TbMn2O5
Non-resonant and Resonant X-ray Scattering Studies on Multiferroic TbMn2O5
J. Koo1, C. Song1, S. Ji1, J.-S. Lee1, J. Park1, T.-H. Jang1, C.-H. Yang1, J.-H. Park1,2, Y. H. Jeong1, K.-B. Lee1,2,∗
T.Y. Koo2, Y.J. Park2, J.-Y. Kim2, D. Wermeille3,† A.I. Goldman3, G. Srajer4, S. Park5, and S.-W. Cheong5,6
eSSC and Department of Physics, POSTECH, Pohang 790-784, Korea
Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang 790-784, Korea
Ames Laboratory, Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
Rutgers Center for Emergent Materials and Department of Physics and Astronomy,
Rutgers University, Piscataway, NJ 08854, USA
Laboratory of Pohang Emergent Materials and Department of Physics, POSTECH, Pohang 790-784, Korea
(Dated: November 1, 2018)
Comprehensive x-ray scattering studies, including resonant scattering at Mn L-edge, Tb L- and
M -edges, were performed on single crystals of TbMn2O5. X-ray intensities were observed at a
forbidden Bragg position in the ferroelectric phases, in addition to the lattice and the magnetic
modulation peaks. Temperature dependences of their intensities and the relation between the mod-
ulation wave vectors provide direct evidences of exchange striction induced ferroelectricity. Resonant
x-ray scattering results demonstrate the presence of multiple magnetic orders by exhibiting their
different temperature dependences. The commensurate-to-incommensurate phase transition around
24 K is attributed to discommensuration through phase slipping of the magnetic orders in spin
frustrated geometries. We proposed that the low temperature incommensurate phase consists of the
commensurate magnetic domains separated by anti-phase domain walls which reduce spontaneous
polarizations abruptly at the transition.
PACS numbers: 77.80.e-, 75.25.+z, 64.70.Rh, 61.10.-i
In recent years, much attention has been paid to mul-
tiferroic materials, in which magnetic and ferroelectric
orders coexist and are cross-correlated [1, 2, 3, 4, 5,
6, 7, 8, 9, 10], due to theoretical interests and poten-
tial application to magnetoelectric (ME) devices. Ma-
nipulation of electric polarizations by external magnetic
fields has been demonstrated in some of these materi-
als [4, 5]. Orthorhombic TbMn2O5, one of the multi-
ferroic materials, displays a rich phase diagram. Upon
cooling through TN ∼ 41 K, TbMn2O5 becomes anti-
ferromagnetic with an incommensurate magnetic (ICM)
order which transits to a commensurate magnetic (CM)
phase with spontaneous electric polarization at T c1 ∼
36 K, and reenters a low temperature incommensurate
magnetic (LT-ICM) phase at T c2 ∼ 24 K. Anomalies
of ferroelectricity and dielectric properties were observed
concurrently with these magnetic phase transitions [4, 9].
Especially, the reentrant LT-ICM phase is a phenomenon
peculiar to RMn2O5 multiferroics while commensurate
phases are more common as the low temperature ground
states. Since the CM to LT-ICM phase transition is also
accompanied with an abrupt loss of spontaneous polar-
izations, it is critical to elucidate the natures of the in-
commensurability of the material, including the mecha-
nism of the CM to LT-ICM phase transition.
The origin of the complex phases of the material is at-
tributed to the coupling between magnetic moments of
Mn ions and lattice [8, 9]. It is suggested that, when a
magnetic order is modulated with a wave vector qm, the
exchange striction affects inter-atomic bondings result-
ing in a periodic lattice modulation with a wave vector
qc = 2qm [5, 6, 7, 8, 9]. Recently, Chapon et al. pro-
posed for RMn2O5 systems that ferroelectricity results
from the exchange striction of acentric spin density waves
for the CM phases [9]. Indeed, Kimura et al. insisted
that CM modulations are indispensable to the ferroelec-
tricity in the LT-ICM phase, from their neutron scat-
tering results on HoMn2O5 under high magnetic fields
[11]. However, lattice distortions derived from ICM spin
structures turned out to describe well the spontaneous
polarizations of YMn2O5 even in the ICM phase [12],
implying that commensurability is not a necessary con-
dition for the ferroelectricity. In order to understand the
intriguing magnetoelectricity well, detailed information
on the lattice and spin structure changes is necessary.
However, only limited crystallographic data are available
and even any direct evidence on the symmetry lowering
has not been reported yet [9, 10, 11, 12, 13, 14].
