Extensive infrared spectroscopic study of CuO: signatures of strong spin-phonon interaction and structural distortion

25 Pages·1 MB·English

by  A. B. Kuz'menko

Extensive infrared spectroscopic study of CuO: signatures of strong spin-phonon
interaction and structural distortion
A.B.Kuz’menko1, D. van der Marel2, P.J.M. van Bentum3, E.A.Tishchenko1, C.Presura2 and A.A.Bush4
1P.L.Kapitza Institute for Physical Problems RAS, Kosygina str., 2, Moscow, 117334, Russia
2Solid State Physics Laboratory, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
3High Field Magnet Laboratory, University of Nijmegen, 6525 ED, Nijmegen, The Netherlands
0 4Moscow State Institute of Radiotechnics, Electronics and Automation, Vernadskogo pr. 78, Moscow, 117464, Russia
0 (10 October 1999)
0
2 Optical properties of single-crystal monoclinic CuO in the range 70 - 6000 cm−1 were studied at
temperatures from 7 to 300 K. Normal reflection spectra were obtained from the (001) and (010)
n
crystalfacesthusgivingforthefirsttimeseparatedatafortheAu andBu phononmodesexcitedin
a
J thepurelytransverseway (TO modes). Modeparameters, includingpolarizations of theBu modes
not determined by the crystal symmetry, were extracted by the dispersion analysis of reflectivity
2
curvesasafunctionoftemperature. Spectraofallthecomponentsoftheopticalconductivitytensor
2
wereobtainedusingtheKramers-Kronigmethodrecentlyextendedtothecaseofthelow-symmetry

] crystals. Thenumberofstrongphononmodesisinagreementwiththefactor-groupanalysisforthe
l crystalstructure,currentlyacceptedfortheCuO.However,several”extra”modesofminorintensity
e
- are detected; some of them are observed in the whole studied temperature range, while existence
r of others becomes evident at low temperatures. Comparison of frequencies of ”extra” modes with
t
s the available phonon dispersion curves points to possible ”diagonal” doubling of the unit cell {a,
.
t b, c} → {a+c, b, a-c} and formation of thesuperlattice. The previously reported softening of the
ma A3u mode (∼ 400 cm−1) with cooling at TN is found to be ∼ 10 % for the TO mode. The mode is
very broad at high temperatures and strongly narrows in the AFM phase. We attribute this effect
- to strong resonance coupling of this mode to optical or acoustic bi-magnons and reconstruction of
d
the magnetic excitations spectrum at the N´eel point. A significant anisotropy of ǫ∞ is observed:
n
o it was found to be 5.9 along the b-axis, 6.2 along the [101] chains and 7.8 the [101] chains. The
c ”transverse” effective charge is more or less isotropic; its value is about 2 electrons.
[

PACS numbers: 78.20.Bh, 78.20.Ci, 78.30-j, 71.27.+a, 71.45.Gm
2
v
6
I. INTRODUCTION thanthisvaluealonganyotherdirection. Theanomalous
7
1 temperature dependence of the magnetic susceptibility4
1 Since 1986 the interest to cupric oxide CuO has been pointstolow-dimensional,or,atleast,highlyanisotropic
0 mostly governed by its close relation to the problem of characterofmagneticinteractionsandpersistencyofspin
0 high-T superconductivity. In addition to the role of the correlationsattemperatureswellabovetheN´eelpoint5,6.
0 c
parentcompoundofallthehigh-T materialswithCuO Another feature of the cupric oxide is the low-
/ c 2
t planes,ithasanumberofphysicalandchemicalfeatures symmetrymonocliniclattice,whichdistinguishesitfrom
a
m common to several undoped antiferromagnetic (AFM) the other TM monoxides,e.g. MnO, FeO, CoO andNiO
cuprates, (e.g. La CuO , YBa Cu O ): similar copper withtherock-saltstructure. Itisaprominentmanifesta-
- 2 4 2 3 6
d coordinationandelectronicstate,Cu-Odistances,values tionoftheJahn-Tellereffect: inthehigh-symmetryocta-
n oflocalizedmagneticmoments,superexchangeconstants, hedral position characteristic to the cubic structure, the
o low-dimensionality of magnetism etc. Cu2+ ionwouldhavedegeneratedx2−y2 anddz2 orbitals,
c CuO, however, is a quite interesting system in its which is energetically unfavourable, and therefore tend
:
v own right. Although Cu2+ ions are expected to be in to displace away from the symmetry position. This ten-
i the 3d9 state with one 3d-hole per atom, this transition dency is so strong that CuO has not just a distorted cu-
X
metal(TM)oxideisastronglycorrelatedinsulatorofthe biclattice,butacompletelydifferentmonoclinictenorite
ar ”charge-transfer”typeaccordingtothetheoryofZaanen, structure.
SawatzkyandAllen1;theholesarewelllocalizedforming Several groups7–13 have reported results of infrared
localmagnetic moments. CuO undergoesa 2-stagemag- (IR) spectroscopic studies of powder as well as single-
netic transition: at T = 230 K an incommensurate crystalspecimens of CuO. The interpretationof infrared
N1
magnetic structure is observed, while at T = 213 K spectra was always embarrassedby the low crystal sym-
N2
magnetic moments orderparallelto the b-axis antiferro- metry, especially for the case of polycrystalline samples.
magneticallyalongthe[101]chainsandferromagnetically Kliche and Popovic10 have measured infrared spectra of
along the [101] chains2. From the analysis of the spin- sintered powder samples as a function of temperature
wavevelocity2,3 it wasfound that the exchangeconstant andfor the firsttime assignedstrongIR-activemodes to
alongthe[101]chains(60-80meV)isseveraltimeslarger thespeciesAu andBu bycomparisonoffrequencieswith
1
those in PdO. They also reported an additional broad To study the A TO modes anycrystalplane containing
u
modeatabout414cm−1 the intensityofwhichincreases the b-axis, e.g. (001) face, may suffice. We succeeded to
drastically with cooling down below T and suggested obtain these crystal faces with a sufficiently large area,
N
that it is a zone-boundary phonon mode which becomes allowingtoperformreliablemeasurementsandquantita-
IR-active because of IR absorption from AFM super- tive analysis of the data as described below.
