Domain dynamics in the multiferroic phase of MnWO4
D. Niermann1, C.P. Grams1, M. Schalenbach1, P. Becker2, L.
Bohaty2, J. Stein1, M. Braden1, and J. Hemberger11II.
Physikalisches Institut, Universitat zu Koln, Zulpicher Str. 77,
D-50937 Koln and
2Institut fur Kristallographie, Universitat zu Koln, Greinstr.
6, D-50939 Koln, Germany(Dated: April 26, 2014)
By using broadband linear and non-linear dielectric spectroscopy
we studied the magnetoelectricdynamics in the chiral
antiferromagnet MnWO4. In the multiferroic phase the dielectric
responseis dominated by the dynamics of domains and domain walls
which is strongly dependent on thestimulating electric field. The
mean switching time reaches values in the minute range in the
middleof the multiferroic temperature regime at T 10 K but
unexpectedly decays again on approachingthe lower, first-order
phase boundary at TN1 7.6 K. The switchability of the ferroelectric
domainsdenotes a pinning-induced threshold and can be described
considering a growth-limited scenariowith an effective growth
dimension of d 1.8. The rise of the effective dynamical coercive
field oncooling below the TN2 is much stronger compared to the
usual ferroelectrics and can be describedby a power law Ec 1/2. The
latter questions the feasibility of fast switching devices based
onthis type of material.
PACS numbers: 75.85.+t, 75.78.-n.Fg, 77.80.B-.Fm, 75.30.Mb,
75.60.Ch
A. Introduction
In recent years magnetoelectric multiferroics have at-tracted
considerable interest within the community ofcorrelated
transition-metal compounds1,2. In these com-pounds ferroelectric
order and magnetism do not only co-exist in a single phase but
exhibit strong coupling of theferroic order parameters. Among other
mechanisms theprobably most established magnetoelectric coupling
sce-nario is based on the inverse Dzyaloshinskii-Moriya
(DM)interaction in partially frustrated spiral magnets3,4. Thistype
of magnetically driven ferroelectricity is the under-lying
mechanism, e.g., in the numerously studied familyof multiferroic
manganites such as TbMnO3
5,6 and inprinciple is now well understood. In these compounds
anon-collinear cycloidal spin-structure is directly coupledto a
ferroelectric polarization resulting from the coher-ent distortion
of the Mn-O-Mn bonds perpendicular tothe propagation vector of the
spin-cycloid. However, themanifestation of a magnetoelectrically
coupled multifer-roic phase and the formation of the complex,
magneto-electric order parameter raises questions concerning
thecorresponding dynamics.
One aspect is given by the elementary excitationswithin the
ordered multiferroic phase, the so calledelectromagnons, as they
were detected, e.g., in per-ovskite manganites in a typically
sub-phononic regionbelow terahertz frequencies79. Another aspect is
thelow frequency dielectric response originating from in-trinsic or
extrinsic sample inhomogeneities. In materi-als with a residual
conductivity, which in addition maybe dependent on external fields,
contributions of con-tacts or grain boundaries may add capacitive
or evenmagneto-capacitive contributions, which will cover
theintrinsic sample properties1013. Also one may find re-laxational
features resulting from localized polarons atdefect states as,
e.g., demonstrated for the case of per-ovskite rare-earth
manganites above and within the mul-
tiferroic phase14. But even though one avoids these
lattercontributions by choosing a suitable, i.e. well
insulating,high purity single crystalline material as we did in
thisstudy, the formation of domains and their emergent dy-namics
will dominate the dielectric response of the mul-tiferroic
system1518.
The system MnWO4, the mineral name is hubnerite,represents the
above described class of magnetoelec-tric multiferroics, in which
the ferroelectricity is drivenby the onset of chiral spin order via
the inverse DMinteraction1921. Its crystal structure in the
paramag-netic phase is monoclinic with space group P2/c andcan be
thought of as alternate stacking of the Mn2+ andW6+ ions along the
a-axis, both being octahedrally co-ordinated by oxygen22. Along the
c-direction the Mnsites carrying the partially frustrated S = 5/2
spinsform zig-zag chains. Cooling down from higher temper-atures
the spin-system orders at TN3 = 13.5 K into anincommensurate,
collinear antiferromagnetic, sinusoidalspin-density wave with an
easy spin-axis within the ac-plane. On further cooling at TN2 12.6
K a secondorder phase transition occurs into a non-collinear
phasewith the same propagation vector. In this phase a chi-ral
spin-spiral with a spin-current not parallel to thepropagation
vector emerges breaking the spatial inver-sion symmetry. This
results in the formation of elec-tric polarization along the
b-direction that can be welldescribed by the inverse DM
interaction1921. Finally,below TN1 7.5 K the spin arrangement
becomes com-mensurate and collinear via a first-order phase
transition,losing the ferroelectricity again. To summarize with
re-spect to the dielectric properties the multiferroic
phase(ferroelectric with chiral spin structure) lies in the
tem-perature range TN1 = 7.5 K< T < TN2 = 12.6 K, em-bedded
between a paraelectric phase with collinear sinu-soidal spin order
at higher temperature and a paraelectricphase with collinear
antiferromagnetic spin order at lowertemperature (see Fig. 1). In
this article we report on
arX
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v2 [
cond
-mat.
str-el
] 24
Apr
2014
2broadband spectroscopic investigations of the linear
andnon-linear complex permittivity in high quality MnWO4single
crystals above and within the multiferroic phasefor frequencies
from mHz to MHz and in electric fieldsup to 1000 V/mm in order to
shed light on the dynami-cal dielectric response of the system.