In this letter, we present synchrotron x-ray scatter-
ing results on single crystals of TbMn2O5. Since x-ray
scattering is sensitive to both lattice and magnetic mod-
ulations, x-ray scattering with intense undulator x-rays
allowed simultaneous measurements for qm and qc. Non-
resonant x-ray scattering results show the relationship of
qc = 2qm, confirming lattice modulations are generated
by the magnetic orders. A (3 0 0) forbidden Bragg peak,
which is a direct evidence of the symmetry lowering to
a non-centrosymmetry space group, was observed in the
ferroelectric (FE) phases. Furthermore, the temperature
dependence of the peak intensity, I (300), was found to
coincide with those of the lattice modulation peak inten-
sities, I c, and the spontaneous polarization square,P
2, in
http://arxiv.org/abs/0704.0533v1
the CM phase. This indicates the ferroelectricity is gen-
erated by the lattice modulations. In the LT-ICM phase,
temperature dependences of I c cannot be described by a
single order parameter, implying the presence of differ-
ent magnetic orders. Resonant x-ray magnetic scattering
results at Mn L-, Tb L3- and M5-edges show that each
magnetic order has its own temperature dependence. It
is proposed that CM to LT-ICM phase transition is in-
duced by discommensuration through phase slipping due
to competing magnetic orders under the frustrated ge-
ometry. Moreover, the CM modulations with anti-phase
domain walls are consistent with the temperature depen-
dences of qm and I (300) in the LT-ICM phase, and explain
well the abrupt loss of P at the transition.
Single crystals of TbMn2O5 were grown by a flux
method [4]. The specimen used for the hard x-ray scat-
tering measurements has a plate-like shape with (1 1 0) as
a surface normal direction. Its mosaicity was measured
to be about 0.01◦ at (3 3 0) Bragg reflection. For soft
x-ray scattering, a different sample was cut and polished
to have (2 0 1) as a surface normal direction. Soft x-ray
scattering measurements were performed at 2A beamline
in the Pohang Light Source (PLS). Details of the soft
x-ray scattering chamber were described elsewhere [15].
X-ray diffraction experiments were conducted at the 3C2
bending magnet beamline in the PLS and at the 6-ID
undulator beamline in the Midwest Universities Collab-
orative Access Team (MUCAT) Sector in the Advanced
Photon Source. For non-resonant x-ray scattering exper-
iments, 6.45 keV was selected as an incident x-ray energy
below Mn K -edge (∼ 6.55 keV). All the incident x-rays
were σ-polarized and PG(006) was used to have a σ-to-π
channel at Tb L3-edge.
Nonresonant x-ray scattering measurements were per-
formed to investigate the temperature dependence of qm
and qc simultaneously. The measured lattice modula-
tion peak position of (2 5 -0.5) for the CM phase and
those of its 4 split peaks for the ICM phases are pre-
sented as solid and open circles, respectively, in Fig. 1
(a). For magnetic satellites, (2.5 5 -0.25) peak and its 2
split ones were measured for the CM and ICM phases.
Their positions are presented as solid and open squares,
respectively. The magnetic and lattice modulation satel-
lites for ICM phases are linked with broken and solid
lines to their corresponding main Bragg peaks. Temper-
ature dependences of qm and qc are shown in Fig. 1 (b)
and (c). From the results, it is obvious that relation,
qc = 2qm, holds within experimental errors in the whole
temperature range below TN . It is consistent with the
magnetic order induced lattice modulations. The tem-
perature dependence of qm shown here is qualitatively
similar to the neutron scattering results by others [16].
Below TN , ICM magnetic peaks develop, and qm locks
into a CM ordering at (1
) via a first order transi-
tion at T c1. On further cooling the sample below T c2,
the CM to LT-ICM phase transition takes place. With
FIG. 1: (Color online) Positions of the measured magnetic
satellites (square) and lattice modulation peaks (circle) in
the (h 5 l) reciprocal lattice plane are shown in (a). The
temperature dependences of qxm (square) and q
c (circle), and
those of qzm (square) and q
c (circle) are shown in (b) and (c),
respectively. For direct comparisons with those of qm, the
components of qc are divided by two. Vertical broken lines
indicate TN ∼ 41 K, T c1 ∼ 36 K, T c2 ∼ 24 K and T c3 ∼ 13
K, respectively.
further decreasing temperature, qm of the LT-ICM mod-
ulations evolves and is eventually pinned around (0.486 0
0.308) which can be approximated to a CM value of (17
) at T c3 ∼ 13 K. Such a long-period CM modulation
can be interpreted as the CM modulations (qm = (
)) with domain walls, as is the case for ErNi2B2C [17].
