Excitonic two-phonon progressions in transition metal compounds

Article abstract of DOI:10.1016/S0375-9601(00)00682-4

Evidence of two-phonon structures is reported for some intra-configurational crystal field transitions in layered V- and Cr-halides. In particular, the crystal field spectrum of CrBr₂ (3d⁴) has been shown for the first time, since the exciton-phonon interaction, despite its unfilled e(g) orbitals, vanishes to first order yielding a two-phonon sequence in the ³A₁(G) + ³A₂(F) band. It is suggested that the main mechanism for the occurrence of two-phonon progressions consists in the direct coupling of the incident photon to a two-phonon state via the second-order dipole moment operator. (C) 2000 Elsevier Science B.V.

Full text of DOI:10.1016/S0375-9601(00)00682-4

4 December 2000
Physics Letters A 277 (2000) 281–286
www.elsevier.nl/locate/pla
Excitonic two-phonon progressions in transition metal
compounds
I. Pollini
Dipartimento di Fisica dell’Università di Milano, Istituto Nazionale di Fisica della Materia (INFM), Via Celoria 16, 20133 Milano, Italy
Received 23 July 2000; accepted 19 October 2000
Communicated by J. Flouquet
Abstract
Evidence of two-phonon structures is reported for some intra-configurational crystal field transitions in layered V- and Cr-
4
halides. In particular, the crystal field spectrum of CrBr (3d ) has been shown for the first time, since the exciton–phonon
2
3
3
interaction, despite its unfilled e orbitals, vanishes to first order yielding a two-phonon sequence in the A (G) + A (F) band.
g
l
2
It is suggested that the main mechanism for the occurrence of two-phonon progressions consists in the direct coupling of the
incident photon to a two-phonon state via the second-order dipole moment operator. 2000 Elsevier Science B.V. All rights
reserved.
Transition metal compounds (TMC), especially ox-
ides and halides, are today the object of numerous
studies on the electron–electron interaction, metal–
insulator transitions and polaron formation up to the
recent interest in the high-temperature superconduc-
tors [1]. For many of these compounds the band pic-
ture of electrons fails when the various interactions ne-
glected in the band calculations become larger than
the 3d level bandwidth, such as the non periodic
potentials, the electron–electron interaction and the
electron–phonon coupling. The electron correlation
becomes larger as the nuclear charge increases in the
3d elements and the ionic radii in the six-coordinated
site becomes smaller, increasing the effective electron
density. The metal–insulator transition often appears
at both ends of the 3d period, that is, around Ti, V, Ni
and Cu, and the magnetic insulators (Mott–Hubbard or
charge transfer insulators) are found along the period.
The electron correlation is not so large in the 4d and
5d elements and for most of their compounds (oxides)
the band picture seems to work rather well [2].
In TMCs the effect of the electron–phonon (ep) in-
teraction appears as temperature dependent resistivity
and superconductivity in metals, while in insulating
ionic compounds it determines the polaron formation
and the multiphonon fine structures observed in ab-
sorption or emission spectra. Among TMCs, the lay-
ered crystals with CdCl2 (C19) or CdI2 (C6) structure
form an ample class of binary compounds, and sev-
eral of them, involving transition metals, also present
interesting magnetic properties. A great success of
the spectroscopy of TM ions has been the explana-
tion of the complex absorption structures occurring
in the near infrared and visible range of the spectrum
in terms of electronic transitions between the d lev-
els split by the crystal field (CF) of the surrounding
ions [3].
The existence of a CF in transition metal halides
(TMH), i.e., the dependence of the TM ion electronic
E-mail address: ivano.pollini@mi.infm.it (I. Pollini).
0375-9601/00/$ – see front matter
PII: S0375-9601(00)00682-4
2000 Elsevier Science B.V. All rights reserved.

