Absence of commensurate ordering at the polarization flop transition in multiferroic
DyMnO3
J. Strempfer,1 B. Bohnenbuck,2 M. Mostovoy,3 N. Aliouane,4 D.N. Argyriou,4
F. Schrettle,5 J. Hemberger,5 A. Krimmel,5 and M. v. Zimmermann1
Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, 22605 Hamburg, Germany
Max-Planck-Institut für Festkörperforschung, 70569 Stuttgart, Germany
Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, Netherlands
Hahn-Meitner-Institut, 14109 Berlin, Germany
Experimentalphysik V, Universität Augsburg, 86159 Augsburg, Germany
(Dated: October 26, 2018)
Ferroelectric spiral magnets DyMnO3 and TbMnO3 show similar behavior of electric polarization
in applied magnetic fields. Studies of the field dependence of lattice modulations on the contrary
show a completely different picture. Whereas in TbMnO3 the polarization flop from P‖c to P‖a is
accompanied by a sudden change from incommensurate to commensurate wave vector modulation,
in DyMnO3 the wave vector varies continuously through the flop transition. This smooth behavior
may be related to the giant magnetocapacitive effect observed in DyMnO3.
The ability to control ferroelectric polarization (P )
with an applied magnetic field (H) in manganite per-
ovskites and related materials has caused a resurgence
of interest in magneto-electric phenomena. One of the
most striking effects is the five-fold increase of the dielec-
tric constant of DyMnO3 in magnetic field, named gi-
ant magnetocapacitance.1 The key to this unprecedented
sensitivity is the spiral magnetic ordering stabilized by
competing exchange interactions, which forces positive
and negative ions to shift in opposite directions and
which can be rather easily influenced by applied mag-
netic fields.
Unlike conventional ferroelectrics, in the RMnO3 man-
ganite perovskites such as R=Tb and Dy the emergence
of ferroelectricity2,3 arises from the peculiar coupling of
the lattice to a spiral ordering of Mn-spins.4,5,6 Spiral
ordering is defined by the wave vector κ and the axis
e around which the spins rotate. For R=Tb and Dy
these two vectors are perpendicular to each other.4 The
coupling of a uniform electric polarization P to an inho-
mogeneous magnetization M is phenomenologically de-
scribed by a term linear in the gradient ∇M , the so-
called Lifshitz invariant. Such a coupling breaks the in-
version symmetry of the crystal lattice in the spiral mag-
netic state and induces the direction of the polarization
P= γχM1M2[e×κ] , where γ and χ are a coupling con-
stant and the dielectric susceptibility, M1 and M2 are
amplitudes of the magnetic moments in directions per-
pendicular to e.6 For R =Tb and Dy, κ is parallel to
the b-axis and e parallel to the a-axis, so that the fer-
roelectric polarization induced below the spiral ordering
temperature TC , is parallel to the c-axis (P‖c).
The application of magnetic field either parallel to the
a- (H‖a) or b-axis (H‖b) leads to a flop of the polariza-
tion from P‖c to P‖a. The flop in the polarization is
interpreted as the flop of the vector e from the a- (spins
within the bc-plane) to the c-direction (spins within the
ab-plane). For R=Tb these field-induced flops of P oc-
cur at critical field of HaC∼8 T and H
C∼4.5 T at 4 K for
field parallel to the a- and b-axis respectively and are as-
sociated with a first order transition from an incommen-
surate (IC) low field magnetic ordering to a commensu-
rate (CM) high field phase. The H-T -phase diagram of
DyMnO3 is very similar to the one of TbMnO3, with the
same characteristic flops of P but at lower critical fields,
HaC∼6.5 T and H
C∼1 T at 2 K.
In this paper we show, that although the phase di-
agrams of R=Dy and Tb may be qualitatively similar,
their structural behavior at HC is completely different.
We find that for DyMnO3 the polarization flop is not as-
sociated with a transition to a CM phase as in the case
of R =Tb, but rather the magnitude of the wave vec-
tor changes very little across HC for both H‖a and H‖b
configurations. We argue that the magnitude of the in-
commensurability for R=Dy does not lie sufficiently close
to a CM value, as opposed to R=Tb, making the IC high
field phase energetically more favorable.
For R=Dy, Mn-spins order to form a longitudinal spin
density wave (SDW) below TN∼39 K with wave vector
κ = δmb
∗ with δMnm ∼ 0.36...0.385
3 determined on the
basis of lattice reflections with δl=2δm
3,7,8 that arise from
a coupling of the IC magnetic ordering to the lattice via a
quadratic magneto-elastic coupling.9 With further cool-
ing δMnm decreases down to TC=19 K, where a second
transition into the spiral phase occurs. Coincident with
the transition to a spiral phase a spontaneous electric po-
larization parallel to the c-axis is found.2 Below T
Dy magnetic moments order commensurately with prop-
agation vector 1
∗.8 In the study presented here, struc-
tural first and second harmonic reflections related to the
magnetic first harmonic reflections are investigated.
