Mott-Hubbard versus charge-transfer behavior in LaSrMnO4 studied via optical conductivity

1.3 MB·

by  A. Gössling

Mott-Hubbard versus charge-transfer behavior in LaSrMnO
4
studied via optical conductivity
A.G¨ossling,M.W.Haverkort,M.Benomar,HuaWu,D.Senff,T.Mo¨ller,M.Braden,J.A.Mydosh,andM.Gru¨ninger
II. Physikalisches Institut, Universit¨at zu K¨oln, Zu¨lpicher Str. 77, 50937 K¨oln, Germany
(Dated: September21, 2007)
Usingspectroscopicellipsometry,westudytheopticalconductivityσ(ω)ofinsulatingLaSrMnO4
intheenergyrangeof0.75-5.8eVfrom15to330K.Thelayeredstructuregivesrisetoapronounced
anisotropy. A multipeak structure is observed in σa(ω) (∼2, 3.5, 4.5, 4.9, and 5.5 eV), while only
1
one peak is present at 5.6 eV in σc(ω). We employ a local multiplet calculation and obtain (i)
1
an excellent description of the optical data, (ii) a detailed peak assignment in terms of the multi-
8
plet splitting of Mott-Hubbardand charge-transfer absorption bands, and (iii) effective parameters
0
0 of the electronic structure, e.g., the on-site Coulomb repulsion Ueff=2.2 eV, the in-plane charge-
2 transfer energy ∆a=4.5 eV, and the crystal-field parameters for the d4 configuration (10Dq=1.2
eV,∆eg=1.4eV,and∆t2g=0.2eV).Thespectralweightofthelowestabsorptionfeature(at1-2eV)
n changesbyafactor of2as afunction oftemperature,which can beattributedtothechangeof the
a nearest-neighborspin-spincorrelationfunctionacrosstheNeeltemperatureTN=133K.Interpreting
J
LaSrMnO4 effectively as a Mott-Hubbard insulator naturally explains this strong temperature de-
9 pendence,therelative weight ofthedifferentabsorption peaks,andthepronouncedanisotropy. By
means of transmittance measurements, we determine the onset of the optical gap ∆aopt = 0.4-0.45
] eV at 15 K and 0.1-0.2 eV at 300 K. Our data show that the crystal-field splitting is too large to
l
e explain theanomalous temperature dependenceof the c-axis lattice parameter by thermal occupa-
- tionofexcitedcrystal-fieldlevels. Alternatively,weproposethatathermalpopulationoftheupper
r
t Hubbardband gives rise to the shrinkageof thec-axis lattice parameter.
s
.
t PACSnumbers: 71.20.Be,71.27.+a,75.47.Lx,78.20.-e
a
m
- I. INTRODUCTION CTexcitationsinLaTiO .2 Thiscanbeattributedtothe
d 3
TM -O hopping amplitude t : σ (ω) ∝ t2 for CT
n 3d 2p pd 1 pd
o and ∝ t4 /∆2 for MH excitations (see below). Second,
The insulating behavior of many transition-metal pd
c the polarization dependence may be very different, de-
[ (TM) compounds with a partially filled 3d shell is a
pending on the crystal structure. In layered LaSrMnO ,
clear manifestation of strong electronic correlations. In 4
2 theZaanen-Sawatzky-Allenscheme,1 thesecorrelatedin- the interlayer Mn-Mn hopping is strongly suppressed;
v thus, the contribution of MH excitations should be neg-
sulators are categorized into Mott-Hubbard (MH) and
1
1 charge-transfer (CT) types. In the former, the on-site
7 Coulomb repulsion U is larger than the band width W;
3 thus, the conduction band splits into lower and upper PES IPES
9. Hubbard bands (LHB and UHB, see Fig. 1). At half O2p Ef
0 filling, the lowest electronic excitation is from LHB to
7 UHB, dndn → dn−1dn+1, where dn denotes a TM ion
0 with n electrons in the 3d shell. In a CT insulator, U is U
: larger than the charge-transferenergy ∆; thus, the LHB NB
v
i ispushedbelowthehighestoccupiedbandoftheligands, B AB
X
e.g., O 2p (see Fig. 1). Here, the lowest electronic exci- U
eff
r tation is from O 2p to UHB, p6dn →p5dn+1. Typically,
a
early TM compounds are of MH type, whereas late ones
such as the high-Tc cuprates belong to the CT class.2 LHB –TM3d (cid:39) UHB
For manganites with Mn3+ 3d4 configuration, e.g.,
FIG.1: Sketchof thedensity of states [photoemission (PES)
LaMnO or LaSrMnO , the characterization is not as
3 4 and inverse photoemission (IPES) spectra] for a single, half-
straightforward. The analysis of photoemission data in-
filled3dorbitalanddegenerate,fullO2porbitals. Theon-site
dicates U &∆, i.e., a CT character.3 Yet, most theoret-
Coulomb repulsion U increases from top to bottom, whereas
ical approaches employ an effective Hubbard model (see the charge-transfer energy ∆ is assumed to be constant. EF
below). Both MH and CT types have been proposed denotes the Fermi level. Top: Mott-Hubbard insulator for
on the basis of optical data.2,4,5,6,7,8,9,10 For U ≫ ∆ U≪∆. Bottom: charge-transfer insulator for U≫∆. In the
or U ≪ ∆, there are different ways to disentangle MH absence of hybridization, the bands follow the straight lines
and CT excitations in the optical conductivity. First, withincreasingU. Withhybridization,onehastodistinguish
the spectral weight of CT excitations is larger, e.g., bonding(B), antibonding(AB,bothblack),and nonbonding
σ (ω) ∼500 (Ωcm)−1 for MH and ∼5000 (Ωcm)−1 for bands(NB, gray).