B. Experimental details
Single-crystals of MnWO4 were grown from the meltusing the
top-seeded growth technique, as described inRef. [23]. The samples
are ruby-red transparent and in-sulating above our measurement
capabilities of 200 Tin the regarded temperature regime, which is
indica-tive of a very low concentration of charge-doping de-fects.
Structural and magnetic measurements confirmedthe known behavior:
The samples exhibit the monoclinicspace group P2/c and show the
above described sequenceof phase transitions at TN1 7.6 K, TN2 12.6
K, andTN3 13.5 K1921. The dielectric measurements wereperformed in
a commercial 4He-flow magneto-cryostat(Quantum-Design PPMS)
employing a home-madecoaxial-line inset. The complex, frequency
dependent di-electric response () was measured using a
frequency-response analyzer (Novocontrol) for frequencies from1 mHz
to 1 MHz. For higher frequencies up to 200 MHz amicro-strip setup
was employed and the complex trans-mission coefficient (S12) was
evaluated via a vector net-work analyzer (Rohde & Schwarz). All
measurementswere performed with the electric field along the
crystal-lographic b-axis, the direction in which the
spontaneousferroelectric moment points in zero external
magneticfield20,21. If not denoted otherwise, the measurements
ofthe complex permittivity were carried out with a stimulusof the
order Eac 1 V/mm. Additional measurementsin higher fields up to
1000 V/mm were conducted em-ploying a high-voltage option for the
frequency responseanalyzer (Novocontrol HVB1000). The
non-linearpermittivity contributions were obtained via the
Fouriercomponents of the dielectric response. These higher
har-monics are directly evaluated from the normalized cur-rent
response at multiples of the base frequency n bythe firmware of the
frequency-response analyzer (Novo-control).
The quasi static P (E)-measurements and the P (T )-data
integrated from pyro-current measurements wererecorded using a
high-precision electrometer (Keithley6517B). In all cases, the
contacts were applied to theplate-like single-crystals using silver
paint in sandwichgeometry with a typical electrode area of A 2
mm2and a sample thickness of d 0.3 mm. The uncertaintyin the
determination of the exact geometry together withadditional (but
constant) contributions of stray capaci-tances results in an
uncertainty in the absolute values forthe permittivity of up to 30
%.
In Fig. 2 the real part of the dielectric permittivity(T ) is
shown for different frequencies covering a span
P 0P = 0
TTN2TN1
P = 0
eijeij eij
7.6 K 12.6 K
FIG. 1: Schematic sketch of the magnetically ordered phasesin
MnWO4.[24]
1 1 1 2 T N 2 1 3 1 41 0 . 2
1 0 . 4
1 0 . 6
1 0 . 8
T ( K )
'
1 0 0 m H z . . . . . . 1 0 0 M H z1 2 1 31 0 . 1
1 0 . 2
1 0 . 3 2 0 0 k H zM n W O 4
2 0 0 M H z
FIG. 2: (Color online) Real part of the dielectric permittivity
of MnWO4 for different frequencies between 100 mHz and100 MHz in
equidistant spacing measured with a stimulus of1 V/mm and as a
function of temperature around the mul-tiferroic transition at TN2
12.6 K. The inset shows a zoomon higher frequencies.
of nine decades and a temperature region including both,the
phase transition into a sinusoidal spin density waveat TN3 13.5 K
and the transition into the multiferroicphase at TN2 12.6 K. While
the paraelectric to para-electric transition at TN3 apparently has
no pronouncedeffect on the linear dielectric permittivity, clear
anoma-lies can be detected in the (T ) curves at the para-electric
to multiferroic/ferroelectric transition at TN2.Characteristic for
these anomalies is a distinguished fre-quency dependence. Usually
permittivity measurementswith such small stimuli are performed
using capacitancebridges working at one single frequency, typically
1 kHzor 10 kHz. Using smaller frequencies broadens the tail in(T )
below the transition. Also the peak height at thetransition is
strongly dispersive and suppressed for higherfrequencies (see inset
of Fig. 2). The general behavior,i.e. having a flat non-dispersive
dielectric backgroundon the order of 10, is in accordance with
otherpublished data1921. The small weight of the anomalyat the
transition compared to the dielectric backgroundreflects, that the
ferroelectric moment of the multiferroicphase is nearly four orders
of magnitude smaller thanin ordinary ferroelectrics where a
Curie-Weiss-like diver-gence dominates (T )25. It has to be noted,
that thesmall frequency dependent shift in 10 may be dueto
apparatus-based uncertainties concerning the absolutevalues and
shall not be regarded in the following, the rel-ative uncertainty
is much smaller of course. In the fol-