282
I. Pollini / Physics Letters A 277 (2000) 281–286
energy on the positions of the neighbour ions, im-
plies in general an important electron–phonon inter-
action. The most evident and primary effect of the
ep coupling is represented by the multiphonon struc-
tures observed in the optical absorption spectra of
TMHs. These electronic excitations can be classified
on the basis of the exciton polaron model [4] as vi-
bronic excitons with small excitations transfer. The
observed phonon progressions are in fact reminis-
cent of those predicted theoretically for small Huang–
Rhys factors S0 (S0 < 3) and small exciton bandwidth
(B < 1). The situation is similar to that occurring for
localized centres in semiconductors and insulators [5].
The only difference is that these complex elemen-
tary excitations may interact with phonons via dif-
ferent mechanisms, due to the two exciton degrees
of freedom. In fact, phonons can interact with exci-
tons either through the centre-of-mass translation or
through the hole–electron internal motion. Depend-
ing on which interaction is dominant, one can have
either phonon-assisted processes (in semiconductors)
or trapped excitons (in alkali halides), which inter-
act with phonons in the same way as in local cen-
tres [5,6].
In layered TMHs, for example, the ep interaction
yields in general a complex vibronic structure ob-
served in many CF bands [7]. The quasi-molecular
nature of these crystals, due to their low dimensional
structure and reduced ionicity [8], results in a flat
dispersion of both d–d excitons and optical phonons
(vibronic excitons with small excitation transfer) [4].
This allows for the experimental observation of sharp
phonon progressions in the absorption spectra of
dn + dn parity forbidden transitions. Therefore it ap-
pears that the occurrence of such phonon progres-
sions is a general phenomenon to be considered when
analysing the visible and infrared spectra of TMHs and
have indicated the need of knowing quantitatively the
lattice dynamics of layer structures [9,10]. Moreover,
from these structures one can learn much on the dy-
namics of the excited states. It is known that when the
ep interaction is given by a purely orbital one-electron
operator, a vanishing first-order linear coupling is ex-
pected between an ideal isoconfigurational (phonon-
assisted) electronic transition and even parity phonons.
Second-order phonon progressions would then be pre-
dicted in the sidebands of isoconfigurational transi-
tions.
In intra-configurational transitions of TMHs with
half-filled shells [d3(t2g); d5(t3 eg2); d8(eg)] the orbital
ep coupling vanishes to first2gorder for the Wigner–
Eckart theorem [3]. In particular, if the states have a
half-filled subshell configuration such as t32g, one may
show the calculation of the matrix elements for a low-
symmetry potential V (Γ ),
ꢁ
ꢁ
ꢀ
0ꢂ
3
3
t2gSΓ V (Γ ) t2gSΓ = 0 (Γ = Γ 0),
(1)
ꢁ
ꢁ
only for the combinations
2
2
SΓ = E,2T1 and SΓ 0 = T2,
and vice versa. Similarly, for the e2g configuration, one
finds that
ꢁ
ꢁ
ꢀ
0ꢂ
2
2
egSΓ V (Γ ) egSΓ = 0 (Γ = Γ 0)
(2)
ꢁ
ꢁ
only for the combinations
1
1
SΓ = E and SΓ 0 = A1,
and vice versa. The group-theory results in Eqs. (1)
and (2), valid for the t32g and e2g configurations,
indicate which are the expected electronic bands
likely to be observed in experiments. As for the
tn2gemg configuration, further inspection of the matrix
elements for the case n + m = 5 (case: n = 3, m = 2)
shows again that the only allowed CF transitions are
the ones listed in Table 1.
Thus, a second-order progression is expected to be
the basic vibronic structure, provided that also the
spin-dependent ep interaction (via the phonon mod-
ulation of spin–orbit coupling) be zero. Time ago we
have reported a clear evidence of two-phonon progres-
sions, due to the second-order linear electron–phonon
operator, in NiCl2 and NiBr2 crystals [d8(eg) config-
uration], by comparing the phonon structure observed
1
in the 3A2(F) + E(D) CF bands with the Raman spec-
tra measured on the same samples [11]. The vanishing
of the spin-dependent first-order electron–phonon in-
teraction was then shown to be a necessary condition
for observing prominent second-order phonon struc-
tures in the intra-configurational transitions observed
in these compounds.
The evidence of pure two-phonon progressions
observed in late TMCs (i.e., in nickel and manganese
dihalides) has then suggested to verify whether the
same phenomenon may be observed in early TMHs,
where a different type of electronic structure can