As shown in Fig. 2 (a), measurable x-ray intensi-
ties were observed, in the ferroelectric phase, at (3 0 0)
Bragg position which is forbidden under a space group of
the room temperature paraelectric phase, Pbam. Resid-
ual intensities above T c1 are due to higher harmonic
FIG. 2: (Color online) (a) Rocking curves of a (3 0 0) forbid-
den Bragg peak measured below (open) and above T c1 (solid).
(b) Temperature dependences of the integrated intensities of
a (3 0 0) Bragg peak (circle), CM lattice modulation peak
(square) and squared spontaneous polarization (broken line)
taken from Ref. 4. All the data are properly scaled.
contaminations. Values for full-width-at-half-maximum
(FWHM) of the peak are about 0.01◦, close to those of (4
0 0) main Bragg peak in the LT-ICM phase. The results
explicitly evidenced that inversion symmetry is broken
concomitantly with the FE phase as speculated before.
According to the models suggested by others [9, 10], dis-
placements of Mn3+ are in ab-plane. While b-axis com-
ponents of the atomic displacements mainly contribute to
P, a-axis components enable the emergence of I (300). If
the atomic displacements correspond to the periodic lat-
tice modulations, it is expected that both P2 and I (300)
are proportional to I c, as shown in Fig. 2 (b). (The spon-
taneous polarization data are taken from Ref. 4 and are
shifted in order to get the same values for T c1.) It con-
firms that spontaneous polarization is due to the atomic
displacements driven by magnetic orders: a direct crys-
tallographic evidence of exchange striction as the origin
of ferroelectricity in the material [8, 9, 10, 12]. Also it is
noted that I (300) drops abruptly at T c2 and has a broad
minimum around T c3.
Though many interesting ME phenomena have been
reported in the LT-ICM phases below T c2 [4, 11, 18, 19],
their basic mechanisms still remain to be understood.
Since the lattice modulations reflect basic ME natures,
temperature dependences below T c2 of integrated inten-
sities were measured at the four split ICM peak positions
illustrated in Fig. 1 (a). From the results displayed in
Fig. 3, it is clear that temperature dependences of all four
peaks cannot be described by a single order parameter,
implying the presence of various magnetic orders having
the same qm’s but different temperature dependences.
To investigate different magnetic orders, we performed
resonant x-ray magnetic scattering measurements at Mn
L-, Tb L3- and M5-edges. Figure 4 (a) shows energy pro-
files around Mn L-edge of magnetic satellites at 10 K and
FIG. 3: (Color online) Temperature dependences of the ICM
lattice modulation peak intensities.
x-ray absorption spectroscopy (XAS) at room tempera-
ture. Magnetic peaks and XAS data clearly show reso-
nances at both Mn L2- and L3-edges. XAS results show
broad peaks containing contributions from the multiplet
states of 3d electrons of Mn3+ and Mn4+ ions. Magnetic
satellites show relatively sharp double peaks at both Mn
L-edges. The sharp resonances represent different multi-
plet states of Mn 3d electrons including charge transfer
excitations, while Mn ions are expected to be in the high-
spin configurations with all the 3d electron spins aligned
FIG. 4: (a) Energy profiles of the ICM magnetic peaks (cir-
cle)and XAS (solid line) around Mn L2,3-edges. Vertical bro-
ken lines correspond to 640.8 eV and 644.2 eV, respectively.
(b) Temperature dependences of the ICM (circle) and the
CM (square) magnetic peaks. Open (Solid) symbols denote
the data taken E = 640.8 eV (644.2 eV), respectively. (c)
Temperature dependences of the ICM (open circle) and the
CM (solid square) magnetic peak at Tb L3-edge.
parallel. Therefore, although the resonances do not have
one-to-one correspondences with the magnetic orders of
Mn ions, changes in the resonances at magnetic satellites
reflect the changes in spin ordering which are periodi-
cally modulated with the wave vector qm. Temperature
dependences of x-ray intensities at the ICM peak of Qm
= (qxm 0 q
m) were measured at the two resonances, 640.8
and 644.2 eV. The results are presented in Fig. 4 (b).
Data for a CM peak of Qm = (0.5 0 0.25) at the reso-
nance of 644.2 eV are presented together. It is clear that,
above 15 K, intensities of each resonance have different
temperature dependences from each other. Though the
origin of the anomalous temperature dependences is not
understood in detail, it reflects complicated natures of
magnetic moments of Mn ions under the frustrated con-
figuration.
Magnetic ordering of Tb3+ ions was investigated with
resonant x-ray scattering measurements at Tb L3-edge.
