# Optics of Chromites and Charge-Transfer Transitions

Authors: Andrei V. Zenkov
Journal: Research Letters in Physics
 (2008)

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## Abstract

Specific features of the charge-transfer (CT) states andO2p→Cr3d transitions in the octahedral (CrO6)9− complex are considered in the cluster approach. The reduced matrix elements of the electric-dipole transition operator are calculated on many-electron wave functions of the complex corresponding to the initial and final states of a CT transition.
Modeling the optic spectrum of chromites has yielded a complicated CT band. The model spectrum is in satisfactory agreement with experimental data which demonstrates the limited validity of the generally accepted concept of a simple structure of CT spectra.


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## Body

## 1. Introduction

Since discovering the high-Tc superconductivity in oxides with Cu2+ ions
and the colossal magnetoresistance in Mn3+ systems, a considerable
interest has been renewed in transition-metal oxide systems. An important
problem of the physics of these strongly correlated systems concerns the nature
of their electronic structure and energy spectrum. Optic and magneto-optic techniques
are well suitable for studying them. However, the origin of low-energy electron-hole excitations in 3d-oxides is
still under discussion.First proposed for iron
garnets [1] and developed further for a wider class of ferric oxide compounds [2],
the idea that their optic and magneto-optic properties in the near UV range and
the fundamental optic absorption edge are determined by the oxygen-to-3d metal ion charge-transfer (CT) transitions has
become widespread [3, 4]. However, there is no consistent theory of CT states
and transitions in 3d oxides. In most studies, the idea of CT transitions has
not changed significantly since its appearance. One tries to explain the
peculiarities of optic spectra of these compounds by some “2p-3d” CT
transitions or, at best, keeping in mind the t2g-, eg-classification
of d-electrons in the crystal field, one reasons in terms of “2p→3dt2g,” “2p→3deg” CT transitions [5].
But such one-electron approach to CT
states and transitions is insufficient even for qualitatively explaining the observed optic properties of 3d
oxides. The one-electron band models, including LDA+U, do not solve the problem, since they fail to reproduce the
important intra-atomic correlation effects which form the term structure of the
ground and excited CT states.We consider here the CT
states and transitions in chromites and their optic spectra. The analysis is
based on the cluster model of one-center CT transitions which has been
successfully used to explain the optics and magneto-optics of orthoferrites,
iron garnets, and a number of other 3d oxides [6–12]. The
advantages of this model are its physical clarity and the possibility of taking
detailed account of the electron-electron
correlations and the crystal field effects.