structure. It is evident now that it was a manifestation
of the anomalous softening of the A3 mode reported by
u
Homes et al13. II. CRYSTAL STRUCTURE AND
Sofaritwasaseriousproblemtoobtainsinglecrystals FACTOR-GROUP ANALYSIS
of CuO suitable for quantitative infrared studies. Guha
et al11 has succeededtomeasureinfraredpolarizedspec- Cupric oxide CuO, unlike other TM monoxides, crys-
tra of single crystals of CuO at room temperature and tallizes in a low-symmetry monoclinic tenorite structure
account for low-symmetry effects in data analysis. They (Fig. 1). It is generally accepted, following ˚Asbrink
have measured reflectivity from the (110) natural face and Norrby16, that at room temperature (RT) the space
and modelled spectra by the dielectric function formulas groupisC6 (C2/c);therearefourCuOmoleculesinthe
2h
adapted to monoclinic crystals14. However, due to in- unitcellwithdimensionsa=4.6837˚A,b=3.4226˚A,c=
convenientcrystal orientationin their experiment mixed 5.1288˚A,β =99.54◦ andtwoCuOunitsintheprimitive
LO-TO modes were excited, the properties of which de- cell; the copper and oxygen occupy the C and C sym-
i 2
pend on the wave vector direction. metry positions correspondingly. Each copper atom is
Homes et al13 were the first to present single-crystal situated in the center ofthe oxygenparallelogram. Each
infrared spectra as a function of temperature. Again, oxygenatom,in turn, has a distortedtetrahedralcopper
however,onlythe (110)crystalsurfacewasaccessiblefor coordination. The adjacent CuO parallelograms form
4
optical experiments, and mixed LO-TO modes were ac- two sets of ribbons propagating along the [110] and the
tually observed. An appreciable (about 5 %) sharp soft- [110] directions. The structure can be also considered as
eningofthe 440cm−1 reststrahlenbandfortheE b being composed from two types of zig-zag Cu-O chains
∼ ⊥
upon cooling down was definetely registered at the N´eel running along the [101]and the [101] directions (Fig. 2).
transition. Spectra were fitted with introduction of 3Au The Cu-O-Cu angle is 146◦ in the [101] chains and 109◦
and3Bu phononmodesonly. Nonew phononstructures in the [101] chains.
atthe magneticallyorderedphasewerereportedindicat- For the C6 space group the factor-group (FG)
2h
ing absence of a crystal superlattice below TN2. analysis17 gives the following set of the zone-center lat-
This statement sounds puzzling in a view of obser- ticemodes: Γ=A +2B +3A +3B +3 translational.
g g u u
vation by Chen et al15 of five new modes at low tem- Out of these, 3 modes (A +2B ) are Raman-active, 6
g g
peratures in the Raman spectra. Authors have assigned modes (3A +3B ) are IR-active. The A modes are
u u u
thesemodestofoldedphonons;asafoldingmechanism,a polarized along the b-axis. The dipole moments of the
strong spin-phonon interaction was proposed. The most B modes lie within the ac-plane, but due to the low
intense new mode 240 cm−1 hardens strongly at cool- syummetry their directionsarenot exactlydeterminedby
ingdown,whichwasattributed15 toanadditionallattice the crystal structure.
rigidity due to magnetization. More recently ˚Asbrink and Waskowska18 have refined
There is a serious inconsistency concerning structure theCuOstructureat196Kand300Kusingthesocalled
and parameters of IR-active phonon modes, especially ”less significant reflections” in the X-ray data analysis
at high frequencies. For instance, the deviations in res- and found that less symmetric space-group C4 (Cc) is
s
onance frequency of these modes reported by different also consistent with the X-ray diffraction data for both
groups are too significant to be explained by experimen- phases. They suggested that the C6 space-groupmight
2h
tal errors, isotope effect, crystal non-stoiochiometry etc. result from the time-averaging or site-averaging of non-
In our opinion, the explanation lies in the intermediate equivalent (due to valence fluctuations) atom positions
LO-TO nature of the observed modes and correspond- of lower symmetry. Some lattice distortions, especially
ing uncertainty of phonon parameters, especially for the changes of the Cu-O distances, were clearly detected
high-frequency intense modes with large LO-TO split- when passing from RT to 196 K. In general, one can
ting. Moreover, no infrared data so far were reported state, that the C6 space-groupis a good approximation
2h
where the Au and Bu modes were completely separated. to the realstructure of the cupric oxide,but some minor
Parametersofthe Au modeswereextractedatbestfrom deviationsfromthis donotcontradicttothe X-raydata.
the single-crystalspectra for E c where the B modes
u
⊥
are also present.
In this paper we aimed to resolve this uncertainty by III. EXPERIMENTAL
separatemeasurementofthecharacteristicsofpurelyTO
A and B modes. For monoclinic crystals the only op-
u u
tion for observation of the B TO modes is to measure
u
normal reflectivity from the (010) face (the ac-plane).
2
A. Sample preparation and characterization The polarizer was mounted in the optical path of the
incident beam; no additional polarizers (analyzers) were
Single crystals of CuO were obtained from a CuO - put inbetween sample and detector. The transmission
PbO-Bi O melt. Thedetailsaredescribedelsewhere19. propertiesofthepolarizersweremeasuredindependently
2 3
After cooling down the crucible contained randomly ori- and, when necessary, special care of the correction for
ented large single-crystal pieces of CuO along with in- the unwanted polarization leakage was taken. Polarizer
clusions of other phases. From this conglomerate the rotationwas performed using a computer-controlledme-
largest CuO single crystals were extracted and oriented chanical rotator.
using the X-ray diffraction. As usual, natural crystal An original
faces were presumably of (110) and (110) orientation. ”three-polarization” measurement technique21 was used
This face orientation was used in previous papers where involving the measurement of three reflectivity spectra
infraredreflectivitymeasurementswereperformed. How- per crystal face for different polarizations of almost nor-
◦ ◦
ever,forthereasonsmentionedabove,weaimedtoobtain mally incident light: vertical (0 ), horizontal (90 ) and
◦
largeenoughthe (001)(theab-plane)andthe(010)(the diagonal(45 ). Inprinciple,theknowledgeofthesespec-
ac-plane) crystalfaces. These two mutually perpendicu- tra should be enoughto calculate the reflectivity for any
lar faces were cut on one selected single-crystal sample, other polarization direction. In particular, the relation
◦ ◦ ◦ ◦
which was used for measurement of all the reflectivity R(0 )+R(90 ) = R(45 )+R( 45 ) should work. We es-
−
spectrapresentedin this paper. Cuts werepolishedwith pecially checked the validity of this relation and experi-
afine0.06µmAl O powder. Microscopicanalysisofthe mentally proved that it holds with a good accuracy.