1
2
ligible in σc(ω). In contrast, CT excitations contribute optical data. For instance, in LaSrMnO , one expects
1 4
to both σa(ω) and σc(ω) due to the octahedral O co- that the AB band shows the pronounced anisotropyand
1 1
ordination of the Mn sites. Third, the spin and orbital the strong temperature dependence discussed above for
selection rules are different, giving rise to a different be- the MH case. Thus, “MH or CT” is not the essential
haviorofthespectralweightasafunctionoftemperature question for U ∼ ∆ and strong hybridization. In this
T.8,9,10,11,12,13,14,15,16,17,18 As an example, we consider a sense, we analyze our data in terms of an effective Hub-
MH insulatorwitha single 3dbandandone electronper bardmodelwitharathersmallvalueofU =2.2eV.Ex-
eff
TM site. In the case of ferromagnetic order, the spec- citations from NB to UHB are treated as CT and from
tral weight of MH excitations is zero due to the Pauli AB to UHB as MH. We find that these effective MH ex-
principle(neglectingspin-orbitcoupling,thetotalspinis citations are significantly lower than the CT excitations.
conserved in an optical excitation). Thus, one expects a The effective model does not contain the B band, which
drasticchangeofthespectralweightuponheatingacross is important for optical or photoemission measurements
the magnetic ordering temperature. In contrast, the O at higher energies. However, we fully take into account
2p band is completely filled and the spectral weight of the multiplet splitting of the MH and CT bands caused
CT excitations is independent of the magnetic proper- by the multiorbital structure of the 3d shell.
ties. For comparisonwith experimentaldata, the orbital Here, we focus on LaSrMnO , which crystallizes in
4
multiplicity has to be taken into account and the op- the layered K NiF structure with tetragonal symmetry
2 4
tical spectra of MH excitations contain valuable infor- I4/mmm.20 The lattice constants at room temperature
mation on orbital occupation and nearest-neighbor spin area=3.786˚A andc=13.163˚A.AllMnionshaveanom-
and orbital correlations. This kind of analysis has been inal valence of +3 (3d4 with spin S=2). Antiferromag-
applied to a number of different TM compounds (Mn, netic order has been observed below T =133 K.21,22,23
N
V,Ru,Mo).8,9,10,11,12,13,14,15,16,17,18 InLaMnO ,thereis Neglecting hybridization, the four 3d electrons occupy
3
some disagreement on the experimental side: LaMnO the xy, yz, zx, and 3z2-r2 orbitals with parallel spins,
3
has been interpreted as MH type due to a pronouncedT whilex2-y2isempty.24SimilartoLaMnO ,alsothechar-
3
dependence observedby spectroscopic ellipsometry9 and acter of LaSrMnO – MH vs CT – has been discussed
4
as CT type due to the absence of a significant T de- controversially.4,7,25,26,27,28,29 Previousopticalstudiesre-
pendence across the Neel temperature TN in reflectivity ported σ1a(ω) for 300 K (Ref. 4) and very recently for 10
measurements.8Notethatitisstillunclearinwhichcom- K.7Bymeansofspectroscopicellipsometry,wedetermine
poundsthiskindofanalysiscanbeapplied. Forinstance, theopticalconductivitytensorσ(ω)between0.75and5.8
in YTiO , the lowest MH excitation shows a strong T eV as a function of temperature. Using a local multiplet
3
dependence but only a weak dependence on the mag- calculation, we interpret the observed absorption bands
netic properties.19 However, our analysis of LaSrMnO in terms of effective Mott-Hubbard and charge-transfer
4
fully corroboratesthe intimate relation between spectral excitations. This assignment utilizes the points raised
weight and magnetism reported by Kovaleva et al.9 for above, i.e., the pronounced anisotropy, the difference in
LaMnO . spectral weight, and the strong temperature dependence
3
of the spectral weight. Using transmittance measure-
Does this prove that LaMnO and LaSrMnO are of
3 4 ments, we determine the optical gap ∆ =0.4-0.45 eV at
MH type? The d5 configuration is particularly stable. a
15 K and 0.1-0.2 eV at 300 K. Our data indicate that
Thus, the d4 configuration has a strong d5L contribu-
the anomalous shrinkage of the c-axis lattice parameter
tion,whereLdenotesaligandholeandtheO2porbitals
with increasing temperature cannot be attributed to a
certainly play an important role. As stated above, with
thermal occupation of local crystal-fieldlevels22,30,31 but
U &∆,3 themanganitesmaybe categorizedasCTtype.
rather to a thermal population of the UHB.
However, for the analysis of, e.g., optical data, it is im-
Section II describes the experimental details. Our op-
portant to consider the symmetry. Let us discuss the
tical data and a detailed analysis of the spectral weight
simplified case of a single, half-filled 3d band and degen-
are reported in Sec. III. The local multiplet calculation,
erate, full O 2p bands. Due to hybridization, one has
the effective parameters of the electronic structure, and
to distinguish bonding (B), antibonding (AB), and non-
thecalculationofσ(ω)basedonthemultipletcalculation
bonding (NB) bands below the Fermi level (see Fig. 1).
arediscussedinSec.IV.Finally,inSec.V,wediscussthe
The AB band is the highest occupied one. It has mainly
peakassignmentintermsofthemultipletsplittingofMH
TM character for U ≪ ∆ and mainly O character for
and CT absorption bands, the relationship between the
U≫∆. For the intermediate situation U ∼∆, the char-
spectral weight and superexchange, and the anomalous
acterisstronglymixed. However,inthemanganiteswith
thermal expansion.
a less than half-filled 3d shell, the symmetry of the AB
bandisdeterminedbythesymmetryofthe3dband,i.e.,
it can be described in terms of a Wannier orbital with
II. EXPERIMENTAL
d symmetry centered around a Mn site. In particular,
the spin and orbital selection rules mentioned above for
a MH insulator apply also to the AB band. These se- Single crystals of LaSrMnO have been grown using
4
lection rules are most important for understanding the the floating zone technique following Ref. 20. The sam-
3

8 6 1.66 a axis (0.75, 5.50) eV 1.16
a) LaSrMnO T
4 N c axis
6 4 1.62 1.12

4 2 1.58 1.08
a axis
2
2 0 a a xis
15 K 200 K 1.14 (0.75, 4.00) eV 0.56
52 K 250 K
6 100 K 295 K 4 eff 1.10 (4.00, 5.50) eV 0.52
120 K
N
330 K
4 2
150 K 1.06 0.48
c axis
2 0 a axis
(0.75, 2.80) eV
b) 3.0 0.16 0.40
400
) 2.0 200 (2.80, 4.00) eV
-1 cm 0 0.12 0 .36
-1 1.0 1 2 3

3 a axis
0 0 100 200 300
(1 0.0
1 4.0 15 K 200 K Temperature (K)

52 K 250 K
100 K 295 K FIG. 3: (Color online) Top: effective carrier concentration
2.0 120 K 330 K Neff(ω1,ω2) for the a and c directions with ω1=0.75 eV and
150 K ω2=5.5 eV. Middle and bottom: Neff for the a direction for
different energy ranges.