Single crystalline samples were prepared using the
floating zone technique at the HMI. Details of sample
preparation and characterization are given elsewhere.8
Due to the high neutron absorption cross section of Dy,
in-field neutron diffraction is not ideal to investigate
field induced magneto-structural transitions in DyMnO3.
Rather to investigate the structural response to the field
http://arxiv.org/abs/0704.1285v1
induced polarization flop we have utilized in-field syn-
chrotron x-ray diffraction with the two field configura-
tions H‖a and H‖b. Measurements with H‖a were per-
formed at beamline X21 at the National Synchrotron
Light Source at Brookhaven National Laboratory with
a photon energy of 9.5 keV, using a 13 T Oxford cry-
omagnet with vertical field. Measurements in the H‖b
configuration were carried out at beamline BW5 at HA-
SYLAB with a photon energy of 100 keV using a 10 T
Cryogenics cryomagnet with horizontal field. Magne-
tization measurements were performed with a Physical
Properties Measurement System (PPMS) on a 14.5 mg
DyMnO3 sample. The spontaneous electric polarization
as a function of field and temperature was determined
from the pyro-current recorded in a PPMS-system using
an electrometer.
Measurements of the spontaneous electric polarization
performed on the same samples used in our diffraction ex-
periments in magnetic field configurations H‖a and H‖b
(insets in Fig. 1c and Fig. 2 a) confirm that spontaneous
ferroelectric polarization is present below TC=19 K as
already reported in Ref. 3. The application of H‖b be-
low TC(Dy) results in the suppression of P‖c (inset of
Fig. 1c). Kimura et al. show in addition that this de-
crease is accompanied by an increase in P‖a indicative
of the flop in the ferroelectric polarization.3
In Fig. 1a-b we show the temperature dependence of
the wave vector and integrated intensity of the second
harmonic reflection (0, 4-2δ, 0), both for decreasing and
increasing temperature. The dependences are compared
for zero field (P‖c), and µ0H‖b = 10 T (P‖a). In both
data sets, we find a significant hysteresis in the intensity
as well as in the magnitude of δ around TC=18 K, which
is associated with the onset of ferroelectricity. However,
despite the fact that P lies along different axes for 0 and
10 T, we observe no significant change between these two
measurements. In Fig. 1c-d, we show the field depen-
dence of δ and of the integrated intensity of the same
reflection at T=2 K. Here we find a small initial increase
of δ up to µ0H
C=1 T where the flop in polarization is
found while the intensity of the same reflection shows a
steady increase with increasing field. Above HbC , we find
a small decrease of δ with increasing field. This behavior
is in sharp contrast to TbMnO3 where δ varies slowly
with increasing field and locks in above HbC into a CM
value of κ= 1
∗ at HbC .
In Fig. 1e-f, the temperature dependence of δ and
the intensities of first and second harmonic reflections is
shown for data measured in field cooling with µ0H‖b =
2.5 T. Here we find a different behavior in the intensities
of IC reflections. For wave vector along the b∗-direction
(0, 4-2δ, 0), a strong hysteresis is observed in its inten-
sity as a function of temperature, whereas this hystere-
sis is absent for wave vectors that are mainly along the
c∗-direction ( (0, δ, 5) and (0, 2δ, 5)) (Fig. 1f). Neverthe-
less, δ and its hysteresis are the same for all reflections
(Fig. 1e). The described intensity behavior is similar to
what we have recently observed in zero field temperature
 µ0H=10T
0 10 20 30 40
T (K)
(0 4−2δ 0)
(a) H||bTC
0 10 20 30 40
T (K)
t. In
sity (a
 µ0H=0T
0 2 4 6 8 10
µ0H (T)
0 2 4 6 8 10
µ0H (T)
t. In
sity (a
(0 4−2δ 0)
0 10 20 30 40
T (K)
µ0H||b = 2.5 T
TC TNTPF
0 10 20 30 40
T (K)
t. In
sity (a
(0 δ 5)(f)
TNTPF
(0 2δ 5)*10
(0 4−2δ 0)
0 10 20 30 40
T (K)
) H||b
FIG. 1: (color online) Temperature dependence of (a) the in-
commensurability δ and (b) the respective intensities of the
(0, 4-2δ, 0) structural reflection. Data are shown for µ0H = 0
T and µ0H‖b = 10 T for decreasing (open symbols) and in-
creasing (closed symbols) temperature. In panel (c) and (d),
δ and intensity variation as function of magnetic field, respec-
tively, are shown for a sample temperature of T = 2 K, in the
same axes ranges as in (a) and (b). In the inset, spontaneous
electric polarization P‖c is shown as function of tempera-
ture for magnetic field orientation H‖b. Temperature depen-
dence of (e) wave vector and (f) the respective intensities for
µ0H‖b = 2.5 T and wave vectors (0, δ, 5), (0, 2δ, 5) and (0,
4-2δ, 0) for decreasing (open symbols) and increasing (closed
symbols) temperature. The (0, 2δ, 5) intensities in (f) are
multiplied by a factor of 10.
dependent measurements using resonant x-ray scatter-
ing from a single crystal of DyMnO3.