Figure 4 (c) shows that ordering temperature of Tb mag-
netic moments is the same with that of Mn, TN , which is
consistent with neutron scattering results [9]. The modu-
lation wave vector of Tb magnetic order is the same with
the values of qm measured in nonresonant x-ray scatter-
ing. Soft x-ray magnetic scattering measurements were
also performed at Tb M 5-edge and the result not shown
here confirms that observed x-ray intensities in Fig. 4
(c) reflect magnetic order of Tb 4f electrons which grows
monotonically below TN .
From the results shown in Fig. 4 (b) and (c), it is clear
that there exist multiple magnetic order parameters hav-
ing the same qm’s but different temperature dependences.
The contributing portions of each magnetic order to scat-
tering factors of magnetic satellites are different depend-
ing on Qm(= QBragg + qm), and it results in different
temperature dependence for each magnetic peak and its
corresponding lattice modulation peak intensities, which
explains the temperature dependences presented in Fig.
Since the magnetic orders are located under the spin
frustrated geometry, it is reasonable to suppose that
phase-slips take place due to competitions between the
magnetic orders, as their order parameters grow with
different temperature dependences. The discommensu-
ration results in the transition to the LT-ICM phase.
Anti-phase domain walls for the phase slips are consis-
tent with the aforementioned long-period CM modula-
tions below T c3. Assuming the model suggested by oth-
ers [9], atomic displacements are canted antiferroelectric
type. Across an anti-phase domain wall, directions of
the atomic displacements and the spontaneous polariza-
tions are reversed. Therefore, not only the polarizations
from domains separated by the domain wall cancel each
other but also x-ray scattering amplitudes for the (3 0
0) Bragg peak are canceled due to the crystal symme-
try. Then, only remnants resulting from unequal popu-
lations of the domains contribute to P and I(300). Since
a density of the domain walls determines qm, tempera-
ture dependences of P, I(300) and qm down to T c3 can be
explained consistently in terms of CM modulations with
the anti-phase domain walls. This indicates that CM
modulations are preferred as its low temperature ground
state. Then, the low temperature phase seems to have
a higher entropy due to the domain walls than the high
temperature CM phase, violating the entropy rule. How-
ever, due to the geometrical frustration and the presence
of multiple magnetic orders many different energy scales
can exist. The complicated temperature dependences of
the magnetic orders in Fig. 4(c) reflect the presence of
the different energy scales. Smaller energy scales become
important at low temperatures and induce discommen-
suration. Upturns of the electrical polarization and I(300)
below T c3 are attributed to lattice modulations enhanced
by increasing Tb magnetic moments, which is consistent
with results of others demonstrating couplings between
Tb moments and lattices [18, 19, 20].
In summary, we have shown that exchange striction
is the driving mechanism for the magnetoelectricity in
the material. The same temperature dependences of x-
ray intensities at a (3 0 0) forbidden Bragg peak and a
lattice modulation peak in the CM FE phase, together
with observation of the relation, qc = 2qm, demonstrate
that spontaneous electric polarization is due to atomic
displacements driven by the exchange striction of mag-
netic orders. Resonant x-ray magnetic scattering results
confirm the presence of multiple magnetic orders hav-
ing different temperature dependences. The CM to LT-
ICM phase transition is attributed to discommensura-
tion through phase slipping in the competing magnetic
orders in the frustrated configurations. Temperature de-
pendences of qm, P and I(300) in the LT-ICM phase are
explained in terms of the CM modulations with anti-
phase domain walls.
We thank D.J. Huang for the useful discussions. This
work was supported by the KOSEF through the eSSC
at POSTECH, and by MOHRE through BK-21 pro-
gram. The experiments at the PLS were supported by
the POSTECH Foundation and MOST. Use of the Ad-
vanced Photon Source (APS) was supported by the U.S.
Department of Energy, Office of Science, Office of Ba-
sic Energy Sciences, under Contract No. W-31-109-Eng-
38. The Midwest Universities Collaborative Access Team
(MUCAT) sector at the APS is supported by the U.S.
Department of Energy, Office of Science, Office of Basic
Energy Sciences, through the Ames Laboratory under
contract No. DE-AC02-07CH11358. Work at Rutgers
was supported by NSF-DMR-0520471.
∗ Electronic address: kibong@postech.ac.kr
† Present address: European Synchrotron Radiation Facil-
mailto:kibong@postech.ac.kr
ity, BP 220, F-38043 Grenoble Cedex 9, France
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[4] N. Hur et al., Nature 429, 392 (2004).
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  Comprehensive x-ray scattering studies, including resonant scattering at Mn
L-edge, Tb L- and M-edges, were performed on single crystals of TbMn2O5. X-ray
intensities were observed at a forbidden Bragg position in the ferroelectric
phases, in addition to the lattice and the magnetic modulation peaks.