c axis
0.0
c) 0.2 a axis lam VASE) equipped with a retarder between polarizer
and sample. By measuring on a polished ac surface,
we determined the normalized Mu¨ller matrix elements
-1 m) 0.0 mk =Mk/Mk (i=1-3,j=1-4,k=1-2),32 where k=1 (2)
ij ij 11
-13 c10 -0.2 11122300KK-- 111152K0K pccioedrnerdneisccpeuolwnardassto7to0t◦hm.eeWpalseaunroeebmtoaefinnitnesdciwdεeiatnhcaent.dheTεcaheb(yca)nfigatltxeiinsogfpteihnre--
(1 0.2 1330K- 1230K nonvanishing elements mk12, mk21, mk33, and mk34.33 We
have checked that the results fulfill the Kramers-Kronig
consistency. The ellipsometric measurements have been
0.0
performed from 15 to 330 K in a UHV cryostat with
p < 10−9 mbar. The effect of the cryostat windows has
-0.2
c axis beendeterminedusingastandardSiwafer. Ourdataare
consistent with spectra of Refs. 4 and 7.
1 2 3 4 5
Inordertodeterminetheopticalgap,wemeasuredthe
Energy (eV) transmittancefrom5to300KusingaFourier-transform
FIG. 2: (Color online) [(a) and (b)] Dielectric constant and spectrometer(BrukerIFS66v). Thesamplewasapprox-
optical conductivity of LaSrMnO4 for the a and c directions imately 70 µm thick and has been prepared in the same
between 0.75 and 5.80 eV for different temperatures. (c) way as described above.
Change of the optical conductivity: σ1(330 K)-σ1(230 K),
σ1(230K)-σ1(120K),and σ1(120K)-σ1(15K).
III. RESULTS
ple quality and stoichiometry were checked using polar-
A. Ellipsometry and interband excitations
izationmicroscopy,neutrondiffraction,andx-raydiffrac-
tion. The two nonvanishing, complex entries εa and εc
of the dielectric tensor for tetragonalsymmetry were de- In Fig. 2(a), we plot εl = εl +ıεl (l=a,c) from 0.75
1 2
termined using a rotating-analyzer ellipsometer (Wool- to 5.8 eV. For convenience, the real part σ =(ω/4π)ε
1 2
4
is transferred from 3.5 to 3.0 eV and from 4.5 to 2.0 eV
a) [see Fig. 2(c)].
6 We analyze the T dependence of the SW using the
a 1
effective carrier concentration N ,
eff

4 2mV ω2
N (ω ,ω )= σ (ω)dω (1)
eff 1 2 πe2 Z 1
ω1
4 15 K where m denotes the electron mass, V the unit cell vol-

fit ume, and e the electron charge. Equation (1) translates
a 2
into the f-sum rule for ω →0 and ω →∞.34 As shown
330 K 1 2
2 fit in Fig. 3, the total spectral weight Neff(0.75eV,5.5eV)
15 K decreases(increases)withincreasingT forthea(c)direc-
tion. Inσa,wefindanisosbesticpointatω ≈4.0eV.The
1 i
0 corresponding transfer of SW is evident from the com-
parison of N (0.75eV,4.0eV) and N (4.0eV,5.5eV)
eff eff
(3) (see middle panel of Fig. 3). The transfer of SW sets in
a 2
22 (2) roughly30K belowTN=133K,butthe curvespossesan
(1) 330 K inflection point approximately at T .
N
The direct integration of σ (ω) in Eq. 1 has the ad-
1
00 vantage to be model independent. For a more detailed
0 1 2 3 4 5 6 7 analysis of the T dependence of the individual absorp-
Energy (eV) tion bands, we fit ε1 and ε2 simultaneously using a sum
of Drude-Lorentz oscillators,34
b) 0.20
peak (1) 0.203 ǫ(ω)=ǫ + ωp2,j (2)
0.16 peak (2) 0.146 ∞ Xj ω02,j −ω2−ıγjω
sum of both
where ω , ω , and γ are the peak frequency, the
0.12 0,j p,j j
plasma frequency, and the damping of the jth oscilla-
t = 0.55 eV
tor, and ǫ denotes the dielectric constant at “infinite”
eff 0.08 t = 0.65 eV frequency∞(i.e., above the measured region). The plasma
N
frequency is related to the spectral weight of a single
0.04 0.056 TN Lorentzian,34 ∞σ (ω)dω =ω2/8.
0.040 0 1 p
UsingsevenRoscillators,weobtainanexcellentdescrip-
0.00 tion of both εa and εa, which clearly demonstrates the
1 2
Kramers-Kronig consistency [see Fig. 4(a)]. The peak
0.16
frequency of one of these seven oscillators is outside the
0.14 measured region (dashed line). It corresponds to the
peak (3) strong feature observed at about 7 eV by Moritomo et
0.12 al. at room temperature.4 The parameters ω and γ of
0
0 100 200 300 this strong oscillator have been assumed to be indepen-
Temperature (K) dent of T. Since ellipsometry determines both ε and ε
1 2
FIG. 4: (Color online) (a) Lorentzian fit of ǫa (top panel) independently,thecontributionsofhigher-lyingbandsto
1
and ǫa2 (middle and bottom) for T=15 and 330 K. (b) Neff the measured region can be fixed quite accurately. For
of peaks(1)-(3) as obtained from theDrude-Lorentzfit. The the lowest three oscillators, the effective carrier concen-

horizontallinesindicatetheoreticalestimatesofNeff forT ≪ tration Neff obtained from the fit is displayed in Fig.