I. Pollini / Physics Letters A 277 (2000) 281–286
283
Table 1
Electronic transitions where possible second-order phonon transitions are predicted (only for 1S = 0,1)
Electronic configuration
Electronic transitions
Predicted
Observed
3
3
2+
2+
4
5
6
3
2
2
(t ) 3d (V ; Cr 3+)
A (F) → E(G)
E(G) in VCl ; VBr
2
2
2
2g
3
4
2+
3+
3
3
3
3
3
4
1
3
(t , e ) 3d (Cr ; Mn
)
E(D) → E(H), A (G), A (F), E(D)
A (G), A (F) in CrBr
1 2 2
g
1
2
2g
3
2
5
d
2+
3+
4
4
4
4
(t e ) 3 (Mn ; Fe
)
A (S) → A (G), E(G), E(D)
E(G) in MnX ; E(D) in MnCl
2 2
1
1
g
2g
2
8
2+
1
1
1
(e ) 3d (Ni
)
A (F) → E(D), A (G)
E(D), A (G) in NiCl and NiBr
2
1
1
2
2
g
occur, owing to a stronger covalence and a lower
electronic correlation of the early transition metal
compounds [12,13]. Moreover, as said before, the
occurrence of a pure two-phonon progression is a
rather rare case, since the configurational mixing
in the CF levels can switch on a weak first-order
ep coupling and mask the two-phonon contribution.
Nevertheless, the theoretical prediction of a second-
order structure often provides a key of interpretation
for the complicated phonon structures which have
been often observed in other 3d-metal compounds.
Such a selection rule is fulfilled by the transitions
listed in Table 1, where it is shown which second-order
phonon progressions are possible.
This Letter is devoted to the optical study of the in-
teresting phonon structures measured in the CF spec-
trum of newly grown materials, such as the layered
vanadium and chromium dihalides. The special case
of the electronic 3d4(t2geg) configuration present in
CrBr2 crystals has been in particular considered, since
in it, despite the unfilled eg semi-shell, a vanishing
ep interaction for some transitions between monocli-
nally split levels has been found. This work follows
a similar experimental study on the optical effects of
the magnon structures observed in the CF region of Fe
dihalides at low temperature [14].
weighted quantity of CrBr3 in a U tube at 350–400◦C
for 6–10 h. White tiny crystals are thus obtained.
They are rather hygroscope and rapidly oxidised in air.
Hygroscope samples have been treated in a glow-box,
filled with nitrogen or argon gas, in order to prevent
deterioration due to moisture. In the visible region a
double-beamCary 14 spectrophotometerwas used and
the temperature was checked by a CLST sensor by
Oxford Instruments.
The crystals under consideration belong to the D33d
space group, with the cation at a D3d site surrounded
by a octahedral cage of halogen ions. Since the
trigonal distortion of the ligand field is small, the
electronic levels can still be classified in terms of
the cubic (Oh) irreducible representations. On the
contrary, the zone centre phonons strongly reflect
the crystal anisotropy and have to be labelled by
the trigonal irreducible representations. For example,
vanadium dihalides crystallize in a layered structure
of the CdI2 type and belong to the trigonal space
group D33d. This structure consists of hexagonal sheets
of metal atoms sandwiched between two hexagonal
sheets of anions. The nearest neighbours of a metal
atom form a slightly distorted octahedron. A factor
group analysis yields four optical modes at the Γ
point, A1g + Eg + A2u + Eu, i.e., two Raman-active
modes (even) and two infrared-active (odd) modes.
Owing to their structures and their reduced ionicity,
these crystals present rather flat dispersion curves
associated with the optical mode Eg and a sharp peak
at ω(Eg) in the Eg projected phonon density is in
general expected. The CrBr2 compound belongs to the
space group C32h [15] and is a special case.
Crystals of VCl2, VBr2 and CrBr2 have been
grown from the vapour phase, using pure elements
as starting materials. Usually the crystals grow in the
form of large, thin platelets (ca. 10 × 10 × 0.1 mm3)
perpendicular to the c-axis. A flow-system method
has been in general used, where the halogen gas
carried by dry nitrogen attacks the pure powdered
metal at growing temperature typical for each crystal
(500–800◦C). In particular, the crystals of CrBr2
were obtained by reduction (with very pure H2) of a
The experimental results on vanadium and chro-
mium dihalides are now presented and discussed in
the light of the theoretical concepts exposed before.