11 In these mea-
surements a similar hysteresis was observed to be associ-
ated with the induced ordering of Dy-spins with the same
propagation vector as that for the Mn spin ordering. Fi-
nally for this field configuration we note that at 2.5 T,
the polarization flop from P‖a to P‖c is expected with
increasing temperature at TPF ∼ 12 K (inset in Fig. 1c).
However our diffraction measurements find no anomaly
either on the temperature dependence of the wave vector
or in the intensities at this temperature as it was found
in TbMnO3.
We now turn our attention to measurements conducted
0 2 4 6 8 10
µ0H (T)
t. In
sity (a
its)(0 2δ 5)
Hc(a)
(0 1−δ 5)
0 2 4 6 8 10
µ0H (T)
Hc(a)
0 10 20 30 40
T (K)
) H||a
FIG. 2: (color online) Field dependences with field H‖a of (a)
the incommensurability and (b) the integrated intensity mea-
sured at T = 8 K. The error bars in (a) represent the HWHM
of the superlattice reflection. In the inset, spontaneous elec-
tric polarization P‖c is shown as function of temperature for
magnetic field H‖a.
in the H‖a configuration. In Fig. 2a-b the field depen-
dence of the intensity and wave vector of the first and
second harmonic reflections (0, 1-δ, 5) and (0, 2δ, 5) is
shown, measured at T = 8 K above the ordering tempera-
ture of Dy of T
∼ 5 K. The second harmonic reflection
decreases in intensity with increasing field and vanishes
at 5 T, while the first harmonic appears only at a field
of 4 T and saturates in intensity at 7 T. This behavior is
not directly related to the polarization flop but reflects a
variation of the modulation direction of the strain wave
leading to the superlattice reflections. However the most
remarkable behavior is found for the field dependence of
the wavevector. Here, the wave vector of the first har-
monic reflection does not change significantly through the
polarization flop transition at µ0H
C∼ 6.5 T.
3 Again this
is in sharp contrast to the behavior of TbMnO3, where a
discontinuous transition to a CM phase is found.
Below 6K, Dy spins order commensurately with δDym =
. Previously we have argued that the lattice distor-
tion associated with this magnetic ordering is not CM
but rather IC with δl ∼ 0.1b
∗.8 In our measurements we
found the half-integer magnetic reflection to be extremely
weak and we focused our attention to the lattice δl ∼ 0.1
satellite measured at (0, 0.9, 5). In Fig. 3a we show a
series of scans at different fields applied along the a-axis
at 3 K which show the rapid suppression of the δl ∼ 0.1
satellite which vanishes for fields µ0H‖a > 1 T. The CM
magnetic reflection (0, 0.5, 5) is only measurable at zero
field and can not longer be observed at 1 T. The tem-
perature dependence of the intensity and wavevector of
the (0, 0.9, 5) reflection is shown in Fig. 3b-c, revealing
the rapid suppression of the intensity of this reflection
at low temperature in accordance with the appearance
of ferromagnetic order (inset Fig. 3c), indicating an easy
axis along the b-direction. The suppression of this re-
flection with magnetic field is analogous to a similar be-
havior found for R =Tb which coincided with the ferro-
magnetic ordering of Tb-spins for the same field size and
configuration.10
The polarization flop is driven by the field-induced
0.4 0.6 0.8
k (r.l.u.)
s) (a)
µ0H=0T
µ0H=1T
µ0H=1.5T
(0 0.9 5), µ0H = 0T
(0 0.9 5), µ0H = 0.5T
(0 2δ 5),  µ0H = 0T
(0 0.9 5), µ0H = 1T
0 5 10 15 20
T (K)
(0 0.9 5)
0 2 4 6 8 10
B (T)
) H||b (T=2K)
H||a (T=8K)
FIG. 3: (color online) (a) Scans along (0, k, 5) at T = 3 K for
different applied magnetic fields with intensity in logarithmic
scale. (b) Temperature dependence as function of field H‖a of
the integrated intensity of the superlattice reflections (0, 0.9,
5) in the Dy ordered phase and the second harmonic reflection
(0, 2δ, 5) due to Mn order. Open and closed symbols repre-
sent increasing and decreasing temperature, respectively. In
(c) the wave vector of the (0, 0.9, 5) reflection is shown as
function of temperature for different fields. The inset shows
magnetization data of DyMnO3 for H‖a and H‖b.
flop of the axis of rotation of the magnetic spiral e. Its
direction is determined by magnetic anisotropy terms,
which to lowest order of the free energy expansion in
powers of magnetization of Mn spins have the form,∑
α=a,b,c
α. Phenomenologically the spin flop tran-
sition results from the field dependence of the coefficients
aα. Below the critical field HC , ab < ac < aa, which fa-
vors spins rotating in the bc plane (e‖a), while aboveHC ,
ab < aa < ac, favoring the rotation in the ab-plane (e‖c).