2 3
surface19 has shown that the crystal is twinned. Fortu- Thesamplewasmountedwithagoodthermalcontact
nately, one twinorientationwasalmostcompletely dom- in a continuous-flow cryostat (Oxford Instruments) with
inating; the domains of the alternative twin orientation an automatic temperature control. Spectra were mea-
formnarrowstripescoveringlessthan5%ofsurfacearea. sured at temperatures 300, 250, 240, 230, 220, 210, 200,
Such domination was also confirmed by the X-ray Laue 180,150,100and7K,sothat,specialattentionhasbeen
snapshots,where no detectable reflectionscorresponding paidtotherangeinthe vicinityofTN1 =230KandTN2
to the alternative twin orientation were observed. The = 213 K.The temperature setting accuracywas about 1
structure of twins is such20 that the b-axis direction is K.
the same for different twin orientations; all twin reflec- A reference for the absolute reflectivity was provided
tions are within the ac-plane. So a minor (less than 5 by in situ evaporation of a gold layer on the surface and
%)contributionofothertwindomainsis possible forthe consecutive repetition of the same set of measurements
(010) face reflectivity spectra. For the case of reflection for every temperature. Such a procedure has compen-
from the (001) face, when E b, all twins contribute in sated errors associated with not only non-ideality of the
the samewayandtwinninghaksnoeffect. TheLauegram samplefacebutalsothethermaldeformationofthecryo-
has shown that (001) and (010) crystal faces were cut statcoldfinger. Toaccountforapossibledriftofasingle-
with accuracy of 1.8◦ and 2.1◦respectively. The electron beamintensityduetosourceanddetectorinstability,ev-
Augermicroscopyhasshownthepresenceofonlycopper ery sample-channel measurement was accompanied by a
andoxygenatoms on the both crystalfaces. The areaof measurementoftheintensityofthelightbeampassedvia
the (001) face suitable for quantitative optical measure- the second channel without reflection from the sample.
ments(i.e. containingnoimpurityinclusions,havingthe
lowest fraction of the alternative twin orientation), was
3 mm2; that of the (010) face was 4 mm2. IV. SPECTRA TREATMENT
∼ ∼
A. The dispersion analysis
B. Reflectance measurement
Let us introduce the orthogonalsystem of coordinates
Infrared reflectivity spectra were measured from 70 to xyz : x a,y b,z a,z bsothatthereisaslight
6000 cm−1 using a Bruker IFS 113v FT-IR spectrome- i{nclin}ationk( 9k.5◦) be⊥tween⊥axes z and c. Due to the
ter. The average angle of incidence was about 11◦. A monoclinic s∼ymmetry the whole 3D dielectric tensor ǫˆis
set of different light sources, beamsplitters, polarizers the composition of two components: the scalar ǫb = ǫyy
and detectors were used to cover this frequency range. ǫ ǫ
The mid-infrared (MIR) spectra from 400 to 6000 cm−1 along the b-axis and the 2D tensor ǫˆac = (cid:20) ǫxzxx ǫxzzz (cid:21)
were measured using a globar source, KBr beamsplitter, within the ac-plane (ǫ = ǫ is expected without ex-
xz zx
KRS-5 polarizer and DTGS and MCT detectors. The ternal magnetic field). The dispersion formulas are:
far-infrared(FIR)region70-700cm−1 wasstudiedwith
the aid of the Hg lamp, a set of mylar beamsplitters, a ω2
∞ p,i
ǫ (ω)=ǫ + , (1)
polyethylene polarizer and the helium-cooled Si bolome- b b ω2 ω2 iγ ω
ter. iX,Au TO,i− − i
3
∞ ωp2,i dielectric axes in the ac-plane depend on the frequency,
ˆǫ (ω)=ǫˆ +
ac ac ω2 ω2 iγ ω × which precludes the straightforward application of the
iX,Bu TO,i− − i KK method to the ac-plane reflectance data. For this
cos2θi cosθisinθi , (2) case we used a modified version of this technique, which
×(cid:20) cosθisinθi sin2θi (cid:21) allowstodeterminefrequencydependenceofallthecom-
ponents of the complex reflectivity tensor rˆ , provided
ac
whereω - the transversefrequency,ω - the plasma
TO,i p,i thatthreereflectancespectraR (ω),R (ω)andR (ω)
00 45 90
frequency, γ - the linewidth of the i-th mode, θ - the
i i are measured in wide enough frequency range. The de-
angle between the dipole moment of the i-th mode and
tails of this KK method generalization are described in
∞ ∞
the x-axis (for the Bu modes only), ǫb and ǫˆac are the Ref.22.
high-frequency dielectric tensors. The b-axis complex
For a correct implementation of the KK integration,
reflectivity rb and the reflectance of the (001) plane for the reflectivityin the range6000- 37000cm−1 was mea-
E b are expressed via the dielectric function:
k sured using the Woollam (VASE) ellipsometer system.
Athigherfrequencies the ω−4 asymptoticswasassumed,
1 ǫ (ω)
r (ω)= − b , R (ω)= r (ω)2. (3) as usual. At low frequencies the reflectivity was extrap-
b 1+pǫb(ω) b | b | olated by a constant value.
p
The complex reflectivity tensor rˆ can be expressed
ac
viathedielectrictensorǫˆ bythematrixformula,which
ac V. RESULTS AND ANALYSIS
is formally analogous to (3):
rˆ (ω)=(ˆ1 ǫˆ (ω)) (ˆ1+ ǫˆ (ω))−1, (4) A. E k b
ac ac ac
− ·
p p
where ˆ1 is the unity tensor. The matrix squarerootnat- The reflectance spectra for the (001) plane, when E
urally means, that the matrix is first reduced to the di- b, areshownat Fig.3. In this configurationonly theAk
u
agonalformbyaproperrotation,thesquarerootisthen TO modes shouldbe active. Exactlythree strongmodes
takenfromeachdiagonalelement,andfinallyitisrotated are observed: A1 ( 160 cm−1), A2 ( 320 cm−1) and
backtotheinitialcoordinatesystem. The”-1”exponent A3 ( 400 cm−1u),∼which confirms tuhe∼FG-analysis pre-
implies calculation of the inverse matrix. diuctio∼ns for the established for CuO crystal structure.