Temperature dependences of their intensities and the relation between the
modulation wave vectors provide direct evidences of exchange striction induced
ferroelectricity. Resonant x-ray scattering results demonstrate the presence of
multiple magnetic orders by exhibiting their different temperature dependences.
The commensurate-to-incommensurate phase transition around 24 K is attributed
to discommensuration through phase slipping of the magnetic orders in spin
frustrated geometries. We proposed that the low temperature incommensurate
phase consists of the commensurate magnetic domains separated by anti-phase
domain walls which reduce spontaneous polarizations abruptly at the transition.

TbMn2O5
Non-resonant and Resonant X-ray Scattering Studies on Multiferroic TbMn2O5
J. Koo1, C. Song1, S. Ji1, J.-S. Lee1, J. Park1, T.-H. Jang1, C.-H. Yang1, J.-H. Park1,2, Y. H. Jeong1, K.-B. Lee1,2,∗
T.Y. Koo2, Y.J. Park2, J.-Y. Kim2, D. Wermeille3,† A.I. Goldman3, G. Srajer4, S. Park5, and S.-W. Cheong5,6
eSSC and Department of Physics, POSTECH, Pohang 790-784, Korea
Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang 790-784, Korea
Ames Laboratory, Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
Rutgers Center for Emergent Materials and Department of Physics and Astronomy,
Rutgers University, Piscataway, NJ 08854, USA
Laboratory of Pohang Emergent Materials and Department of Physics, POSTECH, Pohang 790-784, Korea
(Dated: November 1, 2018)
Comprehensive x-ray scattering studies, including resonant scattering at Mn L-edge, Tb L- and
M -edges, were performed on single crystals of TbMn2O5. X-ray intensities were observed at a
forbidden Bragg position in the ferroelectric phases, in addition to the lattice and the magnetic
modulation peaks. Temperature dependences of their intensities and the relation between the mod-
ulation wave vectors provide direct evidences of exchange striction induced ferroelectricity. Resonant
x-ray scattering results demonstrate the presence of multiple magnetic orders by exhibiting their
different temperature dependences. The commensurate-to-incommensurate phase transition around
24 K is attributed to discommensuration through phase slipping of the magnetic orders in spin
frustrated geometries. We proposed that the low temperature incommensurate phase consists of the
commensurate magnetic domains separated by anti-phase domain walls which reduce spontaneous
polarizations abruptly at the transition.
PACS numbers: 77.80.e-, 75.25.+z, 64.70.Rh, 61.10.-i
In recent years, much attention has been paid to mul-
tiferroic materials, in which magnetic and ferroelectric
orders coexist and are cross-correlated [1, 2, 3, 4, 5,
6, 7, 8, 9, 10], due to theoretical interests and poten-
tial application to magnetoelectric (ME) devices. Ma-
nipulation of electric polarizations by external magnetic
fields has been demonstrated in some of these materi-
als [4, 5]. Orthorhombic TbMn2O5, one of the multi-
ferroic materials, displays a rich phase diagram. Upon
cooling through TN ∼ 41 K, TbMn2O5 becomes anti-
ferromagnetic with an incommensurate magnetic (ICM)
order which transits to a commensurate magnetic (CM)
phase with spontaneous electric polarization at T c1 ∼
36 K, and reenters a low temperature incommensurate
magnetic (LT-ICM) phase at T c2 ∼ 24 K. Anomalies
of ferroelectricity and dielectric properties were observed
concurrently with these magnetic phase transitions [4, 9].
Especially, the reentrant LT-ICM phase is a phenomenon
peculiar to RMn2O5 multiferroics while commensurate
phases are more common as the low temperature ground
states. Since the CM to LT-ICM phase transition is also
accompanied with an abrupt loss of spontaneous polar-
izations, it is critical to elucidate the natures of the in-
commensurability of the material, including the mecha-
nism of the CM to LT-ICM phase transition.
The origin of the complex phases of the material is at-
tributed to the coupling between magnetic moments of
Mn ions and lattice [8, 9]. It is suggested that, when a
magnetic order is modulated with a wave vector qm, the
exchange striction affects inter-atomic bondings result-
ing in a periodic lattice modulation with a wave vector
qc = 2qm [5, 6, 7, 8, 9]. Recently, Chapon et al. pro-
posed for RMn2O5 systems that ferroelectricity results
from the exchange striction of acentric spin density waves
for the CM phases [9]. Indeed, Kimura et al. insisted
that CM modulations are indispensable to the ferroelec-
tricity in the LT-ICM phase, from their neutron scat-
tering results on HoMn2O5 under high magnetic fields
[11]. However, lattice distortions derived from ICM spin
structures turned out to describe well the spontaneous
polarizations of YMn2O5 even in the ICM phase [12],
implying that commensurability is not a necessary con-
dition for the ferroelectricity. In order to understand the
intriguing magnetoelectricity well, detailed information
on the lattice and spin structure changes is necessary.
