Evidence of electro-active excitation of the spin cycloid in TbMnO3

0.28 MB·English

by  A. M. Shuvaev

Evidence of electro-active excitation of the spin cycloid in TbMnO
3
A. M. Shuvaev,1 V. D. Travkin,2 V. Yu. Ivanov,2 A. A. Mukhin,2 and A. Pimenov1
1Experimentelle Physik 4, Universita¨t Wu¨rzburg, D-97074 Wu¨rzburg, Germany
2General Physics Institute, Russian Academy of Science, 119991 Moscow, Russia
(Dated: January 7, 2010)
Terahertz electromagnetic excitations in the multiferroic TbMnO3 at the field-induced magnetic
transitionareinvestigatedfordifferentorientationsofthemagneticcycloid. Inadditiontotheelec-
tromagnon along thea-axis,thedetailed polarization analysis of theexperimentalspectrasuggests
the existence of an electro-active excitation for ac electric fields along the crystallographic c-axis.
0 This excitation is possibly the electro-active eigenmode of the spin cycloid in TbMnO3, which has
been predicted within theinverse Dzyaloshinskii-Moriya mechanism of magnetoelectric coupling.
1
0
2
Multiferroics representan intriguing class of materials tionmustbe parallelto the c-axis(P c)andthe electro-

n k
in whichmagnetismandelectricityare stronglycoupled. magnonsshouldbeexcitedforacelectricfieldsparallelto
a
This magnetoelectric coupling leads to a mutual influ- the a-axis (e˜ a). Accordingly, for the ab-plane oriented
J
k
enceofmagneticandelectricordering,whichresultsina cycloid the polarizationP a and electromagnonsfor e˜ c
7
k k
rich new physics and in various possible applications [1– shouldbeobserved. Thisbasicallycorrespondstothein-

] 4]. Recently, a new class of multiferroics has attracted terchangeoftheaandc-axesintheexcitationconditions.
l
e enormous interest because the ferroelectric polarization Although the orientation of the static electric polariza-
- inthese systemsis inducedbyacycloidalorderingofthe tionhas been confirmedin many experiments [5, 24,25],
r
t magnetic moments [5–7]. The magnetic and electric or- the excitation conditions for the electromagnon contra-
s
. der in these materials are accompanied by coupled spin- dicted the predictions of the model: the selection rules
t
a latticevibrations[8]showingstrongelectricdipoleactiv- for the excitations remained the same (i.e. e˜ a) inde-
m k
ity andtermed electromagnons[9, 10]. Initially detected pendently of the orientation of the cycloid [11–19]. In
- in GdMnO3 and TbMnO3 [11], the electromagnons ap- order to account for this contradiction, a model based
d
peartoexistincycloidalmagneticphasesofmanydiffer- onHeisenbergexchangecouplingbetweenspinshasbeen
n
o ent multiferroics [12–19]. In most cases, distinct struc- proposed recently [18, 26, 27]. According to this model,
c ture of these excitations is seen including two or more the structural peculiarities of orthorhombic multiferroic
[
separate modes. For example, in TbMnO3 one can ob- manganites lead to the selection rules e˜ a regardless of
k
1 serve at least 3 excitations: two with the energy around the orientation of the spin cycloid.