The reflectance of the (010) plane depends on the di- The most drastic temperature changes take place in the
rection of the incident light polarization e=E/E: range350-550cm−1,wherethereststrahlenbandcorre-
| |
spondingtoveryintenselatticemodeA3 issituated. The
R (ω,e)= rˆ (ω)e2. (5) u
ac | ac | reflectivity maximum elevates from 65 % to almost 100
◦ ◦ ◦ %; its gravity center moves to lower frequencies upon
The reflectances for values 0 , 45 and 90 of the angle
between the electric field vector and the x-axis used in cooling down the sample. It indicates, that this mode
the ”three-polarization” measurement scheme21 are ex- experiences strong softening and narrowingas a temper-
ature is decreased.
pressed in terms of the components of rˆ :
ac
Inadditiontothreestrongmodes,atleastfive”extra”
R (ω)= r (ω)2+ r (ω)2 structuresinthese reflectivityspectraaredetectable”by
00 xx xz
R (ω)=|(r (ω|)+r| (ω)2|+ eye” (Fig. 3). The first structure is a dip at 425 cm−1
45 xx xz ∼
| | just on the top of the reststrahlen band, which becomes
+|rxz(ω)+rzz(ω)|2)/2 visuallyevidentbelow210K.Thesecondisa 485cm−1
R90(ω)= rxz(ω)2+ rzz(ω)2. (6) structure also on the top of the same reststr∼ahlen band
| | | |
seenat100Kand7K.Thethirdfeatureisa 630cm−1
The phonon parameters can be obtained by fitting of ∼
peak (see inset), which is very small (but observable) at
the reflectancespectrausing the writtenaboveformulas.
300K,andbecomessignificantatlowtemperatures. The
Toobtainthe Au modesparametersthe Rb(ω)spectrum fourthstructureishigh-frequencymode 690cm−1 (see
is fitted. The characteristics of the Bu modes, including inset), which is very obvious at 7 K (690∼cm−1) and 100
unknownanglesθi,canbeextractedbysimultaneousfit- K (680 cm−1), still detectable at 150 K ( 650 cm−1)
ting of three spectra R00(ω), R45(ω), R90(ω) from the and not seen at higher temperatures, prob∼ably, because
(010) plane.
ofstrong broadening. The fifth structure is seen at165-
170 cm−1 at the top of the reststrahlen band of the A3
u
mode (Fig.4(a)). It is better observable at low temper-
B. The Kramers-Kronig analysis
atures; but even at room temperature the form of the
reststrahlen band differs from a single-mode shape.
For the case E b the Kramers-Kronig(KK) analysis
k The observations ”by eye” should be accompanied by
canbeperformedinausualwaybecauseoneofthedielec-
numerical analysis. The dispersion analysis of spectra
tricaxesisparalleltothisdirection. Duetothelowcrys-
wasperformedin twostages. Onthe firststage,in order
tal symmetry, the directions of the two other principal
4
to determine the characteristics of the principal modes, disappearanceofthesemodesabovetheAFMtransition,
wehavefittedthereflectivitycurveswithintroductionof although they are not clearly seen ”by eye”. Neverthe-
3 modes only. The experimental and fitting curves are less, the transition strongly affects parameter values of
comparedatFig.5(a)for the T = 100K.The fit quality these modes. Both modes strongly soften above T and
N
is good enough; the deviations are observed only in the stronglyhardenbelowT . Themodesarenarrowingbe-
N
range of additional modes. A relative weakness of ad- low T (which facilitates their visual observation), and
N
ditional structures ensures small errors in determination areverybroadathighertemperatureswithastrongmax-
ofmainmodeparameters. Theparametersof3principal imumatthe transitionpoint. Onecancontentonly by a
A phononmodesobtainedbysuchafittingasafunction qualitative conclusions, because the temperature depen-
u
of temperature are shown at Fig. 6. dencies of these modes are masked by large error bars.
From Fig.6 a conclusion can be drawn immediately It can be explained by some correlationbetween param-
thattheA1 andA2 modesbehaveinaquitesimilarway, eters of these modes with ones of the A3 mode. It is a
u u u
while the highest-frequency A3 mode is significantly dif- typical problem for several broad closely located modes.
u
ferent. The A1 and A2 modes are steadily hardening Therefore,it is unreasonableto attribute physicalmean-
u u
with cooling ( 1 %), with some increasing of the slope ing to increasingof the plasma frequency of these modes
∂ω /∂T belo∼w T . In contrast, the A3 mode slightly above200K:theirplasmafrequenciesarejustsubtracted
TO N u
softens with cooling down to the T , then undergoes a from the plasma frequency of the A3 mode without sig-
N1 u
drastic sharp softening ( 10 %) in the vicinity of the nificant influence on the fit quality. For the 690 cm−1
∼
transition temperature and then hardens with further mode the dispersion analysis results confirm visual ob-
cooling from T down to the helium temperature. The servations: anomalouslystronghardeningatcoolingand
N2
A2 andA3 modesarerelativelynarrowat300Kandex- strong broadening with heating. The latter, probably,
u u
hibitfurthernarrowingwithcoolingwithsomedipatthe precludes satisfactoryfitting of this mode athigher tem-
transitiontemperature. Onthecontrary,theA3 modeis peratures.
