Investigation of infrared phonon modes in multiferroic single-crystal FeTe$_{2}$O$_{5}$Br

0.71 MB·English

by  K. H. Miller

Investigation of infrared phonon modes in multiferroic single-crystal FeTe O Br
2 5
K. H. Miller,1 X. S. Xu,2 H. Berger,3 V. Craciun,4 X. Xi,1 C. Martin,1 G. L. Carr,5 and D. B. Tanner1
1Department of Physics, University of Florida, Gainesville, Florida 32611-8440, USA
2Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
3Institute of Physics of Complex Matter, Ecole Polytechnique Federal de Lausanne, CH-1015 Lausanne, Switzerland
4Major Analytical Instrumentation Center, Materials Science and Engineering,
University of Florida, Gainesville, Florida 32611, USA
5Photon Sciences, Brookhaven National Laboratory, Upton, New York 11973, USA
Reflectionandtransmissionasafunctionoftemperature(5–300K)havebeenmeasuredonsingle
3 crystals of the multiferroic compound FeTe2O5Br utilizing light spanning the far infrared to the
1 visibleportionsoftheelectromagnetic spectrum. Thecomplexdielectricfunctionandopticalprop-
0 ertieswereobtainedviaKramers-KroniganalysisandbyfitstoaDrude-Lortentzmodel. Analysisof
2 theanisotropicexcitationspectraviaDrude-Lorentzfittingandlatticedynamicalcalculations have
lead to theobservation of all 52 IR-activemodes predicted in the ac plane and 43 or the53 modes
n
predictedalong theb axis of themonoclinic cell. Assignments togroups (clusters) of phononshave
a
J been made and trendswithin them are discussed in light of our calculated displacement patterns.

4
2
I. INTRODUCTION threecrystallographicaxes. Thesignificantmagnetoelec-

] tric coupling previously shown by the application of ex-
el Recently, significant attention has been given to a ternal magnetic fields did not surface in the far infrared
- class of multiferroics in which specific magnetic ordering to the extent we examined it. However, we present a
r
t breaks inversion symmetry, thus allowing spontaneous comprehensivereportoftheexcitationspectruminsingle
s
. polarizationto arise. This magnetically driven ferroelec- crystal FeTe2O5Br. The modeling of the infrared active
at tric response is the most direct form of magnetoelectric phonons as well as lattice dynamical calculations have
m coupling and is associated with large magnetoelectric1 lead us to make an interesting comparison to a previ-
- and magnetocapicative2 responses. Electric dipoles in- ous infrared study on a similar geometrically frustrated
d duced by the orderingof magnetic dipoles remain highly spin-cluster oxyhalide compound, FeTe2O5Cl,11 where
n susceptible to applied magnetic fields, thus making this an equal number of modes was predicted but a signifi-
o classofmultiferroicsofinterestfromatechnologicalpoint cantly lower number was reported.
c
[ of view.3 Recent studies on materials such as TbMnO3,4 Beckeretal.12solvedthecrystalstructureusingsingle-
RbFe(MoO4)2,5andCoCrO46allshowtheappearanceof crystal x-ray diffraction. The FeTe2O5Br compound
1 spontaneous polarization due to non-collinear magnetic crystallizes in a layered structure where the individual
v ordering via spin-orbit mechanisms, viz., the standard layers comprise the bc plane in the monoclinic system
1
8 spin-current and inverse Dzyaloshinski-Moriya models. (P21/c). The layers are weakly connected via van der
◦
8 Atechnologicalshortcomingofmagneticallydrivenferro- Waalsforcesandslipatan18 angle asthey stackalong
5 electricshasbeenthesmallvalueofinducedspontaneous the normal to the bc plane, thus defining the monoclinc
1. electric polarization observed. Much larger spontaneous a axis. A single layer is composed of [Fe4O16]20− groups
0 polarizationshavebeenpredictedinmaterialswherefer- confined on top and bottom by [Te4O10Br2]6− groups.
3 roelectricity arises from collinear magnetic ordering of Thethreegroupscontaincommonoxygenswhichconnect
1 spins.7,8 In collinear magnetic ordering, moments may them and also serve to create charge neutrality within
v: vary in amplitude but do not vary in direction; there- the layers. The [Fe4O16]20− groups consist of four edge-
i fore, one does not expect the aforementioned spin-orbit- sharing[FeO6]distortedoctrahedra. Allironionspossess
X relatedinteractionsto be important,9 enablingthe much a +3 oxidation state. More detailed descriptions of the
r strongerexchangestrictioninteractionasthemechanism crystal structure are found elsewhere.12
a
by which ferroelectricity is induced. The FeTe O Br compound exhibits nearly-collinear
2 5
◦
In this paper, we report our infrared studies on sin- (7 ofcantingbetweentheFe1andFe2sites)incommen-
gle crystals of the multiferroic FeTe O Br compound, a surate antiferromagnetic ordering of its moments below
2 5
magneticallydrivenferroelectricwithnearly-collinearin- T = 10.6 K.13,14 The amplitude-modulated magnetic
N
commensuratespinorder. ApreviousstudybyPregeljet orderis describedwith the wavevectorq=(1/2,0.463,0).
