Theory of optical spectral weights in Mott insulators with orbital degrees of freedom

Abstract

Introducing partial sum rules for the optical multiplet transitions, we outline a unified approach to magnetic and optical properties of strongly correlated transition metal oxides. On the example of LaVO$_3$ we demonstrate how the temperature and polarization dependences of different components of the optical multiplet are determined by the underlying spin and orbital correlations dictated by the low-energy superexchange Hamiltonian. Thereby the optical data provides deep insight into the complex spin-orbital physics and the role played by orbital fluctuations.

Full text

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arXiv:cond-mat/0403459v2 [cond-mat.str-el] 9 Jun 2004
Theory of optical spectral weights in Mott insulators with orbital degrees of freedom
Giniyat Khaliullin
Max-Planck-Institut f¨ ur Festk¨ orperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
and E. K. Zavoisky Physical-Technical Institute of the Russian Academy of Sciences, 420029 Kazan, Russia
Peter Horsch
Max-Planck-Institut f¨ ur Festk¨ orperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
Andrzej M. Ole´ s
Max-Planck-Institut f¨ ur Festk¨ orperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
and Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, PL-30059 Krak´ ow, Poland
(Dated: 9 June 2004)
Introducing partial sum rules for the optical multiplet transitions, we outline a unified approach
to magnetic and optical properties of strongly correlated transition metal oxides. On the example of
LaVO3 we demonstrate how the temperature and polarization dependences of different components
of the optical multiplet are determined by the underlying spin and orbital correlations dictated by
the low-energy superexchange Hamiltonian. Thereby the optical data provides deep insight into the
complex spin-orbital physics and the role played by orbital fluctuations.
PACS numbers: 75.30.Et, 75.10.-b, 75.10.Jm, 78.20.-e
I.INTRODUCTION
Charge localization in Mott insulators is not perfect
as electrons still undergo virtual transitions to neigh-
boring sites in order to retain partially their kinetic en-
ergy. These high-energy virtual transitions across the
Mott-Hubbard gap ∼ U are crucial for magnetism —
this quantum charge motion leads to superexchange (SE)
interactions1between local degrees of freedom. It is fre-
quently not realized, however, that the same charge ex-
citations are responsible in Mott insulators for the low-
energy optical absorption. Therefore, the intensity of the
optical absorption and the SE energy are intimately re-
lated to each other via the well known optical sum rule,2
which links the integrated optical conductivity and the
kinetic energy. In Mott insulators the latter is due to vir-
tual exchange processes and hence the thermal evolution
of spectral weights and SE energy are related.3
A qualitatively new situation is encountered in Mott
insulators with partly filled d orbitals. Because of or-
bital degeneracy, virtual charge excitations that are seen
in optics reflect the rich multiplet structure of a tran-
sition metal ion determined by Hund’s exchange cou-
pling JH, and orbital degrees of freedom contribute then
to the SE.4When spin and orbital correlations change
the individual components of the optical multiplet re-
flect characteristic spectral weight transfer.
the cubic symmetry is spontaneously broken by orbital
and spin order, and thus one expects anisotropic opti-
cal absorption. Indeed, pronounced anisotropy was re-
ported for LaMnO3,5both for the A-type antiferromag-
netic (AF) phase6and for the orbital ordered phase above
the N´ eel temperature TN. Recently, the anisotropy in
optical absorption and its strong temperature depen-
dence near the magnetic transitions were found for cu-
bic vanadates.7This latter example is even more puz-
Moreover,
zling as the magnetic properties are anomalous,8and
neutron scattering experiments9have revealed nontriv-
ial quasi one-dimensional (1D) correlations of spin and
orbital degrees of freedom that are surprising for crystals
with nearly cubic symmetry. Indeed, a theory of spin
and orbital states in cubic vanadates predicted quasi 1D
spin-orbital correlations due to a spontaneous breaking
of the cubic symmetry in the SE model.10
It is our aim to outline a unified picture that links opti-
cal and magnetic properties at orbital degeneracy. Start-
ing from the low-energy spin-orbital model we derive par-
tial sum rules for the different excited states. Thereby
we provide a rigorous theoretical basis for the analysis of
optical spectral weights and show how the evolution of
magnetic coherence manifests itself in optics as intensity
transfer between different excitations (upper Hubbard
bands). This explains the origin of dramatic variation of
the optical absorption and its anisotropy with temper-
ature T in manganites,5vanadates,7and ruthenates,11
where at low T the high-spin band carries most spec-
tral weight for the directions with ferromagnetic (FM)
spin correlations. We illustrate this idea for the case of
C-type AF (C-AF) phase6of cubic vanadates with de-
generate t2gorbitals. We show that the predicted quasi
1D spin-orbital correlations,10realized in C-AF phase
of LaVO3, are reflected in the T-dependence of optical
weights derived from the SE model.