u
very broadat 300 K, and broadens more with approach- The curves of the b-axis optical conductivity σ (ω) =
b
ing the T . Its linewidth has a pronounced maximum ωImǫ (ω)/4π, obtained by the KK transform of the re-
N b
inbetween T and T . In the AFM phase it quickly flectivity spectra for each temperature, are shown at
N1 N2
narrows with cooling down. Fig. 8. The conductivity is very illustrative to show a
Onthesecondstage,inordertodetermineor,atleast, remarkable difference between the A1 and A2 narrow
u u
estimateparametersofthementioned”extra”modes,ad- modes and the A3 mode exhibiting a puzzling temper-
u
ditionalfitting ofspectrawithintroductionofbothprin- ature transformation. The sharpness of the A1 and A2
u u
cipaland”extra”modeshasbeenperformed(seeFig.7). modes and the absence of the B modes contribution
u
It was possible to fit the structures at 167 cm−1, 425 to this spectrum confirms a good sample quality and its
cm−1,485cm−1 and690cm−1. The630cm−1 peakcan- proper orientation. Some deformations of the lineshapes
notbefittedbytheusuallorentianterm. Thefirstfitwas for T = 100 K and 7 K (in particular, a small negative
performedat7K,when additionalstructures aremostly value of conductivity just below the mode frequencies)
sharp. Other spectra were fitted in sequence 100 K, 150 are most likely the results of uncertainties of the KK
K,...,300K.Ateachsteptheoscillatorparameters,cor- method, whichis verysensitive toexperimentalerrorsin
responding to the previous temperature served as initial the regions where the reflectivity approaches 0 or 1. We
approximation for the least-squares fitting. Parameter shall not attribute any physical meaning to this effect.
confidence limits were always calculated by the ”covari-
antmatrix”method(seeerrorbarsatFig.7),whichtakes
into account possible correlation of parameters. In this B. E k ac
wayitwaspossibleto extendcurvesofmodes 167cm−1,
425 cm−1 and 480 cm−1 up to room temperature; the The reflectance spectra from the (010) plane for three
690 cm−1 mode was fitted only for T 150 K, because polarizations of the incident light (R , R and R )
≤ 00 45 90
at higher temperatures fitting could not give reasonable are shown at Fig. 9. The B TO modes are expected
u
values of parameters for this mode. The errors in deter- to appear in these spectra. The narrow mode B1 (
mination of additional modes are relatively larger than 145 cm−1) is clearly observed in all polarizations.u I∼ts
those for the principal ones, which is natural, in view intensity depends, of course, on the light polarization,
of their small intensity. In general, errors are smaller at i.e. the angle between the electric field vector and the
lower temperatures. modedipolemoment. Strongreststrahlenbandsareseen
The temperature dependence of TO frequency addi- in the 450 - 600 cm−1 range. The shape and the center
tionalmode167cm−1 ismoreorlesstypicalforphonons position of the band is polarization-dependent, which is
(the value of 171 cm−1 at 7 K is an artefact of the dis- consistent with a suggestion that it is actually formed
persionanalysis with no physicalmeaning). On the con- by at least two high frequency intense modes. In the
trary,the 425 cm−1 and 485 cm−1 modes demonstrate a R (E a)andR spectraonecanobservesomeminor
00 45
puzzling temperature dependence, similar to that of the contribuktionfromtheA1 (162cm−1)andA2 (323cm−1)
A3 mode 400cm−1. Firstofall, there is no indicationof u u
u
5
◦
modes. Thepossiblereasonissomemisorientationofthe imum angle change is 4 - 5 , while the change of the
sample. Aspikeatabout130cm−1 isofapparatusorigin relativeanglebetweendifferentoscillatorspolarizationis
◦
and should be ignored. less than 2 . One can state that within experimental
AsisinthecaseE b,someextrastructuresareseen. errors oscillators angles almost doesn’t change.
The firstisabroadbakndintherange380-425cm−1. It To investigate the true shape of the principal phonon
is especially pronouncedfor E a, less evident for inter- modes and additional structures, the KK analysis of the
k
mediate polarization and absent for E a (see the left ac-plane data for the mentioned set of temperatures
insets in Fig. 9). A dip at 425 cm−1, in⊥doubtedly corre- was implemented in the extended form22. At Fig. 12
lateswiththedipatthesamefrequencyatreflectancefor all the components of the optical conductivity tensor
E b. The second is a pronounced structure consisting σˆ (ω)=ωImǫˆ (ω)/4π areplottedforselectedtemper-
ac ac
ofka peak at 480 cm−1 and a dip at 485 cm−1 in atures. Note that the off-diagonal component σ may
xz
∼ ∼
the R spectrum, existing at all temperatures. In spite have any sign unlike the diagonal components σ and
90 xx
of proximity of this frequency to additional structure at σ which must be positive.
zz
Fig. 3, a completely different temperature dependence The polarization angle of the B2 mode is 35◦, which
u
makes one to separate these modes. The third structure is close to the direction of the [101] chains. The B3
u
is a dip at 507 cm−1 on the top of the reststrahlen mode is almost orthogonal to the B2 mode: the angle is
∼ ◦ u
bandofR andR (seetherightinsetsinFig.9). This -55 , which is close to the [101] chains direction. There-
00 45
frequency is very close to the LO frequency of the A3 fore, with some approximation one can state, that the
u
mode, therefore it is most likely the A3 mode which is B2 and B3 modes are stretches of the [101] and [101]
u u u
seen in this spectrum for the same reason as the A1 and chains correspondingly, which is in agreement with sev-
u
A2 modesare. Thefourthstructureisseeninthevicinity eral lattice dynamical calculations10–12,23,24. Note, that
u
oftheB1 mode(Fig.10). Theshapeofthismodeissuch suchorthogonalityis notdeterminedbythe crystalsym-
u
that it is worth to suggest, that it is actually composed metry. Thepolarizationanglesofbothmodesarealmost
of two different modes (see, especially, Fig.10(c). temperature-independent.