al.10 hasreportedsignificantchangesinthemagneticand Simultaneously, a ferroelectric polarization is induced
electric orders when external magnetic fields are applied perpendicular to q and the Fe3+ moments.13 The fer-
alongthedifferentcrystallographicdirections. Strikingly, roelectric order is attributed to the highly polarizable
for Bkb they observed that fields greater than 4.5 T de- Te4+ lone pair electrons. Single-crystal x-ray diffraction
stroyedtheelectricpolarizationcompletely. Inourinves- measurements in the ordered state did not detect any
tigation of magnetoelectric coupling we measured trans- change in crystal symmetry from the high temperature
missioninthefar-infrareddownto15cm−1 (2meV)and phase; however, clearly distinguishable changes in Fe-
in external magnetic fields up to 10 T oriented along all Te and Fe-O interatomic distances were observed that
2
signified exchange striction as the means by which the of our flow cryostat with a copper clamp, the cooling
inversion center is removed, thus allowing for ferroelec- capabilities, below 10 K, agreed to within ±1 K.
tricity to arise.14 Exchange striction is the mechanism In materials where the crystalsymmetry is lowerthan
bywhichmagneticionsshift awayfromtheir centrosym- cubic, electrical excitations strongly depend on the ori-
metric positions to maximize their exchange interaction entation of the electric field. For these low symmetry
energies.3,4 crystals,the dielectric constantis a 3×3 tensor and will
generally have off diagonal components. For every crys-
tal symmetry, however, there exists a set of orthogonal
II. EXPERIMENTAL PROCEDURES Cartesianaxes,calledtheprincipaldielectricaxes,which
diagonalize the dielectric tensor.16 In an optics experi-
SinglecrystalsofFeTe O Brhavebeengrownbystan- ment, the principal dielectric axes are found by rotating
2 5
dard chemical vapor phase method. Mixtures of ana- theorientationofthesamplewhichisplacedbetweentwo
lytical grade purity Fe O , TeO and FeBr powder in polarizers that are crossed and remain fixed. Through-
2 3 2 3 ◦
molar ratio 1:6:1 were sealed in the quartz tubes with outarevolutionof360 ,fourorthogonalorientationswill
electronic grade HBr as the transport gas for the crys- result in zero transmitted light beyond the second po-
tal growth. The ampoules were then placed horizontally larizer. These four dark orientations correspond to the
into a tubular two-zone furnace and heated very slowly electric field of the incoming light aligning itself parallel
by 50◦C/h to 500◦C. The optimum temperatures at the to a principal dielectric axis of the system.
sourceanddepositionzonesforthegrowthofsinglecrys- For a monoclinic system, the crystallographic b axis
tals have been 500◦C and 440◦C, respectively. After six is unique because it is perpendicular to both the a and
weeks,manydarkyellow,almostorangeFeTe O Brcrys- c axes. Accordingly, one principal dielectric axis of the
2 5
talswithamaximumsizeof8×12×1mm3wereobtained. systemis fixed along the crystallographicb axis,but the
Thepowderx-raydiffractionpatternobtainedbyusinga other two axes can orient themselves arbitrarily as long
Rigaku x-ray diffractometer shows the monoclinic space as they remain orthogonal. Consequently, we performed
group P2 /c for all FeTe O Br crystals. single crystal x-ray diffraction on crystal 1 with knowl-
1 2 5
The zero-field temperature-dependent (5–300 K) re- edgeofhowtheprincipaldielectricaxesfellinrelationto
flectance and transmittance measurements were per- the crystal facets in order to determine their orientation
formed on a 1.3×8×6 mm3 single crystal (crystal 1) with respect to the a and c crystallographic directions.
using a Bruker 113v Fourier transform interferometer in X-raydiffractionmeasurementswerecollectedat300K
conjunctionwitha4.2Ksiliconbolometerdetectorinthe on a four-circle Panalytical X’Pert MRD in a parallel
spectral range 25–700 cm−1 and a 300 K DTGS detec- beamgeometrywithKαradiation. Aθ-2θ scanwasused
tor from 700–7,000 cm−1. The crystal was cooled using to check that the sample surface corresponded to the bc
a flow cryostat. Room temperature measurements from plane while pole figure measurements were performed to
7,000–33,000cm−1wereobtainedwithaZeissmicroscope find the spatial orientation of the a axis with respect to
photometer. Appropriate polarizers were employed to the bc plane.
span the desired spectral range.