The paper is organized as follows. First we present a
generic structure of the SE interactions in a Mott insula-
tor with orbital degrees of freedom in Sec. II, and relate
them to the intensities in optical absorption. On the ex-
ample of the SE interactions encountered in LaVO3, we
analyze next spin, orbital, and joint spin-and-orbital cor-
relations which determine the optical intensities. In this
way, we arrive at a set of self-consistent equations which
are solved in Sec. III, where we present the numerical

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results for the optical sum rules for individual high-spin
and low-spin excitations, as well as for the spin and or-
bital SE interactions. These results and their comparison
with experiment are discussed in Sec. IV, where we also
give a summary and more general conclusions.
II.THEORY
The SE interaction in a cubic Mott insulator with ions
having orbital degrees of freedom has a generic form,
HJ= Hs+ Hτ+ Hsτ=
?
n
?
?ij??γ
H(γ)
n (ij),(1)
and consists of separate spin (Hs) and orbital (Hτ) in-
teractions, and of a dynamical coupling between them
(Hsτ). This complex form of HJ, given by Eq. (1), fol-
lows from the terms H(γ)
n (ij) for each bond ?ij? along a
given cubic axis γ = a,b,c, arising from the transitions
to various upper Hubbard bands labelled by n. The opti-
cal intensity of each band n, for the photon polarization
along a cubic axis γ, is determined by the respective SE
energy:
a0¯ h2
e2
?∞
0
σ(γ)
n(ω)dω = −π
2K(γ)
n
= −π
?
H(γ)
n(ij)
?
. (2)
Here, a0is the distance between magnetic ions (the tight-
binding model is implied), and?H(γ)
teraction for a bond ?ij? along axis γ. The first equality
in Eq. (2) follows from the optical sum rule for a given
transition n, and relates the kinetic energy K(γ)
optical conductivity σ(γ)
n (ω) for this band, while the sec-
ond equality relates the associated kinetic energy to the
SE energy via the Hellman-Feynman theorem.2
Experimental data is often presented in terms of an
effective carrier number [see, e.g., Eq. (2) of Ref. 7],
N(γ)
n (ω)dω, where m0is the free
electron mass, and v0= a3
ion. This gives an optical sum rule as follows:
n (ij)?is the SE in-
n
to the
eff,n= (2m0v0/πe2)?∞
0σ(γ)
0is the volume per magnetic
N(γ)
eff,n= −m0a2
0
¯ h2
K(γ)
n
= −m0a2
0
¯ h2
?
2H(γ)
n(ij)
?
. (3)
Each level n of the multiplet represents an upper Hub-
bard band with its own spin and orbital quantum num-
bers. The key point is that while full kinetic energy and
corresponding total intensity may show only modest T-
dependence and almost no anisotropy, the behavior of the
individual transitions is much richer, and directly reflects
the ground state correlations via the spin and orbital se-
lection rules.
Hund’s exchange separates the lowest (high-spin) ex-
citation from the next (low-spin) one by:
in manganites,123JH in vanadates,10and 2JH in
titanates.13When the high-spin excitation, broadened by
its propagation in crystal and by many-body effects, has
∼ 5JH
a smaller linewidth than the above multiplet splitting,
it may show up in optical spectroscopy as a separate
band. This is in fact nearly satisfied for typical values
of JH∼ 0.6−0.7 eV and hoppings t ∼ 0.4 eV (∼ 0.2 eV)
for eg(t2g) orbitals.14Higher bands overlap and mix up
with d − p transitions, though.
In a particular case of vanadates, one has three optical
bands n = 1,2,3 arising from the transitions to: (i) a
high-spin state4A2at energy U−3JH, (ii) two degenerate
low-spin states2T1and2E at U, and (iii)2T2low-spin
state at U + 2JH.10Using η = JH/U we parametrize
this multiplet structure by: R = 1/(1 − 3η) and r =
1/(1 + 2η). In LaVO3xy orbitals are singly occupied,8
and one obtains a high-spin contribution H(c)
bond ?ij? along c axis:
1(ij) for a
H(c)
1
= −1
3JR
??Si·?Sj+ 2
??