For each temperature a fitting procedure with intro-
duction of 3 oscillators, corresponding to principal B
u
modes has been performed. The phonon polarization VI. DISCUSSION
angles were adjusted along with other phonon param-
eters. Spectra R00, R45 and R90 were fitted at the same A. Comparison with previous results
time. In the spirit of the FG-analysis prediciton, three
lattice modes were introduced for spectra fitting: one
A comparison of our data with previosly reported re-
low-frequency, and two high-frequency modes. The fit
sults of IR studies of CuO cannot be direct, because we
quality for T = 100 K is seen on the Fig. 5(b)-(d). One
measured spectra, where the A and B modes are sep-
can see that the B1 145 cm−1 mode as well as the gen- u u
u arated and excited in purely transverse regime. All the
eralshapeofthereststrahlenbandat450-600cm−1 are
quantitative and even qualitative deviations with previ-
satisfactorily reproduced, confirming a suggestion that
ous data (see below) can be ascribed to a different way
only 3 strong phonon modes are present. A bump at
of spectra measurement and analysis.
about 620 cm−1 is fitted without invoking of additional
At the Table I the phonon frequencies at room
Lorentzians: it results from the non-collinearity of the
temperature previously obtained by means of infrared
mode and the incident radiation polarizations. spectroscopy10–13 aswellasneutronscattering23 arecol-
The temperature dependence of the B phonon pa-
u lected. It is seen that the most serious discrepancy be-
rameters is presented at Fig. 11. Unlike the case of the
tween reported values of phonon frequencies takes place
Au modes, there is no significant difference in the tem- for modes A3, B2 and B3, which are very intense and
peraturedependence ofparametersofthe low-andhigh- u u u
manifest the largest LO-TO frequency splitting. Pure
frequencyB modes. Allmodesaremonotonicallyhard-
u TO mode should have the lowest possible frequency,
ening with cooling down, with some positive kink at T
N which is in nice agreement with the current result: our
for the B3 mode and negative kink for the B2 mode.
u u reported frequencies are smaller than those reported in
The plasma frequencies of all modes have slight maxi-
other IR spectroscopy papers. One should mention a
mumatthe transitiontemperature. Twohighfrequency
muchbetter agreementbetweenourdataandthe results
modes are much more intense than the Bu1 mode. The of neutron scattering experiments23, where characteris-
linewidth of all the modes doesn’t decrease with cooling
tics of pure TO modes were determined as well.
down. Instead, it increases at low temperatures. One The softening of the A3 mode was reportedby Homes
should be careful in a straightforward interpretation of et al13, who observed a suudden drop of the phonon fre-
this result, because the lineshape is not described per- quency at the N´eel transition from 450 to 430 cm−1, i.e.
fectly, especially one of the high-frequency modes. The
5%. Ourdataqualitativelyconfirmthisinterestingre-
true linewidth is better seen from the optical conductiv- ∼
sult. We observe even stronger effect: the TO frequency
ity graph (see below). The oscillator polarization angles
do not significantly change with frequency. The max-
6
drops from 410 to 370 cm−1 ( 10 %), which is twice as displacement of the oxygen atoms along the b-axis. It
∼
large as was reported (Fig. 6). results also in a large dipole moment of this mode. As
Ref.13, was thus far the only paper, to our knowledge, a consequence, the Cu-O-Cuchainangle experiences the
where IR spectra of single-crystal CuO at low tempera- largestvariation,whentheA3 modeisexcited. Thecop-
u
tures were studied. Authors didn’t report any new IR- per spins are coupled via the superexchange interaction,
activemodesbelowtheN´eeltemperature;itwasimplied, which is very sensitive to the Cu-O-Cu angle. In the
◦
that no additional lines are present at higher temper- [101] chains the angle is equal to 146 (Fig. 2), which
◦
atures either. However, an absence of extra IR-active is close to the 180 superexchange. It gives a negative
modes is quite strange, if one compares it with an ob- exchange constant and AFM interaction. However, the
servation of at least 5 ”unexpected” lines in the Raman 90◦ superexchange is expected to be positive27 (an in-
spectra15. Conversely,accordingtoourdata,several”ex- direct confirmation is the ferromagnetic exchange along
◦
tra”modesarepresentinIRspectrainthe whole7-300 the [101] chain with angle equal to 109 ), and there ex-
K frequency range. We believe, that better orientation ists some intermediate angle, where the superexchange
of the wave vector and polarization of the incident ra- is changing sign. Therefore, the motion of atoms, corre-
diation may facilitate observation and analysis of minor sponding to excitation of the A3 mode can significantly
u
IR-active modes. vary the value of the superexchange coupling constant.
A strong chain bending probably could alternate the ex-
change sign.
B. The A3u mode anomaly Due to energy and momentum conservation a zone-
center phonon can couple to a pair of magnons (bi-
The A3 mode among other principal IR-active modes magnon) having opposite wave-vectors and one-half fre-
u
behaves in the most anomalous way. It is demonstrated quencyofthephonon. Anotheroptionisinteractionwith
at Fig. 13, where relative RT-normalized TO frequen- a single zone-center optical magnon of the same energy.
cies and relative linewidths of all 6 principal modes are Themagnondispersioncurveshasbeenstudiedbyinelas-
plotted together on the same graph. A close relationbe- tic neutron scattering3,6. One acoustic and one optical
tween magnetic ordering transition at 213 - 230 K and branch were observed; the energy of optical magnon at
temperaturetransformationsofthismodeiswithoutany the Γ point is 5.6 THz (187 cm−1), which is very close
doubt. to one-half of the A3u mode frequency (370 - 380 cm−1
At300Kand,especially,atthetransitiontemperature atlowtemperatures),whilenoopticalmagnonsnear370
the mode is anomalously broad (12 - 15 %), which indi- - 410 cm−1 were observed. Therefore, the ”bi-magnon”
cates, that it is strongly coupled to some system quasi- or,inparticular”opticalbi-magnon”scenarioofresonant
particles. The most probable candidates are the low- phonon-magnon coupling is the most probable. A more
energy magnetic excitations. If one propose, that there detailed theory of this effect has to be fabricated.
is a strong coupling between spin excitations and the
A3 lattice mode, the temperature transformationsofthe
u
mode can be explained by reconstruction of the magnon C. Other signatures of spin-phonon interaction
spectrum upon cooling down below the N´eel tempera-
ture. It is well established3,4,6, that spin correlations in The anomalous properties of the A3 mode is not the
u
the AFM [101] chains are present well above the N´eel onlymanifestationofthespin-phononinteractioninCuO
temperature. Athightemperaturesone canconsiderthe (although the most prominent one). Other modes also
magnetic interaction to be of quasi 1D character. In the demonstrate some anomalies, most likely related to the
1D Heisenberg AFM chains with S=1/2 and exchangeJ magnetic ordering.