v 2 meV (10-20 cm−1) and the third one at 8 meV
8 (≃60 cm−1). ≃ The Heisenberg exchange model assigns the high en-
4 Ferroelectric polarization in spiral magnets has been ergy electromagnons observed between 60 cm−1 and
1 successfully explained on the basis of the inverse 80 cm−1 to the zone edge magnons [18, 26–28], but
1
. Dzyaloshinskii-Moriya (DM) coupling between the mag- the nature of the lower energy elecromagnons close to
1 netic moments [20–22]. Within this model a spiral spin 20 cm−1 remains uncertain. It seems reasonable to re-
0
0 structure lowers the symmetry of the system leading to callthe statements ofthe DMmodel andto assume that
1 an effective magnetoelectric coupling term and an elec- the low-frequency electromagnons are somehow related
: trical polarization P in the form totheexcitationsofthespincycloidobservedbyinelastic
v
neutronscattering(INS)[29–31]becausethecharacteris-
i
X P e S S . (1) tic frequencies coincide closely [29, 32]. This assumption
ij i j
∼ × ×
r issupportedbyarecentobservationofthemagneticexci-
a
Here S and S are the neighboring spins and e is the tationchannelfor electromagnons[32] whichcanbe also
i j ij
latticevectorconnectingthem. Consequently,itwasrea- seenasantiferromagneticresonances(AFMR)withincer-
sonable to assume the same mechanism to explain the tain excitation conditions. However, in order to prove
existence of the electromagnons [23]. In this model the this assumption, the predicted excitation conditions for
electromagnons are the eigenmodes of the spin cycloid the eigenmodes of the cycloid should be found experi-
which can be excited by electric component of the elec- mentally. Most specifically, one should expect the ex-
tromagnetic wave [9]. However, after initial success of citation conditions along the c-axis if the spin cycloid is
this explanation a number of experimental results con- orientedintheab-plane. Suchexcitationconditionswere
tradicted the predictions of the model. The basic exam- not observed up to now [26, 32]. A possible reason for
ple can be given by TbMnO3 at low temperatures: the this fact is the weakness of the dielectric contribution of
DMmodelpredictsthattheexcitationconditionsforthe the spin modes within the DM mechanism. In order to
electromagnon should be tied to the magnetic cycloid, resolvethisexperimentaldifficulty,TbMnO3 seemstobe
i.e. forthebc-planeorientedcycloidtheelectricpolariza- an ideal candidate, because the magnetic cycloid can be
2
rotated between ab-plane and bc-plane in external mag- ν << ν0 ν ≤ ν0 ν ≥ ν0 ν >> ν0
netic fields. Thus the ultimate experiment must follow 4.7 cm-1 15.8 cm-1 20 cm-1 28 cm-1
4.17 4.19 4.17
the c-axis response at the magnetically induced rotation 4.15
of the cycloid.
n
In this work we have carried out detailed polarization
analysis of terahertz excitations in TbMnO3. Special at- 4.15 4.17 4.15 "ab"
10 4.13
tention has been payed to the selection rules of different
etoxcaitba-tpiloannseuipnonexttheernraoltamtiaognnoetfitchfieeslpdinBcybc-laoxidis.froItmwbacs- 0.06 0.06 0.06 B (T) "bc" ICPM
0
foundthatanewexcitationarisesinthe hkigh-fieldphase 0 T (K) 40 0.025
κ
with excitation conditions e˜ c and h˜ a. We argue that
k k
thisexcitationcouldnotbeexplainedbypurelymagnetic
0.02 0.02 0.02
contribution but carries substantial electric component. 0.02
0 2 4 6 2 6 2 6 2 6
The transmittance experiments at terahertz frequen-
B (T) B (T) B (T) B (T)
cies (3 cm−1 < ν < 30 cm−1) have been carried out
in a Mach-Zehnder interferometer arrangement [33, 34] FIG. 1: Dependence of refractive index (n = Re(√εµ), up-
whichallowsmeasurementsofamplitude andphase shift per panels) and absorption coefficient (κ = Im(√εµ), lower
in a geometry with controlled polarization of radia- panels)inTbMnO3 onmagneticfieldB b-axisatvariousfre-
k
quencies on crossing the phase transition from the bc- to the
tion. The experiments in external magnetic fields up
ab-orientedmagneticcycloid. Polarization ofincidentwaveis
to 8 T have been performed in a superconducting split- e˜ c, h˜ a, where e˜ and h˜ are electric and magnetic ac fields
coil magnet with polypropylene windows. Single crys- okfthekelectromagnetic wave. TheinsetshowsB-T phasedia-
talsofTbMnO3 havebeen grownusingthe floating-zone gramofTbMnO3forB b[24]. “ab”and“bc”denoteab-plane
k
method with radiation heating. The samples were char- and bc-plane oriented cycloids, respectively, PM - paramag-
acterized using X-ray, magnetic, dielectric and optical netic and IC - sinusoidal phases.
measurements [9, 35]. The results of these experiments
including the magnetic phasediagramarecloselysimilar
−1
to the published results [24]. refractiveindexbelow10cm . Thechangesobservedat
The paramagnetic phase in TbMnO3 above 40 K is 4.7cm−1 canbewellunderstoodassumingasuppression
followed by a sinusoidally-modulated antiferromagnetic of a Lorentzian mode situated between 5 and 6 cm−1.