TN and T ≫ TN as derived from the kinetic energy for an 4(b). With increasing T, the SW of peak (3) at 3.5 eV
effectiveMn-Mn hoppingamplitudet=0.55-0.65 eV (seeSec. decreases by ∼20%, while the SW of peaks (1) and (2)
V C). at 1-2 eV increases by a factor of 2. Comparing the T
dependence of N below about 3 eV as obtained either
eff
from the Drude-Lorentz fit [Fig. 4(b)] or from the direct
of the optical conductivity is displayed in Fig. 2(b). We integrationofσ (ω) (bottompanelofFig.3), the former
1
find a striking anisotropy. In particular, there is only is even stronger because it separates contributions from
onestrongpeakat5.6eVinσc,whileamultipeakstruc- higher-lying bands. The precise determination of N
1 eff
ture is present in σa (peaks at ∼2, 3.5, 4.5, 4.9, and 5.5 is important for the comparison with the kinetic energy
1
eV). All peaks show a strong temperature dependence. (see Sec. V C below).
With increasing T, σa increases below ∼3 eV and de- We find the same trendinthe c direction. The change
1
creasesabove∼4eV.Inparticular,spectralweight(SW) of the SW of ∼10% obtained from direct integration of
5

a) 1.0 b)
dT TN 1.0
/
T d 0.8
0.5
a axis o
--llnn((TT))==45..50 T N 150 0.6pt (T)
0.4 /
0.0 o
p
5 K (a) 1.0t (
- ln (T) 2 155 K0 (Kc )(a) c axis -ln(T)=0.3 0.8 5K)
150 K (c) 0.6
-ln(T)=0.35
-ln(T)=0.4 0.4
0
0.2 0.4 0.6 0.8 0 100 200 300
Energy (eV) Temperature (K)
FIG.5: (Coloronline)(a)TransmittanceT (toppanel)ofathinLaSrMnO4 sample(d∼70µm)and−ln(T)∝αfor5and150
K. (b) Evolution of theonset of theoptical gap as determined from −ln(T)=const.
σc(ω) may be influenced by a broadening or shift of the W may change due to either a change of the lattice pa-
1
peak (since it is close to the edge of the measured fre- rameters or of the spin-spin correlations (W is reduced
quency range) or by a change in the background origi- in the antiferromagnetically ordered state). The plot of
nating from higher-lying bands. In a fit based on Eq. the derivatived∆a /dT inthe inset ofFig.5(b) andthe
opt
(2), we found a larger change in SW of ∼20%. lower panel clearly show that ∆ (T) changes its slope
opt
atT =133K (independent ofthe choiceofm andm ),
N a c
which reflects the behavior of the lattice constants.22
B. Transmittance and gap
Figure 5(a) shows the transmittance T and −ln(T)∝ IV. MULTIPLET CALCULATION
α(ω) from 0.1 to 0.9 eV for both a and c polarizations.
Here, α(ω) denotes the absorption coefficient. The cal- One may expect that a local multiplet calculation for
culation of σ (ω) additionally requires the knowledge of a single 180◦ Mn-O-Mn bond yields a reasonable as-
1
the reflectivity R in this frequency range. The transmit- signment of the CT (d4p6 →d5p5) and MH excitations
tance is a very sensitive probe in order to determine the (d4d4→d3d5)oftheundopedMottinsulatorLaSrMnO .
4
onset∆ oftheopticalgap. Forthispurpose,αandσ For simplicity, we neglect hybridization; thus, the two-
opt 1
canbeusedequivalently. Assumingareasonablevalueof site states are a simple product of two single-site states.
R=0.15−0.2,we findσa ∼1(Ωcm)−1 at0.5eVat5 K, This affects the excitation energies and the matrix ele-
1
more than 2 orders of magnitude smaller than at 2 eV. ments. Thus, we obtain renormalized parameters, e.g.,
Thus,thedatainFig.5onlyshowtheveryonsetofexci- an effective value of U , which has to be kept in mind
eff
tations across the gap. The absorption below about 0.2 for comparison with results from other techniques. The
eVcanbe attributedto weak(multi)phononexcitations. selectionrulesarenotaffectedbyhybridization,asstated
From linear extrapolation of −ln(T) to zero, we find in the Introduction. We calculated σa(ω) and σc(ω)
1 1
∆a = 0.40−0.45 eV and ∆c > 0.9 eV at 5 K. In by evaluating the matrix elements between all multiplet
opt opt
order to monitor the temperature dependence of the on- states. For more details, we refer to the Appendix and
set of the gap, we solve the equations −ln(Ta) = m Ref. 33.
a
and −ln(Tc) = m with m =5.0 and 4.5 and m =0.40, The multiplet calculation takes into account the
c a c
0.35, and 0.30, respectively, where a and c denote the Coulomb interaction and the crystal-field splitting. The
polarization direction. The results are shown in Fig. former is described by the Slater integrals F0, F2, and
5(b). At 300 K, we find ∆a = 0.1-0.2 eV. The red- F4.37,38 We use only two parameters, F0 and the re-
opt
shift of the onset of the gap with increasing T can be duction factor r in Fk(dn)=rFk (dn) for k=2 and 4,
HF
attributed to either a shift of the peak frequency or an where Fk (dn) denotes Hartree-Fock results for a free
HF
increase of the bandwidth. According to the fit results, dn ion. For the dn states, the tetragonal crystal field
peak (1) shifts by about 0.3 eV from 5 to 300 K [see is parametrized by 10Dq, ∆ , and ∆ , representing
t2g eg
Fig. 4(a)]. This shift may originate from thermal ex- the splitting between t and e levels and the splitting
2g g
pansionandelectron-phononcoupling,35,36 givingrise to within these levels, respectively. The CT energy is given
a change of the effective crystal field. The bandwidth by ∆ =E (d5)+E(p5)−E (d4)−E(p6) for l =a or c,
l 0 0
6
cupied (see Fig. 8). This is supported by our multiplet
TABLE I: Effective electronic parameters obtained from the
calculation. Intheinitialstated4p6,allO2porbitalsare
multiplet calculation by fitting the optical data for T=15 K.
occupied; thus, the excitation and its selection rules are
The factor r is dimensionless; all otherunits are in eV.
dominatedbythed5 partofthefinalstated5p5. Accord-
F0 r 10Dq(d4) ∆t2g(d4) ∆eg(d4) ∆a ∆c ing to the spin selection rule, only d5 states with S=5/2
or 3/2 can be reached from the d4 S=2 ground state.