From the perspective of symmetry there is no restric-
tion that the high field spiral phase must be CM. In this
view the fact that there is a magneto-elastic phase tran-
sition to a CM phase associated with the flops in the
polarization for R =Tb would appear to be a special
case, especially when compared to R =Dy where we find
no such transition at HC . The difference in behavior
between these two multiferroics is not of fundamental
nature but rather simply lies in the magnitude of the
incommensurability. For R=Tb, δm=0.28 r.l.u. is close
to the CM value of 1
. For this CM value of the wave
vector the amplitude of the Mn magnetic moment is not
modulated10 and may thus be energetically more favor-
able than an IC amplitude modulated phase. In the phe-
nomenological approach the CM state with δ = 0.25 r.l.u.
is stabilized by M4 terms in the Landau expansion. For
R=Dy the value of δ=0.38 r.l.u. is further away from a
CM value (1
) and thus a transition to it is not favorable
energetically. Therefore the Mn spin spiral may indeed
flop as expected but without a change in δ.13 Clearly here
the modulation period in real space is much shorter, and
the amplitude of the Mn magnetic moment is modulated.
A significant difference between the two multiferroics
is found in the behavior of the complex magnetic or-
dering of R-ions. For R=Tb, Tb spins are induced to
order along the a-axis below TN with the same period-
icity as Mn-spins and below T TbN =7 K they order sepa-
rately with δTbm =0.42 r.l.u. At low temperatures, when
H‖a∼1 T, Tb-spins are aligned ferromagnetically, while
for field along the b-axis, δTbm jumps discontinuously to
a CM value of 1
at 1.75 T.10 The behavior for R=Dy
is much simpler, as below T
=6 K the Dy spins order
with δDym =
. Here, the suppression of the IC-reflections
together with the magnetization data indicates a melting
of the antiferromagnetic Dy ordering, a behavior different
to TbMnO3.
On the basis of the CM ordering of Mn-spins for the
P‖a phase for R=Tb it has been suggested that ferro-
electricity may arise in the absence of a spiral magnetic
ordering. Here an exchange striction mechanism pro-
posed from competing ferromagnetic and antiferromag-
netic super-exchange interactions predicts a P‖a phase
for a CM ordering with δ = 1
. This model holds strictly
for a CM ordering and suggests that for R=Dy the spi-
ral phase must be maintained at high fields to support a
ferroelectric state.
The smooth magnetic field dependence of the spiral
wave vector in DyMnO3 at the spin flop transition may
explain the large increase of the dielectric constant εa,
observed in this material.1,3 If higher-order terms in the
Landau expansion of free energy could be neglected, then
at the spin flop transition the magnetic excitation spec-
trum of the spiral would acquire a zero mode, since for
aa (HC) = ac (HC) there is a freedom to rotate the spi-
ral plane around the b axis. This mode can be excited
by electric field E‖a normal to the spiral bc-plane and
is the electromagnon studied in Ref. 12. Its softening at
H = HC would result in divergence of static dielectric
susceptibility εa. In reality, due to higher-order terms
in the Landau expansion the spin flop transition is of
first order, the softening of the magnetic mode is not
complete and the peak value of the dielectric constant
is finite. Still, in DyMnO3 this transition is close to a
second-order one in the sense that the spirals above and
below the critical field are essentially the same except for
their orientation. The softness of the spiral magnetic or-
dering at the critical field may be the reason behind the
large magnetocapacitance observed in DyMnO3 which
becomes truly gigantic close to the tricritical point at
the crossing of the collinear and two spiral phases with
P‖c and P‖a, where higher-order terms are small. In
TbMnO3 the spin flop transition is strongly discontin-
uous due to the concomitant IC-CM transition, which
limits the growth of the dielectric constant.
In summary, in-field synchrotron X-ray diffraction
measurements from a DyMnO3 single crystal have shown
that there is no change of the wave vector δ associated
with the flop of the ferroelectric polarization P at HC for
both H‖a and H‖c. This is in sharp contrast to similar
measurements reported for TbMnO3 were a transition to
a CM phase is found at HC for the same field configu-
rations. We argue that the magnitude of the incommen-
surability for R =Dy does not lie sufficiently close to a
CM value, as opposed to R=Tb, making the IC high field
phase energetically more favorable.
Acknowledgments
We would like to thank C.S. Nelson for the assistance
at the experiment at NSLS. Work at Brookhaven was
supported by the U.S. Department of Energy, Division
of Materials Science, under Contract No. DE-AC02-
98CH10886.
1 T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and
Y. Tokura, Phys. Rev. Lett. 92, 257201 (2004).
2 T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima,
and Y. Tokura, Nature 426, 55 (2003).
3 T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A. P.
Ramirez, Phys. Rev. B 71, 224425 (2005).
4 M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm,
J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P.
Vajk, and J. W. Lynn, Phys. Rev. Letters 95, 087206
(2005).
5 H. Katsura, N. Nagaosa, and A.V. Balatsky, Phys. Rev.
Lett. 95, 057205 (2005).