statewhichtransformsbelow28Kintothecycloidalspin Three higher frequency scans (15.8, 20, and 28 cm−1)
structure oriented within the bc-plane [36, 37] (inset in in Fig. 1 show more systematics, and can be reduced
Fig. 1). According to the symmetry analysis [6, 22] and to a growth of the absorption mode around 20 cm−1 in
Eq. (1), static electric polarization along the c-axis is the phase with the ab-plane cycloid. This is a typical
allowed in the low-temperature phase. In external mag- behavior for a Lorentz oscillator which appears close to
neticfieldsthespin-cycloidrotatesfrombc-planetowards 20 cm−1 simultaneously with the ab-plane cycloid. In-
theab-plane[25,31]. Correspondingly,theelectricpolar- deed, strong additional absorption arises near the fre-
ization rotates from P c-axisto the P a-axis [5, 24, 25]. quency 20 cm−1 and is substantially reduced above
Dynamic experimenkts on TbMnO3kin external mag- and belo≃w this frequency (lower panels, 28 cm−1 and
netic fields reveal that the c-axis properties are indeed 16 cm−1, respectively). In addition to a strongly in-
sensitive to the orientation of the cycloid. The exam- creased absorption around the resonant frequency, the
plesofsuchchangesareshowninFig.1whichrepresents refractive index in Lorentzian model may in rough ap-
theterahertzpropertiesofTbMnO3 inexternalmagnetic proximation be simplified to the following statements:
field B b inducing the transition from bc-plane to ab- n(ν) n∞+∆n forν <ν0 andn(ν) n∞ ∆n(ν0/ν)2
k ≈ ≈ −
plane orientedcycloid. The magnetic fieldscans inthese for ν > ν0. Here n∞ is the contribution from the
experiments were made in the geometry with e˜ c and high-frequency processes,∆n reflects the strength of the
h˜ a and at T = 10 K. The data are representedkas re- Lorentzian mode, and ν0 20 cm−1 is the resonance
k ≈
fractiveindexn+iκ=√εµasbothelectricandmagnetic frequency. Therefore, after the growth of the Lorentzian
contributionscould be mixed inthis experimentalgeom- (∆n = 0 ∆n = 0) at the magnetic transition we
etry. The transitionfrom bc-plane to ab-plane cycloidin expect an→increase6 of the refractive index below the
the high magnetic fields is clearly seen. Already at this resonance frequency and a decrease above it. This is
pointitisevidentthattheobservedchangesarestrongly roughly the behavior of the refractive index, observed
−1 −1 −1
frequency dependent. Here the data at 4.7 cm is in- at 15.8 cm (ν < ν0) and 28 cm (ν > ν0). The
fluenced by a Tb-mode around 5 cm−1 [32] which disap- main changes, seen in Fig. 1, appears at the magnetic
pears in the high-field phase with the ab-plane cycloid. transition and are therefore related to the rotation of
This leads to a substantial decrease of the absorption the magnetic cycloid. However, better understanding of
(κ(4.7 cm−1)) and reveals a bit complicated structure in the underlying processescan be obtainedwithin a direct
3
20
on 15 ~~~hhh |||||| aaa,,, ~~~eee |||||| ccc,,, BBB === 057 TTT ∆ε + ∆µ
si 0.1 1) ~h || a, ~e || b, B = 8 T
mis -cm10
ns T~e bIIM bn, O~h3 II a α (0 ∆µ only
a T = 6 K B = 0 T − 5
Tr B = 6 T α
B = 8 T
0.01 0
-5 10 15 20 25
n λ-1 (cm-1)
o
si
mis 0.1 FIG.3: Linearabsorptioncoefficientα=4πκλ−1inTbMnO3
ns T~e bIIM cn, O~h3 II a for different polarizations showing the emergence of an addi-
a T = 6 K B = 0 T tionalmodein thephasewith theab-cycloid (green triangles
Tr B = 5 T and blue crosses). Symbols are experimental data calculated
B = 7 T
µ only fromtransmittancespectraasdescribedinthetext. Linesare
0.01 10 15 20 25 30 model calculations using Lorentz oscillators with the same
λ-1 (cm-1) parameters as in Fig. 2. The data are shifted vertically to
eliminate background absorption in different samples.