Field-dependent transmissionmeasurementsinthe far
infrared at a resolution of 0.25 cm−1 were performed on
a 0.3 × 8 × 5 mm3 single crystal (crystal 2) at beam III. RESULTS AND ANALYSIS
line U4IR of the National Synchrotron Light Source,
Brookhaven National Laboratory. The measurements
A. X-Ray diffraction
employed a Bruker IFS 66-v/S spectrometer in conjunc-
tion with a 10 T Oxford superconducting magnet and a
1.8 K silicon bolometer detector. A free standing wire The diffraction experiment showed that the crystallo-
grid polarizer was oriented along the preferential polar- graphic c axis also coincides with a principal dielectric
ization direction of the synchrotronbeam. axis of the system. Furthermore, the third principal di-
◦
At this point it is important to establish with confi- electricaxismakesan18 anglewiththecrystallographic
dence that we cooled our single crystal below 10 K in a axis. TheXRDpatternsacquiredfromthesamplewith
both the Oxford superconducting magnet and the Janis thesurfacealignedperpendiculartothediffractionplane
flow cryostat. The superconducting magnet is equipped are displayed in Fig. 1. Only very narrow (h00) diffrac-
with a variable temperature insert that cools in liquid tionlines wereobserved,confirming thatthe sample was
He vapors. This same system has been used to accu- ahighqualitysinglecrystal,withthesurfacealignedpar-
rately measure the properties of superconducting mate- alleltothebc plane. Severalacquiredpolefigureshelped
rialsdownto2K.15 Theaccuracyofthecoolingcapacity identify the orientation of the a axis with respect to the
of the flow cryostat was corroborated by comparing ra- bc plane. The inset to Fig. 1 contains the results of our
tios of T /T for the superconductor Nb Ti N with XRDinvestigation,namely,asketchofcrystal1withthe
s n 0.5 0.5
thosesameratiosmeasuredinthe superconductingmag- principal dielectric axes (eˆ , eˆ , and eˆ ) superimposed
A B C
net. With thesuperconductorfastenedtothe coldfinger on the monoclinic crystal axes.
3
4000 can be used to rule out H O. Therefore the structures
2
b. units)3000 (100) (200) (400) desudiffggegereaesnltocanebgsseˆoinBrpeatnnioednrgseˆyCthorafetitnahfreoerhicneigttrhhinefsraiecnqtuisoeonFtcreoyTpety2rOasen5esBnmri.inssTtiohhnee
ar2000 optical conductivity at high frequencies (Fig. 3).
(
y
t
Intensi1000 (600) (700) 800) C. Field-dependent transmittance
0 (
10 20 30 40 50 60
2θ (degree) Crystal 2 transmits at frequencies below the strong
infrared phonons, in the gaps in-between the phonons,
FIG.1. TheXRDpatternforthesamplesurfacealignedper- andin the mid infraredbetween the highest phononand
pendiculartothediffraction plane. Theinsetdepictstheori- the onset of interband transitions. Particular attention
entation of the principal dielectric axes and crystallographic
was given to the transmission below the strong infrared
axes with respect to thefacets of crystal 1.
phonons. No appreciable change in the spectra were
observed for transmittance at 5 K measured along eˆ
B
and eˆ with magnetic fields of 10 T applied along all
B. Reflectance and Transmittance Spectrum C
three crystallographic directions. A class of low energy
magnetic excitations called antiferromagnetic resonance
The temperature-dependent reflectance spectrum of modes (AFMR) are predicted to exist at finite frequen-
FeTe2O5BrforelectricfieldorientedparalleleˆA, eˆB, and cies in zero field and shift upon the application of exter-
eˆC inthefrequencyinterval30–1,000cm−1 (4–120meV) nal fields. AFMR modes in the FeTe2O5Br have been
is shown in Fig. 2. A strong sharpening of many modes reportedin a recentelectron spin resonance study below
accompanied by a hardening of resonance frequencies is 400 GHz (∼13 cm−1).17 However, in an external field of
observed with decreasing temperature. No drastic de- 10 T the modes remain slightly below our measurable
viations from the room-temperature spectrum were ob- frequency range (15 cm−1).
served along any of the three directions when cooling to
5K.Particularattentionwasgiventotheexcitationspec-
trum slightly above and below the 10.6 K multiferroic
D. Determination of optical properties
ordering temperature. The absence of anomalies in the
spectra upon cooling below 10.6 K gives strong support
to the observation of no crystal symmetry change in the We have used the measured reflectance and transmit-
ordered state; however, a subtle contradiction exists.13 tance spectra of crystal 1 to extract the complex dielec-
The high temperature P2 /c space group is centrosym- tric function. Because Kramers-Kroniganalysis requires
1
metric, but ferroelectricity, for which non centrosymme- a single-bounce reflectance spectrum over a broad fre-
tryisastrictrequirement,isobservedbelowT . Thisin quency region, we must first correct the measured re-
N
turnsuggeststhatnewinfraredmodesshouldaccompany flectancespectruminregionswherethecrystaltransmits
the transition. However, the small value of polarization byusingacombinedreflectionandtransmissionanalysis.