However, only limited crystallographic data are available
and even any direct evidence on the symmetry lowering
has not been reported yet [9, 10, 11, 12, 13, 14].
In this letter, we present synchrotron x-ray scatter-
ing results on single crystals of TbMn2O5. Since x-ray
scattering is sensitive to both lattice and magnetic mod-
ulations, x-ray scattering with intense undulator x-rays
allowed simultaneous measurements for qm and qc. Non-
resonant x-ray scattering results show the relationship of
qc = 2qm, confirming lattice modulations are generated
by the magnetic orders. A (3 0 0) forbidden Bragg peak,
which is a direct evidence of the symmetry lowering to
a non-centrosymmetry space group, was observed in the
ferroelectric (FE) phases. Furthermore, the temperature
dependence of the peak intensity, I (300), was found to
coincide with those of the lattice modulation peak inten-
sities, I c, and the spontaneous polarization square,P
2, in
http://arxiv.org/abs/0704.0533v1
the CM phase. This indicates the ferroelectricity is gen-
erated by the lattice modulations. In the LT-ICM phase,
temperature dependences of I c cannot be described by a
single order parameter, implying the presence of differ-
ent magnetic orders. Resonant x-ray magnetic scattering
results at Mn L-, Tb L3- and M5-edges show that each
magnetic order has its own temperature dependence. It
is proposed that CM to LT-ICM phase transition is in-
duced by discommensuration through phase slipping due
to competing magnetic orders under the frustrated ge-
ometry. Moreover, the CM modulations with anti-phase
domain walls are consistent with the temperature depen-
dences of qm and I (300) in the LT-ICM phase, and explain
well the abrupt loss of P at the transition.
Single crystals of TbMn2O5 were grown by a flux
method [4]. The specimen used for the hard x-ray scat-
tering measurements has a plate-like shape with (1 1 0) as
a surface normal direction. Its mosaicity was measured
to be about 0.01◦ at (3 3 0) Bragg reflection. For soft
x-ray scattering, a different sample was cut and polished
to have (2 0 1) as a surface normal direction. Soft x-ray
scattering measurements were performed at 2A beamline
in the Pohang Light Source (PLS). Details of the soft
x-ray scattering chamber were described elsewhere [15].
X-ray diffraction experiments were conducted at the 3C2
bending magnet beamline in the PLS and at the 6-ID
undulator beamline in the Midwest Universities Collab-
orative Access Team (MUCAT) Sector in the Advanced
Photon Source. For non-resonant x-ray scattering exper-
iments, 6.45 keV was selected as an incident x-ray energy
below Mn K -edge (∼ 6.55 keV). All the incident x-rays
were σ-polarized and PG(006) was used to have a σ-to-π
channel at Tb L3-edge.
Nonresonant x-ray scattering measurements were per-
formed to investigate the temperature dependence of qm
and qc simultaneously. The measured lattice modula-
tion peak position of (2 5 -0.5) for the CM phase and
those of its 4 split peaks for the ICM phases are pre-
sented as solid and open circles, respectively, in Fig. 1
(a). For magnetic satellites, (2.5 5 -0.25) peak and its 2
split ones were measured for the CM and ICM phases.
Their positions are presented as solid and open squares,
respectively. The magnetic and lattice modulation satel-
lites for ICM phases are linked with broken and solid
lines to their corresponding main Bragg peaks. Temper-
ature dependences of qm and qc are shown in Fig. 1 (b)
and (c). From the results, it is obvious that relation,
qc = 2qm, holds within experimental errors in the whole
temperature range below TN . It is consistent with the
magnetic order induced lattice modulations. The tem-
perature dependence of qm shown here is qualitatively
similar to the neutron scattering results by others [16].
Below TN , ICM magnetic peaks develop, and qm locks
into a CM ordering at (1
) via a first order transi-
tion at T c1. On further cooling the sample below T c2,
the CM to LT-ICM phase transition takes place. With
FIG. 1: (Color online) Positions of the measured magnetic
satellites (square) and lattice modulation peaks (circle) in
the (h 5 l) reciprocal lattice plane are shown in (a). The
temperature dependences of qxm (square) and q
c (circle), and
those of qzm (square) and q
c (circle) are shown in (b) and (c),
respectively. For direct comparisons with those of qm, the
components of qc are divided by two. Vertical broken lines
indicate TN ∼ 41 K, T c1 ∼ 36 K, T c2 ∼ 24 K and T c3 ∼ 13
K, respectively.
further decreasing temperature, qm of the LT-ICM mod-
ulations evolves and is eventually pinned around (0.486 0
0.308) which can be approximated to a CM value of (17
) at T c3 ∼ 13 K. Such a long-period CM modulation
can be interpreted as the CM modulations (qm = (
)) with domain walls, as is the case for ErNi2B2C [17].