1
4−? τi·? τj
?
,(4)
while for a bond in an (a,b) plane:
H(ab)
1
= −1
6JR
??Si·?Sj+ 2
??
1
4− τz
iτz
j
?
.(5)
In Eq. (4) pseudospin operators ? τi describe low-energy
dynamics of (initially degenerate) xz and yz orbital dou-
blet at site i; this dynamics is quenched in H(ab)
1
3(?Si·?Sj+ 2) is the projection operator on the high-spin
state for S = 1 spins. The terms H(c)
excitations (n = 2,3) contain instead the spin operator
(1−?Si·?Sj) (which guarantees that these terms vanish for
fully polarized spins on a considered bond, ??Si·?Sj? = 1):
1
(5). Here
n (ij) for low-spin
H(c)
2
= −1
12J
?
?
1 −?Si·?Sj
??
??
7
4− τz
iτz
j− τx
iτx
j+ 5τy
iτy
j
?
,
H(c)
3
= −1
4Jr1 −?Si·?Sj
1
4+ τz
iτz
j+ τx
iτx
j− τy
iτy
j
?
,
(6)
while again the terms H(ab)
by orbital operators:
= −1
8J
H(ab)
3
8Jr
n
(ij) differ from H(c)
n (ij) only
H(ab)
2
?
1 −?Si·?Sj
??
??
19
12∓1
2τz
i∓1
2τz
j−1
3τz
iτz
j
?
,
= −1
?
1 −?Si·?Sj
5
4∓1
2τz
i∓1
2τz
j+ τz
iτz
j
?
,
(7)
where upper (lower) sign corresponds to a(b)-axis bonds.
First we present a mean-field (MF) approximation for
the spin and orbital bond correlations which are deter-
mined self-consistently after decoupling them from each
other in HJ (1). Spin interactions,
Hs= Js
ab
?
?ij?ab
?Si·?Sj− Js
c
?
?ij?c
?Si·?Sj,(8)
depend on exchange constants:
Js
c=1
2J
?
?
ηR − (R−ηR−ηr)(1
4+ ?? τi·? τj?)−2ηr?τy
iτy
j?
?
,
Js
ab=1
4J1−ηR−ηr + (R−ηR−ηr)(1
4+ ?τz
iτz
j?)
?
, (9)

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3
determined by orbital correlations. In the orbital sector
one finds
Hτ=
?
?ij?c
?Jτ
c? τi· ? τj− J(1 − sc)ηrτy
iτy
j
?+ Jτ
ab
?
?ij?ab
τz
iτz
j,
(10)
with:
Jτ
c =
1
2J
1
4J
?
?
(1 + sc)R + (1 − sc)η(R + r)
?
,
Jτ
ab= (1 − sab)R + (1 + sab)η(R + r)
?
, (11)
depending on spin correlations: sc= ??Si·?Sj?cand sab=
−??Si·?Sj?ab. In a classical C-AF state (sc = sab = 1),
this MF procedure becomes exact, and the orbital prob-
lem maps to Heisenberg pseudospin chains along c axis,
weakly coupled (as η ≪ 1) along a and b bonds,
H(0)
τ
= JR
??
?ij?c
? τi· ? τj+1
2η
?
1 +r
R
??
?ij?ab
τz
iτz
j
?
,(12)
releasing large zero-point energy. Thus, spin C-AF order
and quasi 1D quantum orbital fluctuations support each
other.10
In addition to spin-orbital SE HJ(1), orbitally degen-
erate systems experience the Jahn-Teller (JT) interac-
tions — coupling of orbitals to lattice distortions may
lead to a structural transition, lifting orbital degeneracy
by the term,
HV = Vab
?
?ij?ab
τz
iτz
j− Vc
?
?ij?c
τz
iτz
j,(13)
in the present vanadate model.10Interactions Vab > 0
originate from the coupling of nearest-neighbor t2g or-
bitals in (a,b) planes to the bond stretching oxygen vi-
brations in corner-sharedperovskite structure. They gen-
erate antidistortive oxygen displacements and staggered
orbital order (supporting SE), whereas the Vc> 0 term
due to the GdFeO3-type distortion15favors ferro-orbital
alignment along c axis, and thus competes with SE.