1.20 0.64 1.20 0.2 1.4 4.51 4.13 Following Hund’s rule, the lowest d5 state corresponds
to a high-spin S = 5/2 multiplet, in which the five 3d
orbitals are equally occupied. For the orbital selection
where E (dn) is the lowest energy of the dn multiplets. rules, one thus has to consider the overlap between the
0
Thep5 statesareassumedtobedegenerate. Theseseven O2porbitalsandtheinitiallyunoccupieddx2−y2 orbital.
electronicparameters(seeTab.I)determineallpeakfre- This is only finite along the a direction but zero along
quenciesandtherelativeweightofdifferentpeakswithin c. Therefore, we cannot identify the peak at 5.6 eV in
one polarization. A constrained fit of the experimen- εc2 with the lowest CT transition. The second lowest CT
tal data requires seven more parameters (for the width, excitationinthe strongcrystal-fieldlimit correspondsto
the absolute value, and higher-lying bands, see the Ap- a transfer of one electron from O 2p into the degenerate
pendix). Altogether, we use 14 parameters, i.e., much dxz/dyz orbitals, i.e., to a final state with 3d5 S=3/2.
less than those in the Drude-Lorentz model (22 param- Theoverlapisfinite,bothintheaandcdirections. This
eters only for the a direction, see above). Moreover, assignment of the peak at 5.6 eV in εc2 is supported by
the discussion of the peak assignment below will show our multiplet calculation (cf. Fig. 6). However, the cal-
that the pronounced structure of the experimental spec- culationresolvesthe contributionsofdifferent multiplets
tra provides severe constraints for the electronic param- to the peak at 5.6 eV, and it gives the relative weight of
eters. The spectra with the lowest χ2 are plotted in Fig. the different CT bands.
6. The overall agreement is excellent. We find F0=1.2 The calculated spectrum (see Fig. 6) shows only one
eVandr=0.64,resultinginU =2.2eVandHund’scou- strongCTbandat5.6eVinεc,whileinεaanotherstrong
eff 2 2
pling J =0.6 eV (cf. Ref. 39). The energy levels of the CT band is observed at 4.5 eV. The latter results from
H
d3,d4,andd5 multipletsareshowninFig.7asafunction an excitation into the lowest d5 final state with S=5/2
of the crystal-field parameters. (6A1g). The next d5 states (4A2g, 4Eg, and 4B1g) are
found 0.9 - 1.5 eV above the 6A multiplet (see Fig. 7).
1g
The calculation shows that the second lowest excitation
V. DISCUSSION actually corresponds roughly to a transfer from O 2p to
3d [see the sketchofd5(4A )inFig.9(b)], but excita-
xy 2g
Our first goalis to disentangle CT excitations d4p6 → tions to d5(6A1g) and d5(4A2g) are forbidden along c by
d5p5 and MH excitations d4d4 → d3d5. As discussed in theorbitalselectionrule,asdiscussedaboveinthestrong
the Introduction, the spectral weight of MH excitations crystal-fieldlimitforthelowestCTabsorption. Onlythe
is weaker. In layered LaSrMnO4, the interlayer Mn-Mn transitions to d5(4Eg) and d5(4B1g) are allowed in the c
hopping is strongly suppressed and MH excitations can direction [see sketch of the d5 states in Figs. 9(a) and
be neglected in the c direction. This is the main reason (c)]. These constitute the peak at 5.6 eV.
for the pronounced anisotropy observed experimentally Along a, the peak frequency is somewhat lower (5.5
and suggests the following interpretation: the peak at eV), reflecting the excitation to the 4A2g final state and
∼5.6 eV in εc(ω) is a CT excitation and the same holds a small anisotropy of the CT energy. From the fit of the
2
true for the strong excitations in the same energy range entire spectrum, we find ∆a = 4.51 eV and ∆c = 4.13
in εa(ω). The weaker features below ∼4 eV in εa(ω) are eV.Thisisreasonablebecausethein-planeO(1)siteand
2 2
MH excitations. The detailed analysis discussed below theapicalO(2)sitearecrystallographicallydifferent.22,29
will support this assignment. Weemphasizethattheassignmentisunique. Thelow-
est CT excitation (hopping from O 2p to 3dx2−y2) is the
strongestone in σa(ω)=(ω/4π)εa. Interpreting the peak
1 2
A. Charge-transfer excitations at 3.5 eV or even the 2 eV band as the lowest CT exci-
tation does not yield sufficient weight around 4.5 eV in
In the c direction, we attribute the whole spectral σa(ω). Moreover,theselectionrulesshowunambiguously
1
weighttoaCTpeakat5.6eVandtotheonsetofhigher- thatthepeakat5.6eValongccorrespondstoexcitations
lying processes. To get an idea about the initial and fi- to the d5(4Eg) and d5(4B1g) multiplets, which are 1.2 -
nalstatesofthis CTexcitation,westartfromthe strong 1.5eVabovethelowestd5 state. Thus,weconcludethat
crystal-field limit (i.e., neglect electron-electron interac- the lowest CT energy is & 4 eV.
tions). Inthe d4 groundstate,the tetragonallydistorted The increase of spectral weight in σc(ω) with increas-
1
MnO octahedraindicatethatthreeelectronsoccupythe ing temperature (see top panel of Fig. 3) can partially
6
xy, yz, and zx orbitals and the fourth electron occupies be attributed to the decrease of ∼0.5% of the Mn-O(2)
the d3z2−r2 orbital,22,24 whereas dx2−y2 remains unoc- distance dc from 20 to 300 K.22 With tpd ∝ d−c4 (Ref.