284
I. Pollini / Physics Letters A 277 (2000) 281–286
2
1
Fig. 1. Two-phonon progression observed in VCl crystals in the crystal field E(G) and T (G) bands at 5 K.
2
2
2
Fig. 2. Two-phonon progression observed in VBr crystals in the crystal field band E(G) at 5 K.
2
Figs. 1 and 2 show the 2E(G) and 2T2(G) absorp-
tion bands of VCl2 and VBr2 compounds at 5 K, re-
spectively. These bands are well separated by a deep
minimum around 11.900 and 12.100 cm−1. The spin–
orbit coupling accounts for the splitting observed in
nor the trigonal field perturbation can lift the degener-
acy of the 2E(G) band [3]. While the small splitting of
84 cm−1 in VCl2 and 122 cm−1 in VBr2 could also
be due to optical magnons (quickly washed out by in-
creasing temperature), the broad sidebands observed
above the 2E(G) band cannot have but a phonon origin.
2
the T2(G) band, but neither the spin–orbit coupling

I. Pollini / Physics Letters A 277 (2000) 281–286
285
3
3
Fig. 3. The crystal field spectrum of CrBr crystals at 5 K. The two-phonon progression observed in the A (G) + A (F) electronic band is
2
1
2
reported in the insert.
4
4
In fact, the spacing of 404 and 260 cm−1 corresponds
quite well to twice the respective Raman Eg frequen-
cies [10,16]. In principle, all frequencies associated
with the above transitions should be slightly different
and shifted with respect to the Raman frequencies, due
to the different relaxation of the excited states. First-
and second-order phonon spectra have been also stud-
ied by Bauhofer et al. [16], who have measured two-
phonon infrared absorption spectra and discussed the
mechanisms responsible for the two-phonon infrared
absorption in polar crystals. While the first mechanism
they discuss is the same which is active in our com-
pounds (the direct coupling of the photon to a two-
phonon state via the second-order dipole moment op-
erator), they also considered the effect of the cubic an-
harmonicity, which can couple the incident photons
with transversal optical lattice modes and yield the
phonon sidebands observed in the optical spectra.
Nice one-phonon progressions have been also ob-
served in MnCl2 and MnBr2 in the CF bands 4T3(D)
and 4E(D) [7,17] and in 4E(G), 4A1(G) in MnI2
[18]. As for the intra-configurational transitions, the
6A1(S) → E(G) + A1(G) transition in both com-
pounds shows a puzzling phonon structure, together
with the notable common feature that the spacings be-
tween the first two sharp peaks are nearly twice the
Raman Eg frequencies (see Fig. 2 in [17]). However,
these examples will not discussed any more, since
they have been already presented in detail in previous
works [7,17,19].
While in 3d3, 3d5 and 3d8 configurations a vanish-
ing first-order ep coupling descends from the group
theory [3] for the transitions shown in Table 1, in the
3d4 configuration, this occurs accidentally. For this
reason, the special case of the d4(t2geg) configuration
in CrBr2 (space group C3 [15]) has been considered.
Thus, good quality CrB2r2h crystals have been grown
and the crystal field spectrum has been measured and
shown in Fig. 3. The fitting of the observed transitions
to the octahedral crystal field diagram, including the
spin–orbit coupling [20], has given a CT parameter
10 Dq ∼ 12000 cm−1. Only one vibronic structure was
observed in the whole spectrum. This structure is as-
sociated with the nearly degenerate transitions 3A2(F),