6 M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006).
7 T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Taka-
hashi, K. Ishizaka, , and Y. Tokura, Phys. Rev. B 68,
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13 We note that a value of δ = 1
is observed for
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097202 (2006).

  Ferroelectric spiral magnets DyMnO3 and TbMnO3 show similar behavior of
electric polarization in applied magnetic fields. Studies of the field
dependence of lattice modulations on the contrary show a completely different
picture. Whereas in TbMnO3 the polarization flop from P||c to P||a is
accompanied by a sudden change from incommensurate to commensurate wave vector
modulation, in DyMnO3 the wave vector varies continuously through the flop
transition. This smooth behavior may be related to the giant magnetocapacitive
effect observed in DyMnO3.

Absence of commensurate ordering at the polarization flop transition in multiferroic
DyMnO3
J. Strempfer,1 B. Bohnenbuck,2 M. Mostovoy,3 N. Aliouane,4 D.N. Argyriou,4
F. Schrettle,5 J. Hemberger,5 A. Krimmel,5 and M. v. Zimmermann1
Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, 22605 Hamburg, Germany
Max-Planck-Institut für Festkörperforschung, 70569 Stuttgart, Germany
Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, Netherlands
Hahn-Meitner-Institut, 14109 Berlin, Germany
Experimentalphysik V, Universität Augsburg, 86159 Augsburg, Germany
(Dated: October 26, 2018)
Ferroelectric spiral magnets DyMnO3 and TbMnO3 show similar behavior of electric polarization
in applied magnetic fields. Studies of the field dependence of lattice modulations on the contrary
show a completely different picture. Whereas in TbMnO3 the polarization flop from P‖c to P‖a is
accompanied by a sudden change from incommensurate to commensurate wave vector modulation,
in DyMnO3 the wave vector varies continuously through the flop transition. This smooth behavior
may be related to the giant magnetocapacitive effect observed in DyMnO3.
The ability to control ferroelectric polarization (P )
with an applied magnetic field (H) in manganite per-
ovskites and related materials has caused a resurgence
of interest in magneto-electric phenomena. One of the
most striking effects is the five-fold increase of the dielec-
tric constant of DyMnO3 in magnetic field, named gi-
ant magnetocapacitance.1 The key to this unprecedented
sensitivity is the spiral magnetic ordering stabilized by
competing exchange interactions, which forces positive
and negative ions to shift in opposite directions and
which can be rather easily influenced by applied mag-
netic fields.
Unlike conventional ferroelectrics, in the RMnO3 man-
ganite perovskites such as R=Tb and Dy the emergence
of ferroelectricity2,3 arises from the peculiar coupling of
the lattice to a spiral ordering of Mn-spins.4,5,6 Spiral
ordering is defined by the wave vector κ and the axis
e around which the spins rotate. For R=Tb and Dy
these two vectors are perpendicular to each other.4 The
coupling of a uniform electric polarization P to an inho-
mogeneous magnetization M is phenomenologically de-
scribed by a term linear in the gradient ∇M , the so-
called Lifshitz invariant. Such a coupling breaks the in-
version symmetry of the crystal lattice in the spiral mag-
netic state and induces the direction of the polarization
P= γχM1M2[e×κ] , where γ and χ are a coupling con-
stant and the dielectric susceptibility, M1 and M2 are
amplitudes of the magnetic moments in directions per-
pendicular to e.6 For R =Tb and Dy, κ is parallel to
the b-axis and e parallel to the a-axis, so that the fer-
roelectric polarization induced below the spiral ordering
temperature TC , is parallel to the c-axis (P‖c).
The application of magnetic field either parallel to the
a- (H‖a) or b-axis (H‖b) leads to a flop of the polariza-
tion from P‖c to P‖a. The flop in the polarization is
interpreted as the flop of the vector e from the a- (spins
within the bc-plane) to the c-direction (spins within the
ab-plane). For R=Tb these field-induced flops of P oc-
cur at critical field of HaC∼8 T and H
C∼4.5 T at 4 K for
field parallel to the a- and b-axis respectively and are as-
sociated with a first order transition from an incommen-
surate (IC) low field magnetic ordering to a commensu-
rate (CM) high field phase. The H-T -phase diagram of
DyMnO3 is very similar to the one of TbMnO3, with the
same characteristic flops of P but at lower critical fields,
HaC∼6.5 T and H
C∼1 T at 2 K.
In this paper we show, that although the phase di-
agrams of R=Dy and Tb may be qualitatively similar,
their structural behavior at HC is completely different.
We find that for DyMnO3 the polarization flop is not as-
sociated with a transition to a CM phase as in the case
of R =Tb, but rather the magnitude of the wave vec-
tor changes very little across HC for both H‖a and H‖b
configurations. We argue that the magnitude of the in-
commensurability for R=Dy does not lie sufficiently close
to a CM value, as opposed to R=Tb, making the IC high
field phase energetically more favorable.