FIG. 2: Transmittance spectra of TbMnO3 in external mag-
netic fields B b for different experimental geometries. Sym-
k
bolsareexperimentaldataandsolidlinesarefitswithLorentz results agree well with the original explanation of the
oscillators as discussed in the text. electromagnons as electrically active eigenmodes of the
cycloidal structure [9, 23].
In order to make the discussion quantitative, the ex-
analysisofthe spectrainthe relevantfrequencyrangeas
perimentalspectraintheupperpanelofFig.2werefitted
presented below.
with magnetic Lorentz oscillator. If we now take the pa-
Figure2showsthe fielddependentspectrafortwodif- rameters of the mode from the geometry with e˜ b and
k
ferent geometries of the experiment. The thicknesses of plot the expected transmittance spectra for the geome-
the samples are similar for both orientations: 1.24 mm trye˜ cweobtainthe absorptionvaluewhichistooweak
k
(upper panel) and 1.33 mm (lower panel), respectively. compared to the experiment (the “µ only” curve in the
The spectra in the lower panel with e˜ c and h˜ a cor- lower panel of Fig. 2). The only possible explanation is
k k
respond well to the known results [26, 32] and show a thatthismodehasdistinctnon-zeroelectriccontribution
mode at about 21 cm−1 which appears after the field in- along the c-axis. The actual fit for this geometry was
ducedreorientationofspincycloidtotheab-plane. Based obtainedbytakingparametersofthe magneticoscillator
on the weakness of this mode, both in Ref. [26] and in from e˜ b, h˜ a geometry and adding an electric oscillator
Ref. [32] it has been concluded that the mode around with thke sakme resonance frequency ν0 = 20.7 cm−1 and
21 cm−1 is of purely magnetic origin and represent an line width γ = 4.9 cm−1 as the magnetic one. The rea-
antiferromagnetic resonance of the magnetic cycloid for soningbehindthisassumptionisthatbothcontributions
h˜ a-axis. Indeed, the strength of this mode (∆ε 0.05, are electric and magnetic parts of the same eigenmode
k ∼
assuming electric origin) is extremely weak compared to ofthe spin cycloid. The strengths ofboth components is
electromagnon observed for e˜ a (∆ε 2) [9, 11]. The given by ∆µ=0.0038 and ∆ε=0.05, respectively.
mode in Fig. 2 is observed forkthe ab-∼plane cycloid and Figure 3 shows the linear absorption coefficients α =
withinh˜ aexcitationconditions. Tracingthismodeback 4πκλ−1 which allow direct comparison of different ex-
into thekbc-orientedcycloid in zero external fields, it can perimental geometries. Symbols were calculated from
be expected to originate from the excitation conditions transmittance spectra T using the expression T = (1
h˜ c. (Thiscorrespondstotheinterchangingofthea-axis R)2exp( αd), where R= (√εµ 1)/(√εµ+1)2 is th−e
ankd c-axis). Indeed, an AFMR mode excited for ˜h c of reflectan−ceontheboundary| betwe−entheairandt|hesam-
k −1
the similar strength has been observed around 21 cm ple, and d is the sample thickness. Solid lines are model
in the phase with the bc-plane cycloid [32]. calculationsusingthe sameparametersasinFig.2. One
A careful comparison of both panels in Fig. 2 reveals canseeagainthatthemodeat21cm−1 isstrongerinthe
interesting difference between two excitation conditions. case of e˜ c and ˜h a excitation. (A weak narrow mode
The strength of the mode in the geometry where e˜ b is seen closekto 22 cmk−1 for e˜ b, h˜ a geometry is possibly
k k k
roughlythehalfofthatwheree˜ c. Thisstronglysuggests due to impurities in the sample. The strength of this
k
that for geometryin whiche˜ c the electric dipole contri- mode is at least an order of magnitude smaller than the
k
butionisindeedmeasurableandrepresentthepreviously strengthofthe broadmodeanddoesn’tchangethe over-
unobservede˜ ccounterpartoftheelectromagnon. These all picture.)
k
4
The mode intensity for the “main”e˜ a electromagnon by RFBR (09-02-01355).
k
(∆ε 2 [11]) is about 40 times stronger than electric
a
contrib≃ution along the c-axis (∆ε 0.05) observed in
c
≃
the present experiment. The large electromagnon ab-
sorptionalongthea-axiswasoneofthechallengingques-
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