## 2. Ct States and Transitions in Chromites

Slightly distorted
octahedralCrO6 complexes are the main optic centers of oxide
compounds such as perovskite-like RCrO3 (R is a trivalent rare-earth or yttrium
cation). The ground state configuration of the (CrO6)9− complex
includes filled molecular orbitals (MOs) O1s-2p predominantly
anionic in nature, filled “cationic” MOs Cr1s-3p and
3d-type MOs. The ground state of the complex is the orbital singlet |γ2p6t2g3A2g4〉. The excited CT
configuration of the complex arises at the transition of an electron from the
“anionic” γ2p MO (γ=t2u(π),t1u(π),t1u(σ)) into the 3d-type MO (t2g, eg) of the central Cr3+ ion of the complex. The CT configuration can be written as γ˜2p13d4 where  γ˜2p1 denotes the hole in the anion MO core. The transition
between the ground and excited configurations is the CT transition γ2p→3d.The electric-dipole
CT transitions from the groundA2g4 state of the complex
are only allowed to the T2u4 terms of γ˜2p1t2g4 and γ˜2p1t2g3eg configurations (electron transfer to t2g and eg shell, resp.). Among the highest-energy 2p-type MOs, there are two MOs
with the t1u symmetry (t1u(σ),t1u(π)) and one t2u(π)-type
MO. Thus, there arise six low-energy one-electron CT transitions, namely, t2u,t1u(π),t1u(σ)→t2g, and t2u,t1u(π),t1u(σ)→eg.
These one-electron  transitions give
rise to the following electric-dipole allowed many-electron CT transitions of A2g4→T2u4 type: γ2p6A1g1; t2g3A2g4: A2g4→γ2p5γ2u; t2g4T1g3: T2u4 (one-electron
γ2p→t2g transition) and γ2p6A1g1; t2g3A2g4: A2g4→γ2p5γ2u; t2g3A2g4; eg1E2g(E2σ+1g): T2u4 (one-electron γ2p→eg transition).
Here, σ takes the values 1 and 2.The
transition intensity measure is the line strength: the squared modulus of the
reduced matrix element (RME) of the operator of a transition between states.
The RME of the electric dipole moment on many-electron wave functions of the
final and initial configurations corresponding to one-electronγ2p→t2g CT transition has the form
(1)〈γ2p5γ2u;t2g4T1g3:T2u4∥d^∥γ2p6A1g1;t2g3A2g4:A2g4〉=3(−1)j(γ){T1T2γT1T2A2}〈t2g∥d^∥γu〉.
Here, j(γ) is the phase factor which is even for
representations γ=A1,E,T2 of the cubic group, and odd
for γ=A2,T1; {⋯⋯} is the 6Γ symbol. According to (1), three one-electron γ2p→t2g CT transitions beget
three many-electron A2g4→T2u4 CT transitions, the RME on many-electron wave
functions being equal to (−〈t2g∥d^∥γu〉) both for γ=t1 and γ=t2.In the
case of the one-electronγ2p→eg transition, the RME is
(2)〈γ2p5γ2u;t2g3A2g4;eg1E2g(E2σ+1g):T2u4∥d^∥γ2p6A1g1;t2g3A2g4;eg0A1g1(A2g4):A2g4〉=(−1)j(γ)+σ+13(2σ+1){EEA2T2T1γ}〈eg∥d^∥γu〉.
Three one-electron γ2p→eg transitions give rise
to six many-electron A2g4→T2u4 CT transitions; the RMEs are gathered in Table 1.Table 1
Many-electron CT transitions generated by one-electront2u,t1u(π),t1u(σ)→3deg CT transitions.
γσRMEγσRMET225/2〈eg∥d^∥t2u〉T12−5/2〈eg∥d^∥t1u〉T21−3/2〈eg∥d^∥t2u〉T113/2〈eg∥d^∥t1u〉These results can be
parameterized in the local approximation [13] consisting in the full neglect of
many-center integrals when calculating the RME of the dipole moment. All such RMEs can be expressed in terms of λσ,
λπ; the effective covalency parameters for σ and π bonds. Since the
RME 〈t2u(π)∥d∥eg〉, 〈t1u(π)∥d∥eg〉, 〈t1u(σ)∥d∥t2g〉 go to zero in
the local approximation, it reveals itself as a supplementary selection rule which prohibits the σ→π(t1u(σ)→t2g) and π→σ(t1,2u(π)→eg) transitions
even if they are electric-dipole allowed. Only σ→σ type CT transitions (t1u(σ)→eg) and π→π type ones (t1,2u(π)→t2g) are
allowed in this approximation (‘‘strong’’ transitions, in contrast with ‘‘weak’’ σ→π, π→σ ones).