For R=Dy, Mn-spins order to form a longitudinal spin
density wave (SDW) below TN∼39 K with wave vector
κ = δmb
∗ with δMnm ∼ 0.36...0.385
3 determined on the
basis of lattice reflections with δl=2δm
3,7,8 that arise from
a coupling of the IC magnetic ordering to the lattice via a
quadratic magneto-elastic coupling.9 With further cool-
ing δMnm decreases down to TC=19 K, where a second
transition into the spiral phase occurs. Coincident with
the transition to a spiral phase a spontaneous electric po-
larization parallel to the c-axis is found.2 Below T
Dy magnetic moments order commensurately with prop-
agation vector 1
∗.8 In the study presented here, struc-
tural first and second harmonic reflections related to the
magnetic first harmonic reflections are investigated.
Single crystalline samples were prepared using the
floating zone technique at the HMI. Details of sample
preparation and characterization are given elsewhere.8
Due to the high neutron absorption cross section of Dy,
in-field neutron diffraction is not ideal to investigate
field induced magneto-structural transitions in DyMnO3.
Rather to investigate the structural response to the field
http://arxiv.org/abs/0704.1285v1
induced polarization flop we have utilized in-field syn-
chrotron x-ray diffraction with the two field configura-
tions H‖a and H‖b. Measurements with H‖a were per-
formed at beamline X21 at the National Synchrotron
Light Source at Brookhaven National Laboratory with
a photon energy of 9.5 keV, using a 13 T Oxford cry-
omagnet with vertical field. Measurements in the H‖b
configuration were carried out at beamline BW5 at HA-
SYLAB with a photon energy of 100 keV using a 10 T
Cryogenics cryomagnet with horizontal field. Magne-
tization measurements were performed with a Physical
Properties Measurement System (PPMS) on a 14.5 mg
DyMnO3 sample. The spontaneous electric polarization
as a function of field and temperature was determined
from the pyro-current recorded in a PPMS-system using
an electrometer.
Measurements of the spontaneous electric polarization
performed on the same samples used in our diffraction ex-
periments in magnetic field configurations H‖a and H‖b
(insets in Fig. 1c and Fig. 2 a) confirm that spontaneous
ferroelectric polarization is present below TC=19 K as
already reported in Ref. 3. The application of H‖b be-
low TC(Dy) results in the suppression of P‖c (inset of
Fig. 1c). Kimura et al. show in addition that this de-
crease is accompanied by an increase in P‖a indicative
of the flop in the ferroelectric polarization.3
In Fig. 1a-b we show the temperature dependence of
the wave vector and integrated intensity of the second
harmonic reflection (0, 4-2δ, 0), both for decreasing and
increasing temperature. The dependences are compared
for zero field (P‖c), and µ0H‖b = 10 T (P‖a). In both
data sets, we find a significant hysteresis in the intensity
as well as in the magnitude of δ around TC=18 K, which
is associated with the onset of ferroelectricity. However,
despite the fact that P lies along different axes for 0 and
10 T, we observe no significant change between these two
measurements. In Fig. 1c-d, we show the field depen-
dence of δ and of the integrated intensity of the same
reflection at T=2 K. Here we find a small initial increase
of δ up to µ0H
C=1 T where the flop in polarization is
found while the intensity of the same reflection shows a
steady increase with increasing field. Above HbC , we find
a small decrease of δ with increasing field. This behavior
is in sharp contrast to TbMnO3 where δ varies slowly
with increasing field and locks in above HbC into a CM
value of κ= 1
∗ at HbC .
In Fig. 1e-f, the temperature dependence of δ and
the intensities of first and second harmonic reflections is
shown for data measured in field cooling with µ0H‖b =
2.5 T. Here we find a different behavior in the intensities
of IC reflections. For wave vector along the b∗-direction
(0, 4-2δ, 0), a strong hysteresis is observed in its inten-
sity as a function of temperature, whereas this hystere-
sis is absent for wave vectors that are mainly along the
c∗-direction ( (0, δ, 5) and (0, 2δ, 5)) (Fig. 1f). Neverthe-
less, δ and its hysteresis are the same for all reflections
(Fig. 1e). The described intensity behavior is similar to
what we have recently observed in zero field temperature
 µ0H=10T
0 10 20 30 40
T (K)
(0 4−2δ 0)
(a) H||bTC
0 10 20 30 40
T (K)
t. In
sity (a
 µ0H=0T
0 2 4 6 8 10
µ0H (T)
0 2 4 6 8 10
µ0H (T)
t. In
sity (a
(0 4−2δ 0)
0 10 20 30 40
T (K)
µ0H||b = 2.5 T
TC TNTPF
0 10 20 30 40
T (K)
t. In
sity (a
(0 δ 5)(f)
TNTPF
(0 2δ 5)*10
(0 4−2δ 0)
0 10 20 30 40
T (K)
) H||b
FIG. 1: (color online) Temperature dependence of (a) the in-
commensurability δ and (b) the respective intensities of the
(0, 4-2δ, 0) structural reflection. Data are shown for µ0H = 0
T and µ0H‖b = 10 T for decreasing (open symbols) and in-
creasing (closed symbols) temperature. In panel (c) and (d),
δ and intensity variation as function of magnetic field, respec-
tively, are shown for a sample temperature of T = 2 K, in the
same axes ranges as in (a) and (b). In the inset, spontaneous
electric polarization P‖c is shown as function of tempera-
ture for magnetic field orientation H‖b. Temperature depen-
dence of (e) wave vector and (f) the respective intensities for
µ0H‖b = 2.5 T and wave vectors (0, δ, 5), (0, 2δ, 5) and (0,
4-2δ, 0) for decreasing (open symbols) and increasing (closed
symbols) temperature. The (0, 2δ, 5) intensities in (f) are
multiplied by a factor of 10.
dependent measurements using resonant x-ray scatter-
ing from a single crystal of DyMnO3.
