomet
r
)
. The magne
t
c
k lines) and
X
(
k
= 60°) and
s
. The deform
a
c
ross section
s
r
ies with diffe
r
t
ic field can b
e
X
LD (red lines
,
without mag
n
a
tions of CF
O
s
. a: along the
r
ent angles of
e
applied eith
e
,
enlarged by
n
etic field
O
and BTO du
e
(xz) plane. b:
e
r
e
3
Suppleme
n
measured
u
Suppleme
n
H
= 30° an
d
2
, respecti
v
different ca
s
n
tary Figure
S
u
nder grazing
n
tary Figure
S
d
k
= 60,
H
=
v
ely. c, f: Fiel
d
s
es of uniaxia
S
6 XLD in v
a
incidence (
k
S
7 Magnetic
=
60°, respecti
v
d
dependent
C
l anisotropy.
a
rious magn
e
= 60°) and
H
hysteresis
m
v
ely. b, e: Ma
C
o XMCD bef
e
tic fields. M
a
= 60°. XLD s
p
m
easurement
gnetic field d
e
ore correctio
n
a
gnetic field d
e
p
ectra were s
h
geometry. a
,
e
pendence of
n
(dotted lines
)
e
pendent XL
D
h
ifted verticall
,
d: Measure
m
magnetizatio
n
)
and after co
r
D
for Ti, Co an
d
l
y for more cl
a
m
ent geometr
y
n
direction def
r
rections for t
h
d
Ba ions
a
rity.
y
for
k
= 60°,
ined by
1
an
d
h
ree
d
4
Supplement
a
BTO/CFO co
m
Supplemen
Xra
y
diffr
a
intensity whi
l
that there is
a
with BTO[1
0
to the epitax
i
In order to
q
order of the
B
a possible til
t
twists aroun
d
the
= 2
B
tion defined
including a s
STO and B
T
and for CFO
by a signific
a
i.e. the (xy)
p
tary Figure
S
normal can
e
gonal distort
i
72°. In other
Supplement
a
in CFO (blac
k
0.05) and X
M
insets shows
measured un
a
ry Table S1
m
posite, resp
e
tary Metho
d
a
ction. By
d
l
e rotating th
e
a
crystallogr
a
0
0]CFO[100]
i
al growth ex
p
q
uantify the
h
B
TO/CFO na
n
t
with respect
d
z,
rockin
g
B
ragg positio
n
by
for
B
mall angle (
á
T
O the (031)
the (062) pe
a
a
nt momentu
m
p
lane, as sche
m
S
2a. The an
g
e
asily
b
e esti
i
on of the uni
t
words, the a
n
a
ry Figure S
8
k
line) compa
r
M
CD of Co
3+
i
n
the XMCD in
der normal x

Full width at
e
ctively, as s
h
d
s
d
etecting the
e
sample aro
u
a
phic order i
n
(not shown
h
p
ected from
t
h
igh degree
o
n
ocomposite,
n
to the z axis
g
curves wer
e
n
by changing
B
ragg peaks
á
90°) with t
h
diffraction p
a
k. All of the
m
m
transfer q i
n
m
atically sho
w
g
le between
q
mated by ne
g
t
cell and am
n
gle between
t
8
XMCD sim
u
r
ed to the sim
u
n
octahedral e
the energy r
e
ray incidence
half maximu
m
h
own in Suppl
e
xray diffr
a
u
nd z, it was
f
n
the sample
p
h
ere) in agre
e
t
he literature
o
f crystallogr
a
n
ot only rega
r
but also rega
r
e
measured a
r
the detector
of lattice p
h
e z directio
n
eaks were c
h
m
are charact
e
n
the sample
p
w
n in Supple
m
q
and the s
a
g
lecting the
t
ounts to arct
a
t
he z directio
n
u
lations and
u
lated XMCD
nvironment (
b
e
gion of the C
o
and an appli
e
m
(FWHM) of
x
e
mentary Fig
u
a
ction
f
ound
p
lane
e
ment
[14].
a
phic
r
ding
r
ding
r
ound
posi
lanes
n
. For
h
osen
e
rised
p
lane,
m
en
a
mple
t
etra
a
n3
n
and
the
geo
m
dep
e
add
i
axis
circ
l
wa
v
dat
a
fitte
for
inte
n
2/1,
dist
r
the
f
dire
c
SI
f
sub
s
exp
e
nan
o
hig
h
The
diff
r
experimenta
l
of Co
2+
in oct
a
b
lue line, shift
e
o
L
3
absorptio
e
d magnetic fi
e
x
ray diffracti
o
u
re S2.
lattice
p
lane
s
m
etry, the
w
e
nds on in
p
l
i
tion a weak
. The diffra
c
l
e xray diffr
a
v
elengths
K
1
a
are shown
d
by two Ga
u
each of th
e
n
sities for th
e
it has b
e
r
ibutions kee
p
f
ull width at
h
c
tly to the m
o
f
or all three
c
s
trate, a FW
H
e
rimental err
o
o
pillars a FW
H
h
er, i.e. aroun
same valu
e
r
action peak
w
l
data. The e
x
a
hedral envir
o
e
d vertically b
y
n
edge in mo
r
e
ld of3T alon
g
o
n peaks for
S
s
analysed
h
w
idth of the
ane twist of
sensitivity t
o
c
tograms we
r
a
ctometer wi
t
= 0.7093nm
in Suppleme
n
u
ssian distri
bu
e
two xra
y
e
two xray li
n
e
en ensured
p
this addition
h
alf maximu
m
o
saicity are lis
c
omponents.
F
H
M of 0.030°
o
r. For the
B
H
M is obtain
d 0.25° with
e
s were obt
a
w
idths by ro
t
x
perimentally
o
o
nment (red li
n
y
+0.05 and h
o
r
e detail. Exp
e
g
the sample
n
S
TO substrate
h
ere, is abou
t
diffraction
crystallites a
n
o
tilts with r
e
r
e measured
t
h a Mo xr
a
and
K
2
= 0
.
n
tary Figure
utions, i.e. o
n
y
wavelengt
h
n
es I
K
1
/ I
K
2
tha
t
the t
w
al condition.
T
m
(FWHM) th
a
ted in Supple
m
F
or the STO
is obtained
w
B
TO matrix
ed that is rou
an ap
p
ropria
t
a
ined when
t
ating the sa
m
o
btained XM
C
n
e, shifted ve
r
o
rizontally by