## 3. Modeling of the Ct Transition Band in Chromites

We apply here the expounded theoretical notions to model the optic
properties of chromites likeRCrO3.
They are usually regarded as Mott-Hubbard
insulators, the Coulomb energy being reputedly small in comparison with the CT
energy [3], but this attribution seems to be not universally justified [7]. We
will treat the chromites from the CT point of view using the following
plausible assumptions for modeling the optic spectra.(1) Since the3d4 configuration of the central atom formally corresponding to Mn3+ ion
arises at the CT transition, to compute the Tanabe-Sugano diagram
(see below) for the excited 3d4 CT configuration we use the Racah parameters B and C of the Mn3+ ion ground state [14] in the
octahedral oxygen surroundings.(2) The corrections to the level energies owing to 2p-hole-3d-shell
interaction are neglected. Our estimations [12] show that these corrections may
take on the value of several tenths of an eV.(3) The energies of thenonbonding oxygen states in the (CrO6)9− complex
are supposed to coincide with those in the (FeO6)9− complex [15].
This assumption seems justified since the energies of purely oxygen states
mainly depend on crystalline environment.Thus,
the energy spectrum of theone-electron CT transitions depends on the energies of 3d t2g, eg orbitals and rigidly shifts if the
latter are changed. It remains true for many-electron CT transitions as well. The referencing of the computed theoretical spectrum to
the experimental one has been performed according to the fundamental optic
absorption edge; thereby the positions of all peaks of the computed spectrum
become defined.To find the energies of
many-electron CT transitions and the transition intensities under the mixing of
CT states in (1) and (2), we have computed the Tanabe-Sugano diagram
for d4 configuration with parameters B=0.12 eV and γ=C/B=4.5 [14]. At the crystal field
parameter Dq=0.23 eV [14] we obtain
an intensive CT band with the total extent of about 8 eV, from ≈2 to ≈10 eV: each of the one-electron CT transitions
t2u(π),t1u(π),t1u(σ)→t2g gives
rise to seven many-electron CT transitions, and each of the one-electron CT
transitions t2u(π),t1u(π),t1u(σ)→eg generates four many-electron CT transitions, altogether 33 lines!We have performed a
modeling of the band of electric-dipole allowed CT transitions in the optic
spectrum of orthochromiteYCrO3 (note that in our assumptions the
specific compound affects the reference energy only). Since in the local approximation
the contribution of transitions t1,2u(π)→eg and t1u(σ)→t2g cannot be taken into account, we have introduced ‘‘by hand’’ the
corresponding covalency parameter λπσ≡λσπ. Based on
reasonable physical notions and the concept of strong and weak transitions, we
assumed the following model relationship of covalency parameters: λπ=(1/5)λσ, λπσ=(1/10)λσ. The line half-width Γ is taken to be equal to 0.4 eV for many-electron CT transitions due to weak
transitions, 0.8 eV for those due to strong t1,2u(π)→t2g transitions, and 1.2 eV for those due to strong t1u(σ)→eg transitions. The model Lorentzian line shape used is(3)4ωω0Γ[(ω2−ω02−Γ2)2+4ω2Γ2],ω0 being the
transition frequency.The
computation results are shown in Figure1. The computed total contribution of all
electric-dipole-allowed strong and weak CT transitions to the imaginary part ε2 of the diagonal permittivity tensor component ε=ε1+iε2  is presented in the main panel. The experimental spectra for Lu0.85Y0.15CrO3 [16], YCrO3 [17], and LaCrO3 [17] converted by us
from optic conductivity to permittivity are shown in the inset (lines 1, 2, and
3, resp.). The computation results reasonably agree with them. The 3D
picture of ε2 spectra versus the crystal field parameter Dq is shown in Figure 2. Variation of Dq causes not merely the relative change
of peaks height, but also the restructuring of the whole spectrum.Figure 1
Modeling ofO2p-Cr3d CT band in chromite. The computed total contribution of electric-dipole allowed
CT transitions to Imε and (inset) the experimental spectra of Imε in Lu0.85Y0.15CrO3 [16], YCrO3 [17], and LaCrO3 [17] (lines 1, 2,
and 3, resp.) are shown.Figure 2
Theoretical modeling ofO2p-Cr3d CT band in chromite. The spectral dependence of all electric-dipole allowed CT
transitions contribution to Imε versus the crystal field strength.


## 4. Conclusion

In the cluster approach which
combines the crystal field and MO notions, we have considered the peculiarities
of CT states andO2p→Cr3d CT transitions in the
octahedral (CrO6)9− complex. Using
the Racah algebra for the group of rotations and the cubic point group, we have
calculated the reduced matrix elements of the electric dipole operator on
many-electron wave functions being the initial and final states of a CT
transition. Based on the parameterization of the results obtained, we have
calculated the relative intensities of the allowed CT transitions. Within the
crystal field theory, we have computed the energies of many-electron CT
transitions.Modeling
the optic spectrum of chromites yielded an intricate CT transition band
consisting of 33 lines, with the main maxima at about 6.8 and 9.1 eV and
satellites in the 2–10 eV range. The
total extent of the CT band is about 8 eV. The influence of crystal field
magnitude on the spectrum structure is examined.For all the roughness of
the model assumptions, the computed spectrum is in satisfactory agreement with
the experimental ones. Hence it appears that the rooted opinion of the CT
transitions as having a simple, one- or two-peaked structure is groundless.
There is a need for refining upon the customary theoretical treatment of peculiarities
in the optic spectra of 3d metal-based oxide compounds.



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*Source: 749305-2008-08-11.xml*