measured (8.5 µC/m2) leads one to suspet that a subtle An attempt to solve for the single bounce reflectance by
transitionoccursandadditionalinfraredmodesarelikely inverting the full reflection and transmission equations
below our experimental resolution (<0.5 cm−1). leads to a transcendental equation with infinitely many
Figure 3 displays the optical conductivity along the solutions. Nevertheless, using the method employed by
three principal dielectric axes in the frequency interval Zibold et al.,18 i.e., assuming that k is small in the re-
30–33,000 cm−1. The strong anisotropy observed in the gion of interest, leads to an approximation of reflection
farinfraredpersistsathighfrequenciesresultinginthree and transmission that can be solved numerically for a
distinct absorption edges. The inset of Fig. 3 shows the single solution.
300 K reflectance up to 33,000 cm−1 along eˆ , eˆ , and The measured reflectance (not shown) and transmit-
A B
eˆ . tance(Fig.4)inthefrequencyinterval1500–10000cm−1
C
Crystal 1 exhibits transmission at frequencies above were significantly lower than expected throughout this
the infrared phonon modes and below the absorption regionoflowabsorption(Fig. 3). The lowmeasuredval-
edge. The dimensions of the crystal only allowed for ues were attributed to the scattering of light from facets
transmission with light polarized along eˆ and eˆ . As existing on the back surface of crystal 1. To compen-
B C
shown in Fig. 4, a sharp dip at 1850 cm−1 as well as a sate, we assumed a mask on the back surface of crys-
broadabsorptioncenteredat3250cm−1arepresentalong tal 1 which lead to scaling the measured reflectance and
both polarizations. Structures at these particular fre- transmittance up by a factor of 1.4 in the interval 1500–
quenciescalltomindtheabsorptionbandsofH O,which 10000 cm−1, thus explaining the discrepancy between
2
in turn suggest water of hydration in the crystal struc- Fig. 4 and Fig. 5. The scaled reflectance and transmit-
ture. But the anisotropic strengths of these absorptions tance yielded a single bounce reflectance which agreed
4
1.0
5K
0.8 E∥ ˆeB 50K
100K
200K
0.4 300K
0.0
ce0.8 Frequency (cm−1) E∥ ˆeC
n
a
t
c
e0.4
efl
R
0.0
0.8 Frequency (cm−1) E∥ ˆeA
0.4 FIG. 2. (Color online)
Temperature-dependent
reflectance spectrum of
0.0
0 200 400 600 800 1000 FeTe2O5Br along eˆA, eˆB, and
Frequency (cm−1) eˆC.
5000 0.6
0.6 E∥ ˆeC
)4000 ectance0.4 EEE∥∥∥ ˆˆˆeeeCBA ce00..45 E∥ ˆeB
1m−3000 Refl0.2 ttan
c mi0.3
1− 0.0 s
m 0 10000 20000 30000 n
Oh2000 Frequency (cm−1) Tra0.2
(σ1 EEE∥∥∥ ˆˆˆeeeCBA 0.1
1000
0.0
2000 4000 6000 8000 10000 12000
0 Frequency (cm−1)
0 10000 20000 30000
Frequency (cm−1)
FIG.4. (Coloronline)Transmittanceofcrystal1inthemid-
infrared and near-infrared regions.
FIG. 3. (Color online) The optical conductivity in the fre-
quency interval 30–33,000 cm−1. The inset shows the 300
K broadband reflectance out to 33,000 cm−1 from which the
reflectance data was bridged with a Lorentz oscillatorat
optical conductivity was extracted via Kramers-Kronig rela-
tions. 60,000 cm−1. Subsequently, the phase shift on reflection
was obtained via Kramers-Kronig analysis, and the op-
tical properties were calculated from the reflectance and
phase.
wellwith the measuredbulk reflectancein regionswhere
crystal 1 did not transmit, as shown in Fig. 5.