thereisacontinuumoftripletexcitationswithlowerand One type of anomalies is unusually strong hardening
upper boundary curves25,26 ǫ (q) = (πJ/2)sin(q) and of some ”extra” modes below T . The most outstand-
min N
ǫ (q)=πJsin(q/2). AlargelinewidthoftheA3 mode ing example is reported in this work hardening of the
max u
can be explained by its interaction with continuum of 690cm−1 mode from650cm−1 at150 K to 690cm−1 at
magnetic excitations. Below the N´eel point an exchange 7 K and strong hardening of the the Raman-active 240
interaction in another directions gives rise to long-range cm−1 mode found by Chen et al15. To our mind, these
magnetic ordering and a continuum of spin excitations effects are related. We would follow the idea of explana-
should collapse to the magnon dispersion curves, which, tion given in Ref.15. The phenomenon can be viewed as
in turn, results in narrowing of the phonon mode. anon-resonantspin-phononinteraction,whenspinprod-
The reason for an exceptionally strong interaction of uctsintheHeisenbergHamiltoniancanbeapproximated
the A3 mode with spin excitations one should look for by their effective averages. In this case the temperature
u
in analysis of its eigenvector. Several lattice dynami- dependence of the phonon frequency is expressed by:
cal calculations were performed10–12,23,24 which yielded
the lattice mode eigenvectors. According to resultsof all ω2(T)=ω2 + Cn S S (T). (7)
n n0 ij ·h i ji
the calculationsthismode ischaracterizedbythe largest Xij
7
TheCn coefficientsarecharacteristicsofspin-phononin- curvesatlowtemperaturesinbroaderenergyintervalare
ij
teraction; in principle, they may have any sign, depend- desirable.
ing on the eigenvector of the particular phonon mode. Although some ”extra” modes have analogs in the B
Themodestronghardeningissupposedlyduetothesec- or C points, folding of the A and X points to the zone
ond ”spin” term: magnetic orderinggives additionallat- center(the A + Xfolding scheme)is the simplest option
tice rigidity. to explain appearance of all ”extra” modes. It corre-
The same phenomenon is possibly responsible for an- sponds to the ”diagonal”doubling of the unit cell a, b,
{
other anomaly, namely, the change of slope ∂ω /∂T of c a+c, b, a-c (see Fig.14). This scenario looks
TO
} → { }
theprincipalphononmodesattheN´eelpoint(seeFigs.6 attractive, because new crystal axes correspond to prin-
and 11). It is seen that for the modes A1, A2 and B3 cipalanisotropydirectionsforseveralphysicalproperties
u u u
the slope is higher in the AFM phase, while for the B2 (exchange constants, sound velocity, principal dielectric
u
mode the slope is higher at T >T ; for the B1 mode it axes etc.), and the unit cell is the same as the magnetic
N u
doesn’tchangeatall. Suchadifferencescanbeexplained unit cell in the AFM phase2.
by different values and signs of coefficients Cn. In the framework of this scenario the A3 principal
ij u
mode, the 485 cm−1 and the 425 cm−1 ”extra” modes
shouldbe the phononmodesfromthe points Γ,AandX
D. ”Extra” zone-center modes and zone folding correspondinglybelongingtothesamedispersionbranch,
accordingto”rigid-ion”modellingofdispersioncurvesby
Activationofadditionalphononmodesininfraredand Reichardt et al23. It is in a good agreement with some
Raman spectra is usually a signature of unit cell multi- similarity of temperature dependences of parameters of
plication and zone folding. Such activation is in effect in these modes (see Figs. 6 and 7).
CuO.Asisstatedabove,several”extra”IR-activemodes In summary, we propose, that in reality the crystal
are observed. In the Raman spectra 5 new modes were structure is more complicated, than was considered be-
detected at low temperatures15. Authors related their fore; it is the case, to our mind, already at room tem-
frequencies to the phonon dispersion curves obtained by perature, because most of ”extra” IR-active modes are
inelasticneutronscattering23atthezoneboundarypoint. present in the whole temperature range. On the base of
In Ref.15 this point was referred to as Z′. We follow the fact that IR-active and Raman-active modes have
the originalnotation and designate it by X (see Fig.4 in different frequencies one can suggest that the crystal
Ref.23). space-group is still centro-symmetric, although the cop-
At Fig.14 the Brillouin zones corresponding to sev- per atoms are not necessarily located in the Ci posi-
eral schemes of the unit cell multiplication are drawn tion. However, the alternative space-group for the CuO,
(a projection to the ac-plane). In these schemes differ- proposed by Asbrink and Waskowska, is not centro-
ent symmetry points fold to the zone center. It is easy symmetric(C4s);thesolutionofthismismatchisunclear.
to prove, that folding of the X-point to the zone center One of the central issues is the mechanism of the
is equivalent to disappearance of the non-trivial transla- unitcellmultiplicationandformationofsuperstructures.
tion (a+b)/2, or base-centering of the space-group. In Thereexistavarietyofexamplesofsucheffect,when”ex-
other words, activation of the phonons from the X point tra” IR and/or Raman modes are emerging, which are
requires that the unit cell should become the primitive undoubtedly the zone-boundary folded phonons. In the
′
one. extensivelystudiedcompoundsCuGeO3 andα-NaV2O5
In the Table II ”extra” IR active and Raman-active the unit cell doubles as a result of spin-phonon inter-
mode frequencies are collected. Each mode frequency action, and new IR modes are observed28,29. Another
is related to close phonon energy (if any) in symmetry examplepresentcompoundswithachargedisproportion-
points X(1, 0, 0), A(1/2, 0, -1/2), B(1/2, 0, 0) or C(0, ation, out of those the BaBiO3 is probably the most
1/2,0)at 300K. To make comparisonmore reliable,the famous one. In this system the bismuth is dispropor-
”extra” modes frequencies are taken at temperature as tionatedaccordingtoscheme: 2Bi4+ Bi3++Bi5+,and
→
closeaspossibleto300K.Onecansee,thatmanymodes atoms in different valence states form superstructure,
(all Raman-active and severalIR-active ones) have close whichis a reasonfor”extra”quite strongIR line30. One
analogsattheXpoint. Atthesametime,otherIR-active cannotexcludeacollectiveJahn-Tellereffectasanengine
modes(147cm−1,165cm−1,475cm−1,480cm−1)could of superlattice formation. The question about particular
bephononsfromtheApoint,or,insomecases,fromthe type of spin-charge-lattice ordering in CuO is open. It
BorCpoints. The690cm−1 modeisaspecialcase: due could be closely connected with formation of inhomo-
to strong hardening of this mode with cooling and fail- geneity phases in cuprates.