As shown in Fig. 2 (a), measurable x-ray intensi-
ties were observed, in the ferroelectric phase, at (3 0 0)
Bragg position which is forbidden under a space group of
the room temperature paraelectric phase, Pbam. Resid-
ual intensities above T c1 are due to higher harmonic
FIG. 2: (Color online) (a) Rocking curves of a (3 0 0) forbid-
den Bragg peak measured below (open) and above T c1 (solid).
(b) Temperature dependences of the integrated intensities of
a (3 0 0) Bragg peak (circle), CM lattice modulation peak
(square) and squared spontaneous polarization (broken line)
taken from Ref. 4. All the data are properly scaled.
contaminations. Values for full-width-at-half-maximum
(FWHM) of the peak are about 0.01◦, close to those of (4
0 0) main Bragg peak in the LT-ICM phase. The results
explicitly evidenced that inversion symmetry is broken
concomitantly with the FE phase as speculated before.
According to the models suggested by others [9, 10], dis-
placements of Mn3+ are in ab-plane. While b-axis com-
ponents of the atomic displacements mainly contribute to
P, a-axis components enable the emergence of I (300). If
the atomic displacements correspond to the periodic lat-
tice modulations, it is expected that both P2 and I (300)
are proportional to I c, as shown in Fig. 2 (b). (The spon-
taneous polarization data are taken from Ref. 4 and are
shifted in order to get the same values for T c1.) It con-
firms that spontaneous polarization is due to the atomic
displacements driven by magnetic orders: a direct crys-
tallographic evidence of exchange striction as the origin
of ferroelectricity in the material [8, 9, 10, 12]. Also it is
noted that I (300) drops abruptly at T c2 and has a broad
minimum around T c3.
Though many interesting ME phenomena have been
reported in the LT-ICM phases below T c2 [4, 11, 18, 19],
their basic mechanisms still remain to be understood.
Since the lattice modulations reflect basic ME natures,
temperature dependences below T c2 of integrated inten-
sities were measured at the four split ICM peak positions
illustrated in Fig. 1 (a). From the results displayed in
Fig. 3, it is clear that temperature dependences of all four
peaks cannot be described by a single order parameter,
implying the presence of various magnetic orders having
the same qm’s but different temperature dependences.
To investigate different magnetic orders, we performed
resonant x-ray magnetic scattering measurements at Mn
L-, Tb L3- and M5-edges. Figure 4 (a) shows energy pro-
files around Mn L-edge of magnetic satellites at 10 K and
FIG. 3: (Color online) Temperature dependences of the ICM
lattice modulation peak intensities.
x-ray absorption spectroscopy (XAS) at room tempera-
ture. Magnetic peaks and XAS data clearly show reso-
nances at both Mn L2- and L3-edges. XAS results show
broad peaks containing contributions from the multiplet
states of 3d electrons of Mn3+ and Mn4+ ions. Magnetic
satellites show relatively sharp double peaks at both Mn
L-edges. The sharp resonances represent different multi-
plet states of Mn 3d electrons including charge transfer
excitations, while Mn ions are expected to be in the high-
spin configurations with all the 3d electron spins aligned
FIG. 4: (a) Energy profiles of the ICM magnetic peaks (cir-
cle)and XAS (solid line) around Mn L2,3-edges. Vertical bro-
ken lines correspond to 640.8 eV and 644.2 eV, respectively.
(b) Temperature dependences of the ICM (circle) and the
CM (square) magnetic peaks. Open (Solid) symbols denote
the data taken E = 640.8 eV (644.2 eV), respectively. (c)
Temperature dependences of the ICM (open circle) and the
CM (solid square) magnetic peak at Tb L3-edge.
parallel. Therefore, although the resonances do not have
one-to-one correspondences with the magnetic orders of
Mn ions, changes in the resonances at magnetic satellites
reflect the changes in spin ordering which are periodi-
cally modulated with the wave vector qm. Temperature
dependences of x-ray intensities at the ICM peak of Qm
= (qxm 0 q
m) were measured at the two resonances, 640.8
and 644.2 eV. The results are presented in Fig. 4 (b).
Data for a CM peak of Qm = (0.5 0 0.25) at the reso-
nance of 644.2 eV are presented together. It is clear that,
above 15 K, intensities of each resonance have different
temperature dependences from each other. Though the
origin of the anomalous temperature dependences is not
understood in detail, it reflects complicated natures of
magnetic moments of Mn ions under the frustrated con-
figuration.
