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Electric in-plane polarization in multiferroic CoFe2O4/BaTiO3 nanocomposite tuned by magnetic fields - Supplementary information

Authors:
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
etic
h
mitz-Anto
n
a
nd
1
, Bern
h
de
1
hysik and C
rman
y
.
2
Hel
m
esent addres
ic Chemistr
tary Figure
urface. The c
tary Figure
f
the sample.
b
, respectivel
-
plan
e
aTi
ields
n
iak
1
, Detle
f
ard Krum
nter for Nan
m
holtz-Zentru
m
s:
Departmen
and Catalysi
S
1
|
Large-ar
e
ntrast of the
S
2
|
X-ray dif
f
b
-d: scans
a
y
.
pol
O
3
na
n
: Su
p
f
Schmitz
2
,
m
e
1
, Ralf Fe
integration D
Berlin für M
t of Physics,
s
,
Universiteit
a SEM imag
image has b
e
raction rock
round the (0
a
rizat
oco
plem
Pavel Bori
yerherm
2
,
E
u
isbur
g
-Esse
n
terialen und
est Virginia
Utrecht, Univ
e
e
. Large-are
a
en enhanced
ng curves.
1) Bragg pe
ion i
n
pos
enta
s
ov
1,3
, Fran
k
sther Dud
n
(CENIDE),
U
nergie, Albe
niversity, 1
rsiteitsweg
scanning el
e
afterwards.
: Schematic
m
ks for STO,
mul
ite tu
n
y inf
M.F. de
z
ik
2
, Wolfg
a
niversität Du
r
t-Einstein-Str
.
5 Willey Stre
9, 3584 CG
ctron micros
easurement
TO and arou
iferr
ed
rmat
G
root
4
, Sve
n
ng Kleem
i
sbur
g
-Essen,
r.
15, 12489 B
e
e
t, Morganto
w
trecht, Nethe
opy image of
geometry to
d the (062)
o
ic
b
y
i
on
n
Stienen
1
,
a
nn
1
, and
47048
e
rlin,
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
x-rays. a: No
rpendicular t
tary Figure
) of Ti, O, Fe,
tary Figure
t
ic field applie
d
z) plane.
S
4
|
Measure
m
rmal incidenc
o the wave v
S
3
|
XANES a
n
Co, and Ba
m
S
5 |Schemati
c
d
along the y
d
ent geometr
e
(
k
= 0). b:
G
e
ctor k of the
x
d XLD over
easured und
c
magnetic fi
d
irection is sc
ies for XLD.
T
razing incid
x
-rays.
v
iew spectra.
e
r grazing x-r
a
eld induced
d
hematically s
wo measure
e
nce (
k
= 60°
)
XANES (bla
c
a
y incidence
(
eformation
own for two
ment geomet
. The magne
k lines) and
(
k
= 60°) and
s
. The deform
a
ross section
ies with diffe
t
ic field can b
e
LD (red lines
without mag
n
tions of CF
s
. a: along the
ent angles of
applied eith
,
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
tary Figure
nder grazing
tary Figure
d
k
= 60,
H
=
v
ely. c, f: Fiel
d
es of uniaxia
S
6 |XLD in v
a
incidence (
k
S
7 |Magnetic
=
60°, respecti
v
d
-dependent
C
l anisotropy.