ure to observe it at high temperatures, the comparison
to the 300 K dispersion data is impossible. In addition,
the mode energy is higher than the upper limit of the
reported frequency region in the neutron scattering ex-
periments(20THz,or667cm−1). Thephonondispersion
8
∗ ∗
e 3e
E. High-frequency dielectric function Ze= T , e∗ = T . (9)
√ǫ∞ s ǫ∞+2
The reflectivity andthe dielectric function in the mid-
The value of Ze divided to the nominal valence is often
infrared range well above the maximum phonon energy
considered as the degree of ionicity32. For the CuO it
( 0.08 eV) but below the optical gap ( 1.3 eV) are
∼ ∼ appearstobeabout40%. TheSzigetichargeisusefulin
determined by the electronic polarizability. We observe
the context of the polarized point ions model33. In liter-
significant difference between values of mid-infrared re-
ature all these charges are used, so that it is reasonable
flectivity for different polarizations. It results in an ap-
to report all of them.
preciable anisotropyofthe high-frequency dielectric ten-
In the Table III oxygen effective charges for the CuO
sor. Thetemperaturedependenceofthemid-IRreflectiv-
alongwithotherrelatedcopperoxides(Cu O,La CuO ,
ityis small,therefore,wediscussonlyroom-temperature 2 2 4
Nd CuO andYBa Cu O )arecollected. Itis seenthat
data. All the components of the ǫˆ∞ can be found from 2 4 2 3 6
chargevaluesinCuOreasonablyagreetothecorrespond-
the dispersion analysis of spectra, see formulas (1), (2).
ing values in other relevant oxides.
The smallest value of ǫ∞ is observedalong the b-axis:
∞
ǫ = 5.9; it is apparently one of the prinicipal values
b
of the dielectric tensor. The diagonalization of the ten-
VII. CONCLUSIONS
sor gives directions and values of maximal and minimal
levels of ǫ∞ within the (ac)-plane. The maximal value
∞ We have measured far- and mid-infrared reflectivity
ǫ =7.8isobservedalongthedirection,corresponding
max ◦ ∞ spectraofmonoclinicCuOfromthe(010)and(001)crys-
to the angle φ = 36 , the minimal value ǫ =6.2
max − mi◦n talfacesinwidetemperaturerange. Weobtainedforthe
is along the orthogonal direction for φ = 54 . One
min
first time characteristics of pure TO A and B modes
can see that direction φ is very close to direction u u
max
of the [101] chains (φ = 42.5◦) while φ almost separately. Our data finally confirm that there are 3Au
exactly corresponds to[10φ1] −= 52.8◦. In otmheinr words, + 3Bu intense modes, in accordance with prediction of
[101] the FG-analysis for the C6 space-group.
the high-frequency dielectric constant within the (ac)- 2h
We report existence of several”extra” less intense IR-
plane is maximal along the [101] direction, and minimal
active modes in CuO. Analysis of the phonon dispersion
along the [101] direction. Authors31 have measured the
curvesleadstotheconclusionthateach”extra”IR-active
high-frequencydielectricfunctionofpolycrystallinesam-
aswellasreportedearlier15Raman-activemodecouldbe
ple by the ellipsometric method. Their reported value
∞ folded phonon from either X (1, 0, 0) or A (1/2, 0, 1/2)
ǫ =6.45isinagoodagreementwiththeaveragequan-
∞ ∞ ∞ symmetry points. Such folding is compatible with the
tity (ǫ +ǫ +ǫ )/3=6.6 obtained here.
xx yy zz ”diagonal” doubling of the unit cell with the new basis
a+c,b,a-c . Sothespace-groupinrealityislowerthan
{ }
that was considered, but still centro-symmetric.
F. Effective charges
The690cm−1”extra”IR-activemodeexhibitsanoma-
loushardening,similartobehaviourofthe240cm−1 Ra-
Anotherimportantvaluederivedfrominfraredspectra
man mode; the reason could be in additional rigidity of
is an effective ionic charge. There are several definitions
lattice due to magnetization, a special manifestation of
of the effective charge. We would mention the Born, or
the spin-phonon interaction. Another effect, which can
∗ ∗
”transverse” charge e , the Szigeti charge e and the
T s be explained in a similar way, is a slope change of the
Scott charge Ze32. The ”transverse”charges can be cal-
phonon frequencies vs. temperature at the N´eel point.
culated using the sum-rule: The anomalous softening and narrowing of the A3
u
4π (e∗ )2 mode 410 cm−1 we explain by its strong resonance cou-
ω2 = T,k , (8) pling to the optical or acoustic bi-magnons. Reconstruc-
Xi p,i vc Xk mk tion of magnetic excitations spectrum at the AFM tran-
sition strongly affects the phonon characteristics.
where vc is the primitive cell volume, the sum in the left In summary, the CuO demonstrates a variety of
side is over IR-active modes, the sum in the right side is anomalous properties, which show complex interplay of
over all atoms in the primitive cell. For the binary com- spin, charge,and phononsubsystems alreadyin the sim-
poundthis relationincombinationwiththeelectric neu- plest copper(II) oxide. A further insight into physics of
trality condition directly yields the ”transverse” charge CuO may contributeto elaborationofnon-contradictory
of both atoms. In CuO due to anisotropy the transverse picture of antiferromagnetism and superconductivity in
chargeslightly differs for different directions. The values the high-T cuprates.
c
alongthe [010](b-axis)the[101]andthe [101]directions
atroomtemperature are1.92,2.04and2.10correspond-
ingly (the ω are taken from the Figs.6, 11).
p,i
TheScottchargeandSzigetichargesarerelatedtothe
”transverse”charge:
9
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