Kramers-Kronig analysis can be used to estimate
the real and imaginary parts of the dielectric function
E. Oscillator-model fits
from the bulk reflectance R(ω).19 Before calculating the
Kramers-Kronig integral, the low frequency data (0.1–
30 cm−1) were extrapolated using parameters from the ThemeasuredreflectancewasfitwithaDrude-Lorentz
complexdielectricfunctionmodeldescribedinSec.IIIE. modeltoobtainasecondestimate ofthe complex dielec-
At high frequencies (8 × 104–2.5 × 108 cm−1) the re- tric function in the infrared range. The model assigns
flectance was approximated from known x-ray scatter- a lorentzian oscillator to each distinguishable phonon in
ing functions of the constituent atoms. The gap be- the spectrum plus a high frequency permittivity, ǫ∞, to
tween our highest measurable frequency and the x-ray address the contribution of electronic excitations. The
5
1.0
TABLE I. Oscillator parameters for experimentally observed
e T *1.4
anc E∥ ˆeC Rmmeeaassuurreedd*1.4 pwhitohnognrosuaplosnogfeˆpAho(naotn2s0hKa)v.eTbheeenmaostsiiognnsedofwathoemnsthaesspoacitatteerdn
mitt0.8 Rsingle was apparent. The atoms are listed in descending order of
theircalculated net atomic displacement.
s
& Tran0.6 Idx OscSStr ωCt(rcmFr−e1q) γF(WcmH−M1) idDxeigneneˆC Asgn
e 0.4 1 0.207 45.5 2.0 1 Br
c
n 2 1.320 79.6 2.1 5 -
ta 3 0.356 88.4 1.1 6 Br,Te,O,Fe
ec0.2 4 0.042 98.1 1.0 8 Br,Te,O,Fe
efl 5 0.056 107.5 2.1 9 Br,Te,O,Fe
R
6 0.048 137.1 1.9 12 Br,Te,O,Fe
0.0
103 104 7 0.015 157.6 1.6 14 Te,Br,O,Fe
Frequency (cm−1) 8 0.023 166.0 2.2 15 Te,Br,O,Fe
9 0.354 184.9 1.3 16 Te,O,Fe
10 0.519 194.3 2.4 17 Te,O,Fe
FIG. 5. (Color online) Single-bounce reflectance (red) as ap- 11 0.159 211.7 2.0 Te,O,Fe
proximatedfrom thescaled measured reflectance(black)and 12 0.007 236.4 4.9 22 -
the scaled measured transmittance (blue) of crystal 1. The 13 0.084 247.8 1.7 23 -
elevated level of measured reflectance throughout the trans- 14 0.009 256.5 4.0 24 -
mission interval is expected due to additional light reflected 15 0.169 291.9 1.8 27 Fe,O,Te
from the back surface of thecrystal. 16 0.030 302.8 3.4 Fe,O,Te
17 0.033 321.6 3.6 28 Fe,O,Te
18 0.006 328.0 2.4 Fe,O,Te
model has the following mathematical form: 19 0.003 348.5 2.0 29 Fe,O,Te
20 0.102 370.0 2.5 -
∞ S ω2 21 0.008 387.1 2.6 -
j j
ǫ=X +ǫ∞ , (1) 22 0.030 401.3 4.1 -
ω 2−ω2−iωγ
j j 23 0.005 418.6 4.0 -
j=1
24 0.005 426.2 2.6 30 -
whereS ,ω ,andγ signifytheoscillatorstrength,center 25 0.090 435.0 3.9 31 -
j j j
frequency, and the full width at half max (FWHM) of 26 0.119 463.6 5.4 32 O,Fe,Te
thejthlorentzianoscillator. TheDrude-Lorentzcomplex 27 0.004 481.0 1.4 O,Fe,Te
28 0.029 493.2 4.9 33 O,Fe,Te
dielectric function is used to calculate the reflectivity,
29 0.350 575.3 7.5 35 O,Fe
which is compared to the original measured quantity in
30 0.203 666.1 8.0 37 O,Fe
Fig.6. Similarqualitiesoffitswereobtainedforallother
31 0.257 730.5 13.9 O,Fe
temperatures and polarizations.
32 0.018 784.0 9.2 42 -
1.0
data
IV. DISCUSSION
fit
0.8 E∥ ˆeB
100K
A. Group theory and lattice dynamics
e
nc0.6
a Due to the lack of anomalies upon cooling below
t
c
e 10.6 K, we turn our focus to the highly anisotropic far-
Refl0.4 infrared excitation spectrum. The number of phonon
modes expected in FeTe O Br can be found by group-
2 5
0.2 theory analysis. Using the SMODES program,20 we ar-
rive at the following distribution of modes:
0.0
0 200 400 600 800 1000
Frequency (cm−1) Γoptical =54A(Rg)+54B(gR)+53A(IuR)+52B(uIR) , (2)
where(R)and(IR)denoteRamanactiveandinfraredac-
FIG.6. (Coloronline)Experimentalreflectance(bluepoints) tive modes respectively. The 53A modes are expected
u
and calculated reflectance (red line) from the Drude-Lorentz to lie alongthe unique b axis (eˆ ) ofthe monoclinic sys-
B
model of theFeTe2O5Br 100 K eˆB dielectric function. tem. The 52B modes are expected to lie in the ac
u
plane, and one should be able to resolve all 52 modes
6
TABLEII.Oscillatorparametersforexperimentallyobserved TABLE III. Oscillator parameters for experimentally ob-
phononsalongeˆC (at20K).Themotionsofatomsassociated served phonons along eˆB (at 20 K). The motions of atoms
withgroupsofphononshavebeenassigned whenthepattern associated with groups of phonons have been assigned when
was apparent. The atoms are listed in descending order of thepatternwasapparent. Theatomsarelistedindescending
their calculated net atomic displacement. order of their calculated net atomic displacement.