e
rimental data
n
ormal (
H
= 0
,
and
t
18°. In thi
peaks mainl
y
n
d exhibits i
n
spect to the
z
using a fou
r
a
y source wit
h
.
7136 nm. Th
e
S2 and wer
e
n
e distributio
n
h
s. Since th
e
have the rati
o
w
o Gaussia
n
T
he results f
o
a
t is correlate
d
m
entary Tabl
e
single cryst
a
w
ithin a sma
l
and the CF
O
ghly ten time
t
e larger erro
r
analysing th
e
m
ple around
z
C
D of Co ions
r
tically by 

1.8 eV). The
were
k
= 0).
s
y
n
z
r

h
e
e
n
e
o
n
o
r
d
e
a
l
l
l
O
s
r
.
e
z
.
5
The small twisting angle reveals a high degree of
structural order of the sample studied here which is
necessary for any further interpretation of soft xray
absorption data, in particular its XLD.
Magnetic field induced electric inplane polarization in
the BaTiO
3
matrix. A rough estimate of the absolute
values of inplane components of the electric polarization
as discussed in the main text will be given here. An
additional electric polarization caused by flexoelectric
effects [29] will be discussed as well. Electric polariza
tion components continuously varying their directions (as
sin and cos functions, respectively) at the {110} interfaces
of the CFO nanopillars are neglected, since the XLD is not
sensitive to these effects. The local piezoelectric inplane
polarization components of the BTO matrix according to
Figure 4c can be calculated by using Equation (1) of the
main text:
when inserting the piezoelectric and elastic shear con
stants of tetragonal BTO, d
15
= 4 10
10
mV
1
[24] and c
13
= c
23
= 1.1 10
11
Nm
2
[30], the nanopillar height z
0
4
10
7
m , and the surface displacements
x and
y,
respectively (cf. Supplementary Figure S5). The latter
values result from the inplane magnetostriction of
adjacent CFO nanopillars, i.e.
x
=
10
4
and
y
=