The complete model H = HJ+ HV represents a non-
trivial many-body problem. Interactions are highly frus-
trated, leading to strong competition between different
spin and orbital states. We leave this complex problem
for a future study, and present here the conceptually sim-
pler case of LaVO3with C-AF order. In this phase spins
are FM along the c axis at low T, and orbitals fluctuate
on their own. This justifies a posteriori a perturbative
treatment of joint spin-orbital correlations and allows one
to determine them in a simple analytical way.
We begin with the orbital Hamiltonian Hτ+HV [Eqs.
(10) and (13)] which has the form of an XY Z model.
As interchain couplings are weak and of τz
problem is best handled by employing Jordan-Wigner
fermion representation.16After decoupling τz
fermionic density and bond-order terms, one finds that
iτz
jform, the
iτz
jterms in
the staggered orbital order parameter τ = |?τz
bital ordering temperature Tτ, and the temperature de-
pendence of orbital correlations: ?τx(y)
?τz
self-consistent equations:
i?|, the or-
i
τx(y)
j
?c = −1
2κ,
iτz
j?c= −τ2−κ2, ?τz
iτz
j?ab= −τ2, do follow from two
τ =
?
k
?hτ
2εk
?
tanh
?εk
2T
?
,(14)
κ =
?
k
? ˜Jc
2εk
?
cos2k tanh
?εk
2T
?
, (15)
where εk = [˜J2
persion,˜Jc= Jτ
2Vab− Vc) is the effective field. We set kB= 1.
The short-range spin correlations sγ determine Jτ
(11) and are finite also above TN.
by solving exactly a single bond ?ij? within the mean-
field ∝ ?Sz?,17originating from neighboring spins. This
is the simplest cluster mean-field theory known in the
theory of magnetism as Oguchi method.18For a FM
bond along c axis one finds even an analytic solution:
sc=(Z0−Z1−2Z2)/Z, where Z0=1+2coshx+2cosh2x,
Z1= (1 + 2coshx)exp(−2Js
with Z =Z0+Z1+Z2, x = hs/T, hs=(Js
The sabcorrelation function for an AF bond can be found
numerically.
Now we turn to the dynamical coupling between orbital
and spin sectors, denoted as Hsτ term in Eq. (1). In the
present case of C-AF ground state it contains mainly
contributions due to c axis bonds, and reads as follows:
ccos2k + (hτ)2]1/2is the 1D orbiton dis-
c+2κ(Jτ
c−Vc), and hτ= 2τ(Jτ
c+2Jτ
ab+
γ
We derived them
c/T), Z2 = exp(−3Js
c/T),
ab)?Sz?.
c+ 4Js
Hsτ≃ K
?
?ij?c
δ(?Si·?Sj)δ(? τi·? τj).(16)
Here, K =
plies the fluctuating part of an operator, which goes be-
yond the MF decoupling. Treating Hsτ within the high-
temperature expansion, we found that the joint spin-and-
orbital correlations, fij= ?δ(?Si·?Sj)δ(? τi· ? τj)?, are given
as follows:
1
2J(R − ηR − ηr) and δ(A) = A − ?A? im-
fij= −3K
16T
?
?(?Si·?Sj)2? − ??Si·?Sj?2?
,(17)
with ?(?Si·?Sj)2? = 1 + 3Z2/Z in the present Oguchi ap-
proximation. This high-temperature expansion for fijis
valid when spin fluctuations are weak as in the C-AF
phase, and one finds that the joint correlations fij van-
ish at T → 0 when fully polarized spins decouple from
the orbital sector.
III.NUMERICAL RESULTS
Taking the SE energy scale J ∼ 40 meV,9we set
TN = 0.4J, while η ≃ 0.12 follows from spectroscopy.14
It is quite natural in t2gsystems that order and disorder

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4
0.0
0.5
0.2
0.4
0.6
0.8
1.0
−K1
(c)/2J
0.00.20.40.60.81.0
T/J
0.0
0.1
0.2
0.3
0.4
NN correlations
(a)
(b)
sc/2
−<τiτj>c
classical
quantum
−fij
τ
FIG. 1: (color online) (a) Kinetic energy K(c)
spin excitations within classical and quantum models. Solid
(dashed) line with (without) joint spin-orbital fluctuations.
(b) Intersite correlations along c axis: spin sc = ??Si·?Sj?c, or-
bital ?? τi· ? τj?c, and spin-orbital fij. Orbital order parameter
τ is also shown. Dotted line (filled circles) for −fij obtained
from high-temperature expansion (17) (by exact diagonaliza-
tion). Parameters: η = 0.12, Vc = 0.9J, Vab= 0.2J.