Idx Osc Str Ctr Freq FWHM Degen Asgn Idx Osc Str CtrFreq FWHM Asgn
S ω (cm−1) γ (cm−1) idx in eˆA S ω (cm−1) γ (cm−1)
1 4.275 46.7 0.2 1 Br 1 1.388 35.7 0.8 Br
2 1.335 53.9 0.5 Br 2 0.330 43.5 1.4 Br
3 0.951 65.8 1.0 - 3 0.899 53.2 0.8 -
4 0.216 71.7 0.8 - 4 0.289 60.5 0.9 Br,Te,O,Fe
5 0.435 81.2 0.9 2 - 5 0.119 79.1 1.3 Br,Te,O,Fe
6 0.205 89.3 0.9 3 Br,Te,O,Fe 6 0.075 85.0 1.2 Br,Te,O,Fe
7 0.061 97.0 0.8 Br,Te,O,Fe 7 0.052 91.2 1.0 Br,Te,O,Fe
8 0.130 99.0 1.1 4 Br,Te,O,Fe 8 0.138 93.3 1.3 -
9 0.533 109.2 0.8 5 Br,Te,O,Fe 9 0.259 98.0 0.9 -
10 0.294 112.8 1.0 Br,Te,O,Fe 10 1.359 102.0 1.1 -
11 0.369 128.5 0.8 Br,Te,O,Fe 11 0.073 106.9 0.7 -
12 0.127 135.4 0.9 6 Br,Te,O,Fe 12 0.170 123.7 0.7 Te,Br,O,Fe
13 0.411 140.6 0.9 - 13 0.092 126.3 0.9 Te,Br,O,Fe
14 0.857 157.0 0.5 7 Te,Br,O,Fe 14 0.074 131.4 1.1 Te,Br,O,Fe
15 0.107 166.8 1.0 8 Te,Br,O,Fe 15 1.066 184.0 0.4 Te,O,Fe
16 0.212 184.5 0.6 9 Te,O,Fe 16 0.128 190.2 0.7 Te,O,Fe
17 0.039 194.8 1.2 10 Te,O,Fe 17 0.491 198.6 0.8 Te,O,Fe
18 0.066 204.0 1.4 - 18 0.440 210.0 0.3 -
19 0.014 206.3 1.1 - 19 0.023 215.3 1.3 -
20 0.085 221.7 1.1 - 20 0.053 222.0 1.1 -
21 0.101 225.4 0.9 - 21 0.058 240.1 1.3 -
22 0.065 232.6 1.0 12 - 22 0.028 249.0 0.9 -
23 0.107 248.0 1.5 13 - 23 0.274 273.9 0.9 Fe,O,Te
24 0.291 254.2 0.6 14 - 24 0.102 275.8 1.4 Fe,O,Te
25 0.239 274.4 1.1 - 25 0.661 295.5 1.3 Fe,O,Te
26 0.195 284.9 1.2 - 26 0.366 317.6 1.1 Fe,O,Te
27 0.633 294.8 1.4 15 Fe,O,Te 27 0.101 324.3 1.5 Fe,O,Te
28 0.138 319.0 1.9 17 Fe,O,Te 28 0.261 341.7 1.2 Fe,O,Te
29 0.173 349.0 2.2 19 Fe,O,Te 29 0.808 393.7 2.6 Fe,O,Te
30 0.514 426.7 2.4 24 - 30 0.371 418.0 4.1 -
31 1.562 437.0 2.3 25 - 31 0.009 437.7 3.5 -
32 0.088 459.3 3.4 26 O,Fe,Te 32 0.209 462.8 3.2 O,Fe,Te
33 0.006 488.5 4.3 28 O,Fe,Te 33 0.173 478.0 3.3 O,Fe,Te
34 0.067 509.6 9.6 O,Fe,Te 34 0.012 499.0 4.6 -
35 0.260 573.5 5.6 29 O,Fe 35 0.009 508.3 1.2 -
36 0.096 626.7 5.2 O,Fe 36 0.047 595.3 6.9 O,Fe
37 0.015 662.0 3.2 30 O,Fe 37 0.080 626.6 3.6 O,Fe
38 0.061 672.0 5.7 O,Fe 38 0.323 652.0 4.9 O,Fe
39 0.182 693.5 8.9 O,Fe 39 0.018 682.1 8.2 O,Fe
40 0.172 707.4 5.2 O,Fe 40 0.217 728.1 7.8 O,Fe
41 0.101 749.8 9.4 - 41 0.027 746.2 7.4 -
42 0.014 780.4 6.6 32 - 42 0.031 779.9 23.5 -
43 0.033 814.7 6.9 - 43 0.071 836.0 9.6 -
using the two orthogonal polarization spectra measured
in this plane. However, the merging of weaker modes
nearstrongermodes canhinder this count. We therefore
employedlatticedynamicalcalculationstodeterminethe
relative resonance frequency, mode intensity, as well as
displacement pattern for the 105 infrared active modes. spherical cut-off boundary.21 The following two sections
Thecalculations,whichutilizedthestructureandvalence describe the method used to compare the observed and
asreportedbyBeckeret al.,12 werebasedonareal-space calculated spectrum for the A and B modes respec-
u u
summation of screened coulomb interactions involving a tively.