rious magn
= 60°) and
H
hysteresis
v
ely. b, e: Ma
o XMCD bef
e
tic fields. M
a
= 60°. XLD s
p
easurement
gnetic field d
e
ore correctio
a
gnetic field d
e
ectra were s
geometry. a
,
pendence of
(dotted lines
pendent XL
ifted verticall
,
d: Measure
m
magnetizatio
n
and after co
D
for Ti, Co an
d
y for more cl
ent geometr
n
direction def
rections for t
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
X-ra
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
a
ction. By
d
l
e rotating th
e
a
crystallogr
a
0
0]||CFO[100]
al growth ex
uantify the
TO/CFO na
with respect
d
z,
rockin
g
ragg positio
by
for
B
mall angle (
á
O the (031)
the (062) pe
nt momentu
lane, as sche
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
line) compa
M
CD of Co
3+
i
n
the XMCD in
der normal x-
|
Full width at
e
ctively, as s
h
d
s
etecting the
sample aro
phic order i
(not shown
ected from
igh degree
n
ocomposite,
n
to the z axis
curves wer
by changing
ragg peaks
á
90°) with t
h
diffraction p
k. All of the
m
transfer q i
n
atically sho
g
le between
q
mated by ne
cell and am
gle between
8
|XMCD sim
u
ed to the sim
n
octahedral e
the energy r
ray incidence
half maximu
own in Suppl
x-ray diffr
a
u
nd z, it was
f
the sample
h
ere) in agre
e
he literature
f crystallogr
ot only rega
but also rega
measured a
the detector
of lattice p
h
e z directio
n
eaks were c
are charact
the sample
w
n in Supple
m
q
and the s
a
lecting the
ounts to arct
t
he z directio
n
u
lations and
u
lated XMCD
nvironment (
gion of the C
and an appli
e
(FWHM) of
mentary Fig
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
of Co
2+
in oct
a
lue line, shift
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 x-ray diffr
a
v
elengths
K
1
a
are shown
by two Ga
each of th
sities for th
it has b
r
ibutions kee
p
ull width at
tly to the m
or all three
trate, a FW
rimental err
pillars a FW
er, i.e. aroun
same valu
action peak
l
data. The e
x
hedral envir
d vertically b
n
edge in mo
r
e
ld of3T alon
g
n peaks for
analysed
idth of the
ane twist of
sensitivity t
tograms we
ctometer wi
= 0.7093nm
in Suppleme
n
u
ssian distri
bu
e
two x-ra
y
e
two x-ray li
n
en ensured
this addition
alf maximu
o
saicity are lis
omponents.
H
M of 0.030°
r. For the
M is obtain
d 0.25° with
s were obt
idths by ro
perimentally
nment (red li
+0.05 and h
e detail. Exp
the sample
TO substrate
ere, is abou
diffraction
crystallites a
tilts with r
e measured
t
h a Mo x-r
a
and
K
2
= 0
.
tary Figure
utions, i.e. o
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
btained XM
n
e, shifted ve
r
o
rizontally by
-
rimental data
n
ormal (
H
= 0
,
and
t
18°. In thi
peaks mainl
d exhibits i
spect to the
z
using a fou
y source wit
.
7136 nm. Th
e
S2 and wer
e
e distributio
s. Since th
have the rati
o
o Gaussia
he results f
t is correlate
m
entary Tabl
e
single cryst
a
ithin a sma
and the CF
O
ghly ten time
e larger erro
analysing th
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 x-ray
absorption data, in particular its XLD.
Magnetic field induced electric in-plane polarization in
the BaTiO
3
matrix. A rough estimate of the absolute
values of in-plane 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 in-plane
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 in-plane 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 in-plane 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 out-of-plane 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 out-of-
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 in-plane components are measured by
XLD under normal incidence.
Correction of magnetic hysteresis XMCD data. Before
discussing the correction of field-dependent 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 x-ray 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 x-rays 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 x-rays. 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 anti-clockwise 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 high-field
slope of the field-dependent 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
high-field 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, 7327-7332 (1991).
31. Li Z., Fisher S., Liu J.Z.. & Nevitt M.V. Single-crystal elastic
constants of Co-Al and Co-Fe spinels. J. Mater. Sci. 26, 2621-2624
(1991).
... Furthermore, a contraction of the inclusion (the nanopillar) in direction of the magnetic field (in this case the y-direction) of 10 −11 m is identifiable. The experimental observed in-plane average polarizations are estimated as D exp x ≈ 6 · 10 −4 Cm −2 and D exp y ≈ 10 −3 Cm −2 , see [4]. The applied magnetic field in y-direction has a value of 100 kA/m, such that the deformation of the edge of the nanopillar in y-direction matches the one of the experiments. ...
... Furthermore, we computed the average electric polarization as a function of ξ, see Fig. 1, seperately for the inclusion and the matrix. In order to match the simulated in-plane polarization changes D y with the estimated values D exp y of [4], we have to consider the average polarization D y = 1.18 · 10 −3 Cm −2 of the upper part of the microstructure at ξ = 0.27h. This value corresponds to a thickness of about 106 nm of the top layer. ...
... However, experimental measurements are only capable of investigating the surface of the microstructure. The simulations demonstrate that the assumptions of [4] are to simplified and detailed simulations are necessary for an appropriate prediction of the in-plane polarization changes. ...
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