1
for the high-
in the spin and orbital sectors support each other,10,19
and indeed Tτ ≃ TN in LaVO3.7While the microscopic
reasons of this behavior are subtle, we control Tτby tun-
ing lattice mediated couplings Vγ — we found that the
orbital transition occurs near TN for: Vc = 0.9J and
Vab= 0.2J. Then the energy of the C-AF phase is still
lower than that of the G-AF phase, but a slight increase
of Vγ (by a factor 1.3) due to a stronger tilting of VO6
octahedra gives the G-AF phase, observed in YVO3.8
Following Eqs. (9), (11), (14), (15), and (17), we cal-
culated orbital, spin, and joint spin-and-orbital correla-
tions, and next used them to determine the kinetic en-
ergies K(γ)
n
(2) due to each Hubbard subband. For in-
stance,
−K(c)
1/2J =1
3R
???Si·?Sj+2
??
1
4−? τi·? τj
?
−fij
?
. (18)
Quantum effects beyond the MF theory are particularly
pronounced in −K(c)
1
[see Fig. 1(a)]. In the classical
approach −K(c)
1
(18) increases with decreasing T only
if T < TN (when both τ > 0 and ?Sz? > 0). This is
qualitatively different in the quantum model when the
orbitals fluctuate, the orbital order parameter τ is not
more than half of its classical value, and the spin correla-
tions scare finite above TNand decay slowly for T > TN
0
0.1
0.2
Neff
(c)
0.0
0.3
0.6
0.9
−K
(c)/2J
0.0 0.20.4 0.6 0.81.0
T/J
0.0
0.2
0.4
0.6
−K
(ab)/2J
(a)
(b)
n=1
n=2
n=3
n=2
n=3
total
total
n=1
FIG. 2: (color online) Kinetic energy K(γ)
total K(γ)(dashed lines) in units of 2J for: (a) c axis and
(b) ab-plane polarization. Parameters as in Fig. 1. Filled
squares in panel (a) represent the effective carrier number
N(c)
below 3 eV in Fig. 3 of Ref. 7. The experimental data follows
well the calculated intensity of the high-spin transition, n = 1.
n
(solid lines) and
effin LaVO3 which includes the sum of the peaks 1 and 2
[Fig. 1(b)]. In this case −K(c)
by the orbital fluctuations ?? τi·? τj?c≃ −0.43, being close
to those found for a 1D AF spin 1/2 chain. Kinetic en-
ergy gain [Eq. (18)] gradually decreases with increasing
T, and is reduced by half at T ∼ 2TN from its value
at T = 0 [Fig. 1(a)]. We also note that joint spin-and-
orbital fluctuations fijdevelop at finite T and contribute
significantly at T > TN.20An opposite behavior occurs
in the limit of large JT orbital splitting that freezes out
orbital fluctuations19— then the temperature variation
and the anisotropy of optical absorption are quenched,
and ?? τi· ? τj?γapproaches its classical limit (−0.25) in all
directions.
The optical intensities N(γ)
nounced anisotropy between c and ab polarizations (Fig.
2), particularly those of high-spin transitions (n = 1)
at low energy U −3JH. These low-energy intensities be-
have here in opposite way for c and ab polarizations when
temperature increases and the spectral weight is trans-
ferred between the high-spin and low-spin bands. The
total intensities have a much weaker temperature depen-
dence than individual contributions. The theory repro-
duces quite well the observed7variation of N(c)
[Fig. 2(a)]. We recall that the temperature variation
of the kinetic energy K(c)
1
and N(c)
of both spin and orbital correlations; spin-only ordering
with frozen orbitals cannot explain a factor of two en-
1
is enhanced at T = 0
eff,n∝ K(γ)
n
(3) exhibit pro-
effwith T
effis due to evolution

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5
0.0
0.5
1.0
1.5
Jγ
τ/J
0.00.2 0.40.60.81.0
T/J
0.0
0.1
0.2
Jγ
s/J
(a)
(b)
c
ab
ab
c
~1D regime3D regime
FIG. 3: (color online) Exchange constants as functions of T
along c (a/b) axis: (a) orbital Jτ
Parameters: η = 0.12, Vc = 0.9J, Vab= 0.2J.