7
B. 52B modes modes at 20 K are found in Table III.
u
All 52B modes predicted lie in the ac plane and
u
shouldpossessafiniteintensityalongbothmeasuredpo- 20 400
larizations in this plane unless the direction of the in- a 5K data b E∥ ˆeB 5K
dalulecledtodiepitohleermeˆomoernteˆfo.r a(Spmaarltlicaunlagrlevdibervaiatitoionnissfproamr- 1cm)− 15 fit 511005K00KK 3001m)−
A C 1− 10 200K 200c
the parallel case may be hard to detect.) For all other m 300K 1−
h m
emˆodceosrroenspeomnudsintgsotrottohuetswamhiechpehxycsiitcaatliovnibsraaltoionngseˆoAtahnadt (Oσ1 5 100(Oh
C σ1
they are not counted twice. To count the modes, we 0 0
77 79 81 83 85 87 270 275 280 285
used the Drude-Lorentz parameters for each phonon at
Frequency (cm−1) Frequency (cm−1)
20 K as well as the resonant frequency and mode inten-
sityfromourlattice dynamicalcalculation. Withknowl-
edge ofthe opticalconductivity spectraalong eˆ andeˆ FIG. 7. (Color online) The left panel (a) shows unaccounted
A C
at 20 K, modes were grouped together if they were ob- for spectral weight on the high frequency side of the asym-
metric oscillator at 85 cm−1 along with a fit to a symmetric
servedinthesamesmallfrequencyinterval(ontheorder
oscillator (79 cm−1). We suspect the asymmetric shoulder is
of a typical linewidth) of one another in the two spec-
the result of a buried mode. The right panel (b) depicts the
tra. Next, we compared the experimental linewidths of appearanceofaonceburiedmode(∼276cm−1)uponcooling.
the grouped modes to ensure that they would overlap if
plotted side-by-side. As two final criteria, we compared
both the ratio of experimental oscillator strengths with
thecomputedoscillatorstrengths,andalsocomparedthe
displacement patterns generated by our calculation to D. Assignment of Modes
makesuretheywereingoodagreementastowhichexci-
tationscorrespondedtothesamephysicalvibrations. All
The assignment of a particular phonon, observed in
52B modes predicted in the ac plane were observed in
u theexperimentalspectrum,toitspreciseatomicdisplace-
the experimental spectrum. Lorentz oscillator parame-
ment pattern cannot be made without sacrificing objec-
tersforallmodesaswellasmodespresentalongbotheˆ
A tive certainty because of the density of the phononspec-
and eˆ polarizations can be found in Table I and Table
C trum. Assignments to groups of modes, however, can
II.
be made through the displacement patterns generated
by our lattice dynamical calculations. Using a simplified
modelofaphononasadrivenoscillatorwithresonantfre-
C. 53Au modes quencyinverselyproportionaltomass,weproceedtolist
the constituent atoms in the structure from heaviest to
Counting the experimentally observed A modes is lightest: Te, Br, Fe, and O. Normally, the low frequency
u
straightforward;weobserve43ofthe53predictedmodes modes involvethe heaviestatoms,but inthe FeTe O Br
2 5
along this direction. We believe that 10 modes were not structure the Br atoms have a weak interaction with the
resolvedas a result ofweakermodes being buried within other atoms and therefore are responsible for the lowest
stronger modes and merging together in the spectrum. frequency phonons. At a certain frequency the motion
In the optical conductivity, all single phonon excitations of Br atoms will cease. Likewise, at a higher frequency
should be represented by symmetric lorentzian oscilla- the vibration of atoms involving Te will cease, leaving
tors. Figure 7 left panel depicts a slightly asymmetric themotionofFeandOtobeexpectedinthehighestfre-
lorentzian oscillator with a resonance of 85 cm−1. Our quency phonons. Accordingly, the phonon spectrum can
attempt to fit the resonance at 85 cm−1 with a sym- be divided into three clusters that is reflected in Fig. 2
metric lorentzian oscillator yields unaccounted for spec- (namely, below 180 cm−1, between 180 cm−1 and 530
tral weight on the high frequency side of the resonance. cm−1, and above 530 cm−1). The clustering is also ob-
A symmetric lorentzian oscillator centered at 79 cm−1 served in the calculated spectrum via the displacement
and corresponding fit are also included as a reference. patterns produced, in terms of first the Br and subse-
(Note that the additional spectral weight between the quently the Te ceasing to vibrate. Within each cluster
resonances at 75 cm−1 and 85 cm−1 is attributed to trends are to be noted on the following principle: atoms
absorption between the bands and therefore not to be arelistedcorrespondingtotheirnetatomicdisplacement.