7

8 8
a axis c axis
a 14 4
1 c
0 0
data 15 K data 15 K

4 all all 4
a 2 CT
CT

MH higher bands 2 c
higher bands
0 0
1 2 3 4 5 6 1 2 3 4 5 6
Energy (eV) Energy (eV)
FIG. 6: (Color online) Comparison between ǫas obtained from themultiplet calculation and the measured dataat 15 K.
40) and σc ∝ d2t2 ∝ d−6, the decrease of d can only Fig. 8), this transition has the lowest energy according
1 c pd c c
account for a change in SW of ∼3%, in contrast to the to Hund’s rule (as long as ∆eg is not too large); (ii) the
observed gain of ∼10%, see Fig. 3. This may reflect a excitation from either 3z2-r2 or xy or from the degener-
change in the occupation of the 3z2-r2 orbitals, see Sec. ate yz, zx orbitals to the same orbital on the other site
V C. [S(d5)=3/2, see Fig. 9], these excitations have the same
energyinthestrongcrystal-fieldlimitbecausetheorbital
quantum number is preserved in the transition, and all
B. Mott-Hubbard excitations the final states show the same spin quantum numbers;
(iii) again an excitation from 3z2-r2 to x2-y2, but this
Theobservedvalueofσa ofafew100(Ωcm)−1 around time with S(d5)=3/2.
1
2 eV is typical for a Mott-Hubbard absorption band in The Coulomb interaction gives rise to configuration
transition-metaloxides,e.g., in RTiO or RVO .2,16,41,42 mixing37 and lifts the degeneracy of the excitations col-
3 3
TheSWaround2eVcannotbeattributedtolocalddex- lected in (ii). However, the overall features of the result
citations (crystal-field excitations), which are parity for- ofourmultipletcalculationarereproducedratherwellby
bidden within a dipole approximation. A finite SW is the crude approximation of the strong crystal-field limit
obtained by the simultaneous excitation of a symmetry- discussed above. As shown in Fig. 7, the lowest d3, d4,
breaking phonon, typically resulting in σ of only a few andd5 states have 4B , 5A , and 6A symmetries,re-
1 1g 1g 1g
(Ωcm)−1.43,44 spectively. Thus, the lowest MH excitation is from the
First, we discuss the spin selection rule. The ground d4(5A )d4(5A ) groundstate to a d3(4B )d5(6A ) fi-
1g 1g 1g 1g
stateisad4(5A )d4(5A )state(seeFig.7),i.e.,S=2on nal state (Fig. 8). This statement is valid over a wide
1g 1g
both sites. If the spins are parallel (Sz=2 on both sites range of parameters. This transition is assigned to the
i
i=1, 2), only fully spin-polarized states with S(d3) = broad feature observed around 2 eV in σa(ω) (see Fig.
1
3/2 and S(d5) = 5/2 can be reached by the transfer of 6). The width is attributed to the large bandwidth of
one electronwith S=1/2. For antiparallelspins (|Sz|=2, the x2 − y2 band. In the Drude-Lorentz fit described
1
Sz=-Sz), we can reach final states with S(d3)=3/2 and in the previous section, this excitation corresponds to
2 1
S(d5)=3/2 or 5/2 (|Sz|=3/2 in both cases). peaks (1) and (2) [see Fig. 4(a)]. The fact that this fea-
We start the peak assignment again from the strong ture is not well described by a single Lorentzian can be
crystal-field limit. The highest occupied orbital d3z2−r2 attributed to band structure effects of the broad x2−y2
on one site has overlap to both dx2−y2 and d3z2−r2 on band. Note that a similar ”fine structure“ was observed
the other site. In contrast, hopping of an electron from fortheverysimilarlowestopticalexcitationinLaMnO .9
3
xy, yz, or zx is only finite to the same type of orbital. Due to the high-spin character of the d5 final state, the
In LaSrMnO , this selection rule is strict because the spectral weight is largestfor parallelalignment of neigh-
4
O octahedra are neither tilted nor rotated. Thus, one boring spins (see sketch in Fig. 8). As discussed above,
expects only three different Mott-Hubbard peaks in the a d5 final state with S=5/2 and Sz=3/2 is also possible
strongcrystal-fieldlimit: (i)theexcitationfrom3z2-r2to for antiparallel spins in the antiferromagnetic state be-
x2-y2 with a high-spin S(d5)=5/2 in the final state (see low T =133 K, but one expects a reduced SW. Figure
N
8
FIG.7: (Color online) Energy leveldiagrams from themultiplet calculation for thed3, d4, andd5 configurations as afunction
of 10Dq in Oh and as a function of x in D4h for a fixed value of 10Dq. The control parameter x denotes the strength of ∆eg
and ∆t2g, x=1 represents the full strength used for the spectra shown in Fig. 6. The low-lying multiplets are labeled by their
irreduciblerepresentationsinD4h,thosebeingnotrelevantfortheopticaltransitionsareshown inbrackets. Theelectronic fit
parameters are summarized in Table I (for more details, see theAppendixand Ref. 33).