γ (11), and (b) spin Js
γ(9).
hancement of N(c)
the optical data of Ref. 7 indicate that the JT orbital
splitting in LaVO3cannot be large.21
The microscopic reasons of anisotropy in the optical
absorption are revealed by studying the effective ex-
change constants, given by Eqs. (9) and (11). While
the spin sector is always 3D, the orbital one shows a di-
mensional crossover from 3D to quasi 1D correlations
when the C-AF order develops [Fig. 3(a)]. The orbital
singlet correlations along the c axis enhance strongly FM
Js
cat low T. Unlike in pure spin systems, the exchange
interactions Js
γare temperature dependent [Fig. 3(b)],
and Js
cdecreases fast with decreasing intersite orbital
correlations [Fig. 1(b)]. Only at T ≫ TN it is much
weaker than the AF one, in agreement with conventional
Goodenough-Kanamori rules.
effin a range of T < 2TN. Therefore,
IV.DISCUSSION AND SUMMARY
The basic experimental findings in the optical spectra
of LaVO3,7such as: (i) pronounced temperature depen-
dence of c axis intensity (changing by a factor of two
below 300 K), (ii) large anisotropy between the optical
spectral weights along c and a/b axis (both below and
above TN), are qualitatively reproduced by our theory
(see Fig. 2).22This strongly supports the picture of quan-
tum orbital chains in the C-AF phase of vanadates.
The spectral shape of optical absorption in LaVO3is
highly intriguing, developing sharp coherent peak be-
low 3 eV at T < TN.7When its two-peak structure
is interpreted7as following from the multiplet splitting
∼ 3JH, the value of JH would be seriously underesti-
mated, giving JH≃ 0.21 eV, which is much smaller that
the respective value (Kanamori parameter) 0.68 eV in
the free ion.14Therefore, we suggest that the absorption
below 3 eV is arising entirely from high-spin band cen-
tered at U − 3JH. The coherent peak emerging at low
temperature could be then interpreted as a bound state,
similar to what occurs in 1D systems.23This is quite nat-
ural when spins along the c axis are fully polarized and
coherent orbital chains are formed.
While the precise structure of the optical band requires
further work, we may already obtain some useful infor-
mation. Taking the width of 8t for the optical band,23
and fitting the position and width of the spectral den-
sity in Fig. 2(a) of Ref. 7, one finds U − 3JH∼ 2.3 eV,
t ∼ 0.2 eV, and thus JR ∼ 70 meV. As higher bands with
n = 2,3 are not resolved in the experiment, we cannot
fix JH directly from the multiplet structure, but consid-
ering η = JH/U ≃ 0.13 we reproduce basic energy scale
J ≃ 42 meV, being close to J ∼ 40 meV deduced from
neutron scattering data.9In fact, we can also determine
J directly from the comparison of the theoretical result
−K(c)
1
≃ 1.1(2J), and the observed N(c)
[see Fig. 2(a)]. Using Eq. (3) with a0 = 3.91˚ A,8one
obtains then J ≃ 48 meV, a value remarkably consistent
with both above estimates. Finally, we remark that the
present interpretation of the experimental data of Ref. 7
gives (at η ≃ 0.13) JH≃ 0.5 eV and U ≃ 3.8 eV, which
are somewhat lower than the atomic values.14This reduc-
tion may be attributed to covalency and/or many-body
screening effects in a solid.24
Summarizing, we proposed a new approach employing
partial optical sum rules in Mott insulators with orbital
degeneracy, which provides a theoretical framework for
common understanding of the optical and magnetic ex-
periments, both determined by the superexchange. Con-
sidering the example of LaVO3 with C-AF order, we
have shown that pronounced temperature dependence
and strong anisotropy of the optical absorption indeed
follow from quasi 1D quantum spin-orbital correlations,
being radically different from the classical expectations.
A satisfactory agreement between the values of J ex-
tracted independently from the magnetic and optical
data in LaVO3 demonstrates that superexchange inter-
actions are indeed responsible for the distribution of the
optical spectral weight in Mott insulators.
eff≃ 0.21 at T = 0
Acknowledgments
We thank B. Keimer and Y. Tokura for insightful dis-
cussions and T. Enss for his help on the graphical pre-
sentation of the experimental data in Fig. 2. A. M. Ole´ s
would like to acknowledge support by the Polish State
Committee of Scientific Research (KBN) under Project
No. 1 P03B 068 26.

Page 6

6
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21Even taking a small JT splitting, these data cannot be
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TN [see Fig. 2(a)], as actually seen in the data of Ref. 7.
ilz
i≡ 2λSz
iτy