mistaken for a lattice vibration). We suspect that this This approach, in turn, has allowed us to identify an-
asymmetric shoulder is due to a weak buried mode that other characteristic of atomic displacement within the
is not fully resolved. To further support our interpre- three clusters. The atom of focus in a cluster (e.g., Br
tation of buried modes, the right panel of Fig. 7 depicts in the first cluster) has a net atomic displacement ever
theappearanceofaonceburiedmode(∼276cm−1)upon diminishing. Cessation does not arrive abruptly. The
cooling. The Lorentz oscillator parameters of the 52B three clusters are profiled in each of Table III, Table I,
u
8
and Table II. It remains to compare our results to a recent infrared
AproposthethirdclusterthatfocusesonFeandO,an study by Pfuner et al.11 on the similar FeTe O Cl com-
2 5
additional resource is provided by the familiar orthofer- poundwhereanequalnumberofphononswerepredicted.
rite family of compounds because the FeO octrahedral Our analysis ofthe phononspectrum agrees with the in-
6
building block that is present in FeTe O Br is itself a fraredstudyofPfuneretal. inthatwealsobelievemodes
2 5
defining unit of the orthoferrite family. Given the abun- resonating at equivalent energy scales can overlap, pre-
dant literature on vibrational assignments made to the venting them from being resolvedseparately,but we dif-
FeO ochrahedral unit,22,23 we are consequently able to fer on other issues. Pfuner et al. report a combined 38
6
map these well recognized assignments onto our experi- modes along the eˆ andeˆ directions. We observemore
B C
mental findings, thus corroboratingboth perspectives. modes along the unique b axis alone, as well as modes
below 50 cm−1, whereas the study by Pfuner et al. does
not report measurements below this frequency.
V. CONCLUSIONS Wealsoobservedrasticallydifferentandmorestrongly
anisotropic high frequency optical properties. Pfuner
Far-infrared measurements on multiferroic single- et al. report an absorption edge around 4,000 cm−1
crystalFeTe O Br revealno drasticanomaliesinthe ex- in FeTe O Cl, where as we observe low absorption
2 5 2 5
citation spectrum below the multiferroic ordering tem- accompanied by substantial transmission through the
perature. Nonetheless, a thorough inspection of the FeTe O Br crystal in this region. In speculating about
2 5
phonon spectra has lead to the identification of all 52 the differences in high frequency optical properties of
predicted modes in the degenerate ac plane and 43 of the two similar compounds, we point out that spurious
the 53predictedmodes alongthe unique b axis. The ab- changes of slope of the reflectance throughout the mid-
sence of 10 modes along the b axis is presumably due to infrared region, such as those resulting from the contri-
the mergingofweakermodes nearstrongermodes inthe bution of back surface reflection (black line in Fig. 5),
dense excitation spectrum. candrastically change the Kramers-Kronig-derivedopti-
The motions of individual atoms have been assigned cal properties.
to groups of phonons via the displacement patterns pro- Transmission measurements as well as reflectance
ducedthroughourlatticedynamicalcalculation. Theas- along eˆ were not reported in the study by Pfuner et
A
signments divide the overallphononspectrum into three al.. Similar to the FeTe O Br system reported here, the
2 5
clusters,whicharecharacterizedbyanatomthatiscom- FeTe O Cl system also showed no response to magnetic
2 5
montoeveryvibrationinthatcluster. Weobservedthat fieldsaboveorbelowthemagneticorderingtemperature.
as frequency increases, vibrations involving the motion
of Br atoms will progressively cease. Likewise, at higher
frequencies the vibrations involving Te atoms will cease
ACKNOWLEDGMENTS
in the same manner, leaving the motion of Fe and O to
beexpectedinthehighestfrequencyphonons. Moreover,
the particular atoms involvedin a vibration are listed in The authors thank M. Pregelj for providing low-
descending order of net atomic displacement, which in temperature crystallographic information files. This
turn makes clear a trend within each cluster (namely, work was supported by DOE through grant DE-FG02-
theatomoffocusinaparticularclusterhasanetatomic 02ER45984 at UF and DE-AC02-98CH10886 at the
displacement ever diminishing). NSLS.
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