Magnetic ordering of Tb3+ ions was investigated with
resonant x-ray scattering measurements at Tb L3-edge.
Figure 4 (c) shows that ordering temperature of Tb mag-
netic moments is the same with that of Mn, TN , which is
consistent with neutron scattering results [9]. The modu-
lation wave vector of Tb magnetic order is the same with
the values of qm measured in nonresonant x-ray scatter-
ing. Soft x-ray magnetic scattering measurements were
also performed at Tb M 5-edge and the result not shown
here confirms that observed x-ray intensities in Fig. 4
(c) reflect magnetic order of Tb 4f electrons which grows
monotonically below TN .
From the results shown in Fig. 4 (b) and (c), it is clear
that there exist multiple magnetic order parameters hav-
ing the same qm’s but different temperature dependences.
The contributing portions of each magnetic order to scat-
tering factors of magnetic satellites are different depend-
ing on Qm(= QBragg + qm), and it results in different
temperature dependence for each magnetic peak and its
corresponding lattice modulation peak intensities, which
explains the temperature dependences presented in Fig.
Since the magnetic orders are located under the spin
frustrated geometry, it is reasonable to suppose that
phase-slips take place due to competitions between the
magnetic orders, as their order parameters grow with
different temperature dependences. The discommensu-
ration results in the transition to the LT-ICM phase.
Anti-phase domain walls for the phase slips are consis-
tent with the aforementioned long-period CM modula-
tions below T c3. Assuming the model suggested by oth-
ers [9], atomic displacements are canted antiferroelectric
type. Across an anti-phase domain wall, directions of
the atomic displacements and the spontaneous polariza-
tions are reversed. Therefore, not only the polarizations
from domains separated by the domain wall cancel each
other but also x-ray scattering amplitudes for the (3 0
0) Bragg peak are canceled due to the crystal symme-
try. Then, only remnants resulting from unequal popu-
lations of the domains contribute to P and I(300). Since
a density of the domain walls determines qm, tempera-
ture dependences of P, I(300) and qm down to T c3 can be
explained consistently in terms of CM modulations with
the anti-phase domain walls. This indicates that CM
modulations are preferred as its low temperature ground
state. Then, the low temperature phase seems to have
a higher entropy due to the domain walls than the high
temperature CM phase, violating the entropy rule. How-
ever, due to the geometrical frustration and the presence
of multiple magnetic orders many different energy scales
can exist. The complicated temperature dependences of
the magnetic orders in Fig. 4(c) reflect the presence of
the different energy scales. Smaller energy scales become
important at low temperatures and induce discommen-
suration. Upturns of the electrical polarization and I(300)
below T c3 are attributed to lattice modulations enhanced
by increasing Tb magnetic moments, which is consistent
with results of others demonstrating couplings between
Tb moments and lattices [18, 19, 20].
In summary, we have shown that exchange striction
is the driving mechanism for the magnetoelectricity in
the material. The same temperature dependences of x-
ray intensities at a (3 0 0) forbidden Bragg peak and a
lattice modulation peak in the CM FE phase, together
with observation of the relation, qc = 2qm, demonstrate
that spontaneous electric polarization is due to atomic
displacements driven by the exchange striction of mag-
netic orders. Resonant x-ray magnetic scattering results
confirm the presence of multiple magnetic orders hav-
ing different temperature dependences. The CM to LT-
ICM phase transition is attributed to discommensura-
tion through phase slipping in the competing magnetic
orders in the frustrated configurations. Temperature de-
pendences of qm, P and I(300) in the LT-ICM phase are
explained in terms of the CM modulations with anti-
phase domain walls.
We thank D.J. Huang for the useful discussions. This
work was supported by the KOSEF through the eSSC
at POSTECH, and by MOHRE through BK-21 pro-
gram. The experiments at the PLS were supported by
the POSTECH Foundation and MOST. Use of the Ad-
vanced Photon Source (APS) was supported by the U.S.
Department of Energy, Office of Science, Office of Ba-
sic Energy Sciences, under Contract No. W-31-109-Eng-
38. The Midwest Universities Collaborative Access Team
(MUCAT) sector at the APS is supported by the U.S.
Department of Energy, Office of Science, Office of Basic
Energy Sciences, through the Ames Laboratory under
contract No. DE-AC02-07CH11358. Work at Rutgers
was supported by NSF-DMR-0520471.
∗ Electronic address: kibong@postech.ac.kr
† Present address: European Synchrotron Radiation Facil-
mailto:kibong@postech.ac.kr
ity, BP 220, F-38043 Grenoble Cedex 9, France
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