site 1 site 2
multiplets that are less than ∼1.5 eV above the lowest
states. For the identification of the next higher-lying
x2-y2
excitations, we thus have to consider the orbital selec-
3z2-r2 tion rule. For the d4 ground state, we find Γd4 = A1g
(see Fig. 7), where Γ denotes an irreducible represen-
xy
tation of the point group D . The matrix elements
4h
yz, zx hd5i|a†τ|d4kihd3j|aτ′|d4k′i are only finite for Γd5⊗Γa†τ ⊃A1g
and Γd3 ⊗Γaτ′ ⊃ A1g. For excitations with τ = τ′, i.e.,
d4(5A )d4(5A ) d3(4B )d5(6A ) hopping within the same type of orbital (see sketch in
1g 1g 1g 1g
Fig. 9), we find Γd5 = Γd3. According to Fig. 7 we can
thus attribute the peak at 3.5eV in σa(ω)to excitations
FIG. 8: Sketch of the lowest Mott-Hubbard excitation in 1
LaSrMnO4 inthestrongcrystal-fieldlimit,i.e., configuration with the final states d3(4Eg)d5(4Eg), d3(4A2g)d5(4A2g),
mixingisneglected. Inthefinalstate,thed5 siteisinahigh- and d3(4B1g)d5(4B1g) [the higher-lying d3(4Eg)d5(4Eg)
spin S=5/2 configuration. This excitation is assigned to the transition has negligible weight], which roughly corre-
feature observed around 2 eV in σa(ω). The spectral weight spond to the hopping of an electron within the d ,
1 xz,yz
is largest for parallel alignment of neighboring spins. dxy,andd3z2−r2 orbitals,respectively. Theseexcitations
are degenerate within the strong crystal-field limit. Ac-
cording to the multiplet calculation, the splitting is only
small, giving rise to one pronounced feature at 3.5 eV.
2 clearly shows an increase of the SW around 2 eV with Compared to the feature observed around 2 eV, the SW
increasing T, in agreement with our assignment. at low temperatures is larger at 3.5 eV because three
different processes contribute and because of the spin
Both the d3 and the d5 configurations show several
9
site 1 site 2
(c) (a) (b) (c)
x2-y2
3z2-r2
(b)
xy
yz, zx
(a)
d4(5A )d4(5A ) d3(4E )d5(4E ) d3(4A )d5(4A ) d3(4B )d5(4B )
1g 1g g g 2g 2g 1g 1g
FIG. 9: Sketch of Mott-Hubbard excitations to final states with S(d5)=3/2. These excitations are degenerate in the strong
crystal-field limit and are assigned to the peak at 3.5 eV in σa(ω). The spectral weight is largest for an antiferromagnetic
1
arrangement of neighboring spins.
selection rule. Since the final states have S(d5)=3/2, C. Temperature dependence and kinetic energy of
the SW of these transitions is largest for the antipar- the low-energy high-spin transition
allel alignment of neighboring spins. According to the
Drude-Lorentz fit of the previous section, the feature at Thesuperexchangeinteractionbetweenspinsonneigh-
3.5 eV indeed loses weight with increasing temperature boring Mn sites arises from the virtual hopping of elec-
[peak (3) in Fig. 4(b)]. The loss of ∼20%from 15 to 330 trons between the two sites. The intersite excitations
K is not as strong as the gain of the lowest transition. probed in optical spectroscopy are the real-state coun-
The direct integration of σa(ω) from 2.8 to 4 eV even terpart of these virtual excitations. Therefore, the su-
1
yields a slight gain of ∼3% (see bottom panel of Fig. 3). perexchange constant J is related to the spectral weight
As discussed above, this difference can be attributed to of the optical excitations.
achangeofthebackgroundwhichcanbe resolvedbythe Intotal,superexchangeinLaSrMnO favorsantiparal-
4
Drude-Lorentzfit. However,aprecisequantitativedeter- lel spins, but there is a ferromagnetic contribution J ,
FM
mination of the change of SW appears to be difficult in which corresponds to the lowest optical excitation to a
this frequency range, e.g., the background contribution high-spin d3(4B )d5(6A ) final state47 [peaks (1) and
1g 1g
of the CT transitions may have been underestimated in (2) of the Drude-Lorentz fit, see Fig. 4(a)]. The relation
the Drude-Lorentz fit. The temperature dependence is betweenthespectralweightorN ofthisexcitationand
eff
discussed in more detail in the next section. J hasbeenderived18,48 forthed4compoundLaMnO .
FM 3
The c direction of LaMnO with ferro-orbital order of
3
3x2-r2 isequivalenttotheadirectionofLaSrMnO with
4
In comparison with the processes contributing to the 3z2-r2 orbitals. Adoptingtheformalism9 forLaSrMnO4,
peak at 3.5 eV, the excitation from 3z2-r2 to x2-y2 with the effective carrier concentration Neff, the in-plane ki-
S(d5)=3/2islowerinCoulombenergy,butitcostsabout netic energy K, and the ferromagnetic contribution to
∆eg. This can be identified with the SW above ∼4 eV superexchange JFM are related by
in the MH contribution (see Fig. 6). Since τ 6= τ′, the
m(2d )2
orbital selection rule allows also for transitions to final N = a K (3)
states with Γd3 6= Γd5; thus, different multiplets con- eff ~2
3
tribute. However,thesearedifficultto separatefromthe K = J hS~ S~ +6i (4)
FM i j
CT excitations observed in the same energy range. 8
t2
J = (5)
FM
5E
Our assignment is very well compatible with a num-
where2d =3.786˚AistheMn-Mndistance,22,mthefree
ber of different results. In LDA+U calculations,25,45 the a
electronmass, i and j denote nearest-neighborMn sites,
highest occupied band has mainly a Mn 3d3z2−r2 char- t=(pdσa)2/∆ theeffectiveMn-Mnhoppingamplitude,
acter (hybridized with O 2p bands) and the lowest un- a
and E = U −3J +∆ represents the excitation en-
occupied band is a Mn 3dx2−y2 band. Also, our inter- ergy of theeffvirtualHintermegediate state. We determined
pretation of the peak at 3.5 eV is in agreement with the
E from the weighted peak frequencies of peaks (1) and
LDA+U results.25,45 The x-ray data of Kuepper et al.27
(2), E = (N(1)E(1) +N(2)E(2))/N = 2.10 eV at 15
alsosuggestthatthehighestoccupiedstatesmainlyhave eff eff eff
K and 1.76 eV at 330 K. The nearest-neighborspin-spin
Mn character. Our results support the very similar in-
terpretation of the lowest optical excitation in LaMnO3 correlation is given by hS~iS~ji→−4 for T ≪TN and by
in terms of a Mott-Hubbard peak.5,6,9,46 hS~ S~ i→0 for T≫T . Using ∆ =4.5 eV from our anal-
i j N a
10
ysis, we find t=(pdσa)2/∆ ≈0.6 eV. Using t=0.55-0.65 8
a
eV, we derive K(15 K)=34JFM(15 K) = 0.021-0.030 eV 7 (cid:39)a (5K) = 0.45 eV
0na.na2ld0ly3KN[(se3eAffe3F0(F1Ki5g).K=4)(49=bJ0)F]..M04(B03-o30t0.h0K5a6)ta=lnowd0.N0a7nepff7da-ra0a(.t1303h80igKehV)t=ea0mn.d1p4efi6r--- T) (%) 56 (cid:39)aoopptt(5K) = 0.4 eV
B
atures, the calculated values agree amazingly well with k 4
the experimental results. This strongly corroboratesour /(cid:39)act 3
-
interpretation of the feature around 2 eV with the low- (
p
x 2
est Mott-Hubbardexcitation. Moreover,it suggeststhat e
the redistribution of weight with temperature can be at- 1
tributedmainlytoachangeofthenearest-neighborspin-
0
spin correlation function. As discussed above for the c 0 50 100 150 200 250 300
direction, the change of the lattice constant may only T (K)
account for a change of N of a few percent.