11 In these mea-
surements a similar hysteresis was observed to be associ-
ated with the induced ordering of Dy-spins with the same
propagation vector as that for the Mn spin ordering. Fi-
nally for this field configuration we note that at 2.5 T,
the polarization flop from P‖a to P‖c is expected with
increasing temperature at TPF ∼ 12 K (inset in Fig. 1c).
However our diffraction measurements find no anomaly
either on the temperature dependence of the wave vector
or in the intensities at this temperature as it was found
in TbMnO3.
We now turn our attention to measurements conducted
0 2 4 6 8 10
µ0H (T)
t. In
sity (a
its)(0 2δ 5)
Hc(a)
(0 1−δ 5)
0 2 4 6 8 10
µ0H (T)
Hc(a)
0 10 20 30 40
T (K)
) H||a
FIG. 2: (color online) Field dependences with field H‖a of (a)
the incommensurability and (b) the integrated intensity mea-
sured at T = 8 K. The error bars in (a) represent the HWHM
of the superlattice reflection. In the inset, spontaneous elec-
tric polarization P‖c is shown as function of temperature for
magnetic field H‖a.
in the H‖a configuration. In Fig. 2a-b the field depen-
dence of the intensity and wave vector of the first and
second harmonic reflections (0, 1-δ, 5) and (0, 2δ, 5) is
shown, measured at T = 8 K above the ordering tempera-
ture of Dy of T
∼ 5 K. The second harmonic reflection
decreases in intensity with increasing field and vanishes
at 5 T, while the first harmonic appears only at a field
of 4 T and saturates in intensity at 7 T. This behavior is
not directly related to the polarization flop but reflects a
variation of the modulation direction of the strain wave
leading to the superlattice reflections. However the most
remarkable behavior is found for the field dependence of
the wavevector. Here, the wave vector of the first har-
monic reflection does not change significantly through the
polarization flop transition at µ0H
C∼ 6.5 T.
3 Again this
is in sharp contrast to the behavior of TbMnO3, where a
discontinuous transition to a CM phase is found.
Below 6K, Dy spins order commensurately with δDym =
. Previously we have argued that the lattice distor-
tion associated with this magnetic ordering is not CM
but rather IC with δl ∼ 0.1b
∗.8 In our measurements we
found the half-integer magnetic reflection to be extremely
weak and we focused our attention to the lattice δl ∼ 0.1
satellite measured at (0, 0.9, 5). In Fig. 3a we show a
series of scans at different fields applied along the a-axis
at 3 K which show the rapid suppression of the δl ∼ 0.1
satellite which vanishes for fields µ0H‖a > 1 T. The CM
magnetic reflection (0, 0.5, 5) is only measurable at zero
field and can not longer be observed at 1 T. The tem-
perature dependence of the intensity and wavevector of
the (0, 0.9, 5) reflection is shown in Fig. 3b-c, revealing
the rapid suppression of the intensity of this reflection
at low temperature in accordance with the appearance
of ferromagnetic order (inset Fig. 3c), indicating an easy
axis along the b-direction. The suppression of this re-
flection with magnetic field is analogous to a similar be-
havior found for R =Tb which coincided with the ferro-
magnetic ordering of Tb-spins for the same field size and
configuration.10
The polarization flop is driven by the field-induced
0.4 0.6 0.8
k (r.l.u.)
s) (a)
µ0H=0T
µ0H=1T
µ0H=1.5T
(0 0.9 5), µ0H = 0T
(0 0.9 5), µ0H = 0.5T
(0 2δ 5),  µ0H = 0T
(0 0.9 5), µ0H = 1T
0 5 10 15 20
T (K)
(0 0.9 5)
0 2 4 6 8 10
B (T)
) H||b (T=2K)
H||a (T=8K)
FIG. 3: (color online) (a) Scans along (0, k, 5) at T = 3 K for
different applied magnetic fields with intensity in logarithmic
scale. (b) Temperature dependence as function of field H‖a of
the integrated intensity of the superlattice reflections (0, 0.9,
5) in the Dy ordered phase and the second harmonic reflection
(0, 2δ, 5) due to Mn order. Open and closed symbols repre-
sent increasing and decreasing temperature, respectively. In
(c) the wave vector of the (0, 0.9, 5) reflection is shown as
function of temperature for different fields. The inset shows
magnetization data of DyMnO3 for H‖a and H‖b.
flop of the axis of rotation of the magnetic spiral e. Its
direction is determined by magnetic anisotropy terms,
which to lowest order of the free energy expansion in
powers of magnetization of Mn spins have the form,∑
α=a,b,c
α. Phenomenologically the spin flop tran-
sition results from the field dependence of the coefficients
aα. Below the critical field HC , ab < ac < aa, which fa-
vors spins rotating in the bc plane (e‖a), while aboveHC ,
ab < aa < ac, favoring the rotation in the ab-plane (e‖c).