2 10
4
[7], edge lengths 2x
0
2y
0
10
7
m, and virtually
equal shear constants of BTO [30] and CFO [31] accor
ding to
This yields the following peak values of the absolute
values of the inplane polarization components:
where P
rem
0.1 Cm
2
is the value of the remanent
polarization of BTO in an (1,3)type CFO/BTO structure
at room temperature after application of an electric field
[10]. The magnetostrictively induced modulation
amplitudes P
x,y
 reach, hence, about 0.6% and 1% of P
rem
,
respectively. These values are comparable to the flexo
electric outofplane polarization component P
z
of BTO
[29] under the constraint of the adjacent deformed CFO
nanopillars (Figure 4c). They induce gradients of transver
se strains
11
=
x/x
1
and
22
=
y/y
1
along the BTO
thickness z
0
where x
1
y
1
210
7
m are the average inter
nanopillar spacings (Figure 1b and Supplementary Figure
S1). With the flexoelectric constant of BTO at T = 300 K,
f
3311
= f
3322
10
5
Asm
1
[29], we obtain an average outof
plane polarization caused by the flexoelectric effect of
Obviously comparable orders of magnitude of the polari
zation increments are encountered in and perpendicularly
to the plane. Both of them reach about 0.6  1% of the
value of the remanent polarization along the z direction at
300 K, but only the inplane components are measured by
XLD under normal incidence.
Correction of magnetic hysteresis XMCD data. Before
discussing the correction of fielddependent magnetic
hysteresis data obtained by XMCD at the CoL
3
absorp
tion edge, we present the measured XMCD spectrum in
Supplementary Figure S8 measured in magnetic saturation
of CFO under normal xray incidence. The XMCD data at
the Co L
3,2
absorption edges exhibit a spectral shape
similar to the one of Co
2+
in octahedral environment
(simulations with 10Dq = 1.0 eV) revealing only a neg
ligible cation disorder in CFO. Especially the quite flat
absorption signal at the L
2
absorption edge in the range
795 eV E 802 eV is typical for Co
2+
and can be
assigned to its large orbital magnetic moment. For com
parison, the simulated spectrum of Co
3+
in octahedral
environment is presented. Please note that the energy has
been shifted by 1.8 eV for an easier reading. Besides the
completely different spectral shape at the L
2
absorption
egde, also the double peak at the main L
3
peak cannot be
reproduced in that case. The same holds for the
pronounced fine structure at lower energies (about 776.5
eV  778.5 eV) of the L
3
edge as can be seen in the inset
of Supplementary Figure S8. These features can be related
to Co
2+
in octahedral environment. Some disagreement
between simulation and experiment may be due to the
tetragonal distortion caused by the magnetostriction in
CFO, but a qualitative comparison regarding the fine
structure is already possible. Comparison of the
experimental XANES and XMCD intensities with the
simulation gives the possibility to estimate a lower limit of
the magnetic moments of Co
2+
, although the absorption
signal is severely influenced by the Ba M
5
and M
4
absorption edges (cf. Supplementary Figure S3). We find
6
that both spin and orbital magnetic moment are at least
70% of the theoretical value for Co
2+
.
In the following, we discuss the correction of the field
dependent XMCD measured under grazing incidence. The
superconducting split coil magnet used in this experiment
gives the possibility to apply the magnetic field either
parallel to the incident xrays or perpendicular. For the
case of our measurements under grazing incidence this
means that the magnetic field was applied 30° off from the
easy direction of magnetization and the hard axis,
respectively. Since the magnetization is always aligned
along the effective magnetic field, i.e. the vector sum of
anisotropy field and external magnetic field
H
eff
= H
A
+H, it is continuously pulled away from the easy
direction towards the direction of the external field as it is
schematically shown in Supplementary Figure S7a, d.
This yields a change in the measured XMCD asymmetry
which is proportional to the projection of the
magnetization on the wave vector k of incident xrays. In
order to remove the resulting artefact from the data, the
angle
1
between magnetization M and external field
vector H was calculated and the factor between the
absolute value of M and the measured projection on k was
determined as a function of external field magnitude. For
the definition of angles see Supplementary Figure S7a, d.
The positive sign is used for an angle between the vectors
and z axis measured anticlockwise when looking along x.
The effective magnetic field is given by H
eff
= (0, H sin
H
, H cos
H
)
T
and the angle
1
can be
calculated according to:
with the reduced magnetic field h = H/H
A
. The
dependence of
1
on the external magnetic field
magnitude H is plotted in Supplementary Figure S7b, e
(upper graphics) for the two cases used in this experiment,
H
= 30° and
H
= 60°, respectively. Three different
values of the anisotropy field have been chosen. The
lower graphics of Supplementary Figure S7b, e shows the
angle between the effective magnetic field which is
parallel to the magnetization and the easy direction
2
=
H

1
. It can be seen that for the case
H
= 30°, the
main component of the magetization is along the easy
direction (
2
 < 20°) even at high external magnetic
fields. For the case
H
= 60°, although the main
component of the external magnetic field is along the hard
direction, the magnetization exhibits a significant
component along the easy direction. To correct the
measured magnetization as described above, the factor
between the absolute value of the magnetization and the
measured projection on k has to be determined as a
function of external field magnitude. Since the
magnetization was measured under grazing incidence with
k
= 60° for
H
= 30° and
H
= 60°, respectively, the
measured projection of the magnetization on k, M
k
, is
proportional to cos(
1
+90°) and cos
1
, respectively:
The corrected magnetization curves are shown in
Supplementary Figure S8c, f for three different values of
the anisotropy field. It can be seen, that the highfield
slope of the fielddependent magnetization vanishes for
µ
0
H
A
= 2.5T, which is in agreement to the value estimated
from extrapolating SQUID magnetometry data (cf. main
text). For µ
0
H
A
= 3.0T the corrections are too small and
for µ
0
H
A
= 2.0T too large resulting again in a slope of the
highfield magnetization.
Supplementary References
29. Ma, W. H. & Cross, L. E. Flexoelectricity of barium titanate. Appl.
Phys. Lett. 88, 232902 (2006).
30. Li Z., Chan S.K., Grimsditch M.H. & Zouboulis E.S. The elastic
and electromechanical properties of tetragonal BaTiO
3
single
crystals. J. Appl. Phys.70, 73277332 (1991).
31. Li Z., Fisher S., Liu J.Z.. & Nevitt M.V. Singlecrystal elastic
constants of CoAl and CoFe spinels. J. Mater. Sci. 26, 26212624
(1991).