eff
A more detailed analysis requires the knowledge of FIG. 10: Estimate of the thermally activated population of
the temperature dependence of hS~iS~ji. In the three- the UHB using ∆act = (1/2)∆aopt and the temperature de-
dimensionalantiferromagnetLaMnO3,thechangeofNeff pendenceof ∆aopt depicted in Fig. 5(b).
right at T is more pronounced.9 The more gradual
N
changes observed in LaSrMnO qualitatively agree with
4
the expectations for a quasi two-dimensionalcompound,
in which hS~iS~ji is still significant above TN.49 that the 3z2-r2 orbitals are occupied for ∆eg >0.1 eV.
According to the Franck-Condonprinciple, optical ex-
citations are very fast and probe the static crystal-field
D. Crystal-field excitations and thermal expansion splitting,i.e.,forafrozenlattice. Forthethermalactiva-
tion, one has to consider the minimal crystal-field split-
Up to 600K,the c-axislattice parametershrinks with ting ∆reegl after relaxation of the lattice. In optics, the
increasing temperature and the elongation of the octa- peak frequency of a crystal-field absorption band corre-
hedra is reduced. As a measure for the deviation from sponds to the static value ∆eg (neglecting the phonon
undistorted octahedra, we consider the difference be- shift of 50-80 meV required for breaking the parity se-
tween the apical Mn-O(2) and in-plane Mn-O(1) bond lection rule), whereas the onset of the absorption band
lengths, which amounts to dc − da ≈ 0.39 ˚A at 20 K can be identified with ∆reegl. Our transmittance data
and ≈ 0.37 ˚A at 300 K, i.e., it changes by more than for T=5K clearly show that ∆rel >0.4 eV ∼ 4600 K.
eg
5%.22 The anisotropyof the thermalexpansionhas been Thus,weconcludethatthethermalpopulationofexcited
interpreted as an indication for a change of the orbital crystal-field levels, i.e., a local transfer of electrons from
occupation.22 The change of d across T may be ratio- 3z2-r2 tox2-y2,isnotsufficienttoexplaintheanomalous
a N
nalized in terms of the gain of magnetic energy with in- thermal expansion.
creasingJ (inducedbyanincreaseint),butthechangeof Thelowestelectronicexcitationcorrespondstotheop-
d suggestsanorbitaleffect. Onthebasisofnear-edgex- tical gap ∆a ≈ 0.4 eV. The optical absorption process
c opt
ray-absorptionfine structure data, Merzet al. claimed a corresponds to the creation of two particles: an elec-
15% occupation of x2-y2 orbitals at roomtemperature28 tron and a hole in a conventional semiconductor or an
aswellasatransferfromx2-y2 to3z2-r2 withdecreasing “empty” site (here d3) and a “double occupancy” (here
temperature.29 d5)inaMott-Hubbardinsulator. WiththeFermienergy
Daghofer et al.30,31 studied the competition of various lying in the middle of the gap, the thermal activation
exchangecontributions. For∆ =0,theyfindthatx2-y2 energy for a single particle is only ∆ =(1/2)∆a ≈
eg act opt
is occupiedon eachsite for the case ofantiferromagnetic 0.2eV.Incontrast,acrystal-fieldexcitationcorresponds
order. The fact that 3z2-r2 is favored instead is due to to a bound electron-hole pair, i.e., an exciton, for which
∆ > 0. Using ∆ ≈ 0.1 eV ∼ 1160 K, Daghofer et ∆ = ∆ . As discussed above, the lowest Mott-
eg eg act eg
al.31 find a significant redistribution of electrons from Hubbard excitation with a d3(4B )d5(6A ) final state
1g 1g
3z2-r2 to x2-y2 with increasing temperature. However, corresponds to the transfer of an electron from a 3z2-r2
e electrons in general are strongly coupled to the lat- orbital to the x2-y2 band, similar to the local crystal-
g
tice; thus, one expects much larger values, e.g., ∆ >1 field excitations in the scenario proposed by Daghofer et
eg
eV in LaMnO .43 The transmittance is a very sensi- al.30,31 However, the gain in kinetic energy of the delo-
3
tive probe forlow-lyingcrystal-fieldexcitations,43 but in calized d5 final state is essential to obtain a small ac-
LaSrMnO , we do not find any evidence for crystal-field tivation energy. A rough estimate of the thermally ac-
4
excitations below the opticalgap(see Fig. 5). Moreover, tivated population of the x2-y2 UHB is obtained from
our multiplet calculation yields ∆ =1.4 eV (see Table exp(−∆ /k T), using ∆a =0.4-0.45 eV at 5 K, the
eg act B opt
I), in agreement with the strongly elongated O octahe- temperature dependence of ∆a depicted in Fig. 5(b)
opt
dra. More recently, Rosciszewskiand Oles50 pointed out and ∆ = (1/2)∆a . The result is shown in Fig. 10.
act opt