From the perspective of symmetry there is no restric-
tion that the high field spiral phase must be CM. In this
view the fact that there is a magneto-elastic phase tran-
sition to a CM phase associated with the flops in the
polarization for R =Tb would appear to be a special
case, especially when compared to R =Dy where we find
no such transition at HC . The difference in behavior
between these two multiferroics is not of fundamental
nature but rather simply lies in the magnitude of the
incommensurability. For R=Tb, δm=0.28 r.l.u. is close
to the CM value of 1
. For this CM value of the wave
vector the amplitude of the Mn magnetic moment is not
modulated10 and may thus be energetically more favor-
able than an IC amplitude modulated phase. In the phe-
nomenological approach the CM state with δ = 0.25 r.l.u.
is stabilized by M4 terms in the Landau expansion. For
R=Dy the value of δ=0.38 r.l.u. is further away from a
CM value (1
) and thus a transition to it is not favorable
energetically. Therefore the Mn spin spiral may indeed
flop as expected but without a change in δ.13 Clearly here
the modulation period in real space is much shorter, and
the amplitude of the Mn magnetic moment is modulated.
A significant difference between the two multiferroics
is found in the behavior of the complex magnetic or-
dering of R-ions. For R=Tb, Tb spins are induced to
order along the a-axis below TN with the same period-
icity as Mn-spins and below T TbN =7 K they order sepa-
rately with δTbm =0.42 r.l.u. At low temperatures, when
H‖a∼1 T, Tb-spins are aligned ferromagnetically, while
for field along the b-axis, δTbm jumps discontinuously to
a CM value of 1
at 1.75 T.10 The behavior for R=Dy
is much simpler, as below T
=6 K the Dy spins order
with δDym =
. Here, the suppression of the IC-reflections
together with the magnetization data indicates a melting
of the antiferromagnetic Dy ordering, a behavior different
to TbMnO3.
On the basis of the CM ordering of Mn-spins for the
P‖a phase for R=Tb it has been suggested that ferro-
electricity may arise in the absence of a spiral magnetic
ordering. Here an exchange striction mechanism pro-
posed from competing ferromagnetic and antiferromag-
netic super-exchange interactions predicts a P‖a phase
for a CM ordering with δ = 1
. This model holds strictly
for a CM ordering and suggests that for R=Dy the spi-
ral phase must be maintained at high fields to support a
ferroelectric state.
The smooth magnetic field dependence of the spiral
wave vector in DyMnO3 at the spin flop transition may
explain the large increase of the dielectric constant εa,
observed in this material.1,3 If higher-order terms in the
Landau expansion of free energy could be neglected, then
at the spin flop transition the magnetic excitation spec-
trum of the spiral would acquire a zero mode, since for
aa (HC) = ac (HC) there is a freedom to rotate the spi-
ral plane around the b axis. This mode can be excited
by electric field E‖a normal to the spiral bc-plane and
is the electromagnon studied in Ref. 12. Its softening at
H = HC would result in divergence of static dielectric
susceptibility εa. In reality, due to higher-order terms
in the Landau expansion the spin flop transition is of
first order, the softening of the magnetic mode is not
complete and the peak value of the dielectric constant
is finite. Still, in DyMnO3 this transition is close to a
second-order one in the sense that the spirals above and
below the critical field are essentially the same except for
their orientation. The softness of the spiral magnetic or-
dering at the critical field may be the reason behind the
large magnetocapacitance observed in DyMnO3 which
becomes truly gigantic close to the tricritical point at
the crossing of the collinear and two spiral phases with
P‖c and P‖a, where higher-order terms are small. In
TbMnO3 the spin flop transition is strongly discontin-
uous due to the concomitant IC-CM transition, which
limits the growth of the dielectric constant.
In summary, in-field synchrotron X-ray diffraction
measurements from a DyMnO3 single crystal have shown
that there is no change of the wave vector δ associated
with the flop of the ferroelectric polarization P at HC for
both H‖a and H‖c. This is in sharp contrast to similar
measurements reported for TbMnO3 were a transition to
a CM phase is found at HC for the same field configu-
rations. We argue that the magnitude of the incommen-
surability for R =Dy does not lie sufficiently close to a
CM value, as opposed to R=Tb, making the IC high field
phase energetically more favorable.
Acknowledgments
We would like to thank C.S. Nelson for the assistance
at the experiment at NSLS. Work at Brookhaven was
supported by the U.S. Department of Energy, Division
of Materials Science, under Contract No. DE-AC02-
98CH10886.
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