286
I. Pollini / Physics Letters A 277 (2000) 281–286
3A1(G) and presents a spacing of 306 cm−1. As shown
in Table 4 of Ref. [10], this frequency scales quite
well with twice the Raman A1g frequency of VBr2
(316 cm−1) and MnBr2 (302 cm−1) and therefore it
is suggested that it corresponds to a second-order vi-
bronic structure of the same kind shown in vanadium,
manganese and nickel halides.
In conclusion, it has been shown that, owing to
the small dispersion of the phonon branches, it is
possible to observe sharp two-phonon progressions in
the crystal field spectrum of layered transition metal
halides. It is also claimed that the main mechanism
for the occurrence of this exceptional case (one-
phonon progressions are the rule) consists in the direct
coupling of the incident photons to a two-phonon state
via the second-order dipole moment.
[4] H. Sumi, J. Phys. Soc. Jpn. 36 (1974) 770;
H. Sumi, J. Phys. Soc. Jpn. 38 (1975) 825.
[5] B. Di Bartolo, R.C. Powell, Phonons and Resonances in
Solids, John Wiley and Sons, New York, 1976, p. 348.
[6] R.S. Knox, Solid State Phys. Suppl. 5 (1973).
[7] I. Pollini, G. Spinolo, G. Benedek, Phys. Rev. B 22 (1980)
6369, and references therein.
[8] J. Thomas, I. Pollini, Phys. Rev. B 32 (1985) 2522.
[9] Ph.E. Schmid, Adv. Solid State Phys. 16 (1976) 47.
[10] G. Benedek, A. Frey, Phys. Rev. B 21 (1980) 2482.
[11] G. Benedek, I. Pollini, L. Piseri, R. Tubino, Phys. Rev. B 20
(1979) 4303.
[12] A.E. Bocquet, T. Mikozawa, T. Saitoh, K. Morikawa, A.
Fujimori, S.R. Barman, K. Maiti, D.D. Sarma, Y. Tokura, M.
Onoda, Phys. Rev. B 53 (1996) 1161.
[13] I. Pollini, Phys. Rev. B 60 (1999) 16170.
[14] I. Pollini, G. Spinolo, Phys. Lett. 72A (1979) 261.
[15] J.W. Tracey, N.W. Gregory, E.C. Lindgafelter, Acta Cryst. 15
(1962) 672.
[16] W. Bauhofer, G. Guntherhodt, E. Anastassakis, A. Frey, G.
Benedek, Phys. Rev. B 22 (1980) 5873.
[17] L. Piseri, I. Pollini, J. Phys. C: Solid State Phys. 17 (1984)
4519.
References
[18] W. van Erk, C. Haas, Phys. Status Solidi B 70 (1975) 517.
[19] G. Benedek, I. Pollini, G. Spinolo, in: M. Balkanski (Ed.), Pro-
ceedings of the International Conference on Lattice Dynamics,
Paris, 1977, Flammarion, Paris, 1979, p. 68.
[1] N.F. Mott, Metal–Insulator Transitions, Taylor & Francis,
London, 1990.
[2] N. Tsuda, K. Nasu, A. Yanase, K. Siratori, Electronic Conduc-
tion in Oxides, Springer Series in Solid State Science, Vol. 94,
Springer, Berlin, 1991.
[20] E. Konig, S. Kremer, J. Phys. Chem. 78 (1974) 56.
[3] S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition
Metal Ions in Crystals, Academic Press, New York, 1970, p.
153.