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Submitted on 1 Jan 1981
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RAMAN SCATTERING FROM ANOMALOUS
PHONONS IN TRANSITION METALS AND
COMPOUNDS
M. Klein
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C6, supplgment au no 12, Tome 42, de'aembre 1981 page C6-368
RAMAN SCATTERING FROM ANOMALOUS PHONONS I N T R A N S I T I O N METALS AND COMPOUNDS
M. V. Klein
Department of Physics and Materials Research Laboratory, University of IZZinois at Urbana-Champaign, Urbana, Illinois 61 801, U. S. A.
Abstract.-Phonon anomalies in transition-metal compounds often produce enhanced two-phonon Raman spectra. Examples are given and a theoretical explanation sketched. The anomalous Eg phonon and electronic Raman scattering in V3Si are also discussed.
Phonon anomalies in transition-metal compounds occur when scattering of d-electrons near the Fermi surface renormalizes the phonon frequencies by giving them a self- energy .rr(q,w % 0) that is large and negative.' This alters the frequency by an
amount %[-r(q,O)]. The same d-electron-phonon interactions are responsible for strong two-phonon overtone Raman scattering. There is a microscopic connection between the anomalies and the Raman cross-section.2 Apart from the usual Bose factor, the latter is
o(w) = P
I
~(~/z-w~)I=(~.o)I~ (1) 9where P contains a polarizability-like factor. If r(q,O) were unity the sum over q would give simply F(w/2), where F(w) is the phonon density of states. A variable *(q,O) gives selective Raman enhancement for those phonons that are anomalous.
A clean example of this effect is found in the normal phase of the layered
480
transition metal dichalcogenides before
-
they undergo a charge-density-wave (CDW)p
405-\ type of phase transition.2 For example,
in 2H-NbSe2 the LA phonon near
Z q=(2/3)TM softens and eventually con-
3
2
255-
denses. Its overtone gives the strongest Raman feature in the room- temperature as shown in Fig. 1, namely the broad peak at 180 cm-l,'050 100 200 300 400 which softens to 160 cm-' at 100 K.
This spectrum is clearly not the full
RAMAN SHIFT
(cm")
F(w/2) but shows the soft LA region Fig. 1: The A-symmetry Raman spectrum only.
of 2H-NbSe2 at 300 and 100 K. (Ref. 4)
Another example is found in the group Vb transition metal carbides, which have the rock-salt structure. The samples always occur with at least a few percent carbon vacancies, which induce a one-phonon Raman spectrum that is quite close to F(w). This can be seen for acoustic modes in Tacoegg in Fig. 2 in the curves labelled "lph". The curves labelled "2ph" are two-LA-phonon spectra plotted as a function of w/2. These strong two-phonon peaks are not due to the vacancies, but are intrinsic and show enhancements relative to F(w) in the mid-frequency region, where the well-known phonon anomalies lie.
rn
Fig, 2: Raman scattering from Fig. 3: The Eg Raman spectrum of V3Si at acoustic phonons in TaC0.99. (Ref. 5) five temperatures. (Ref. 6) Lines repre- For each symmetry one and two phonon sent fits to a Lorentzian with anti- spectra are compared, the latter as resonance.
a function of w/2.
C6-370 JOURNAL DE PHYSIQUE
A unified microscopic theory of all these effects has been ~ r e s e n t e d ~ , ~ , starting with Kawabata's Greens function formulism for Raman scattering.8 One must calculate essentially the imaginary part of an irreducible four-vertex function. Examples are shown in Fig. 4. The incident photon enters at vertices 1 and 4 and leaves at 2 and
k 1 3. Final state "cuts" are taken through the central \ region of the diagrams. Diagram (a) gives interband electronic scattering if afc. We believe that such processes are responsible for the broad Raman con- tinuum seen in essentially all transition metals. A / 1 - \
( a )
\cut through the phonon line in Diagram (b) gives a
dressed 1-phonon final state. Cuts through (c,a) or /
(cl,a') in Diagram (b) give electron-hole-pair final
b' states that will interfere with Diagram (a) to produce
/
,
a Breit-Wigner-Fano a n t i r e s o n a n ~ e . ~ ~ ~ In the case of(b)
V3Si and other A15 compounds, the important contribu-tions to bands (a,c) and (al,c') resulr when these
\
'
I bands arise from the r12 point, very close to thei
:
l
j
Fermi energy. loA cut through both phonon lines in Diagram (c) gives
1 2-phonon Raman scattering that leads to Eq.
(I),
if,/ \
\ as expected, large intermediate state damping prevents
(c)
strong resonance Raman enhancements. Other final states and Fano resonances are possible, but will be Fig. 4: Feynman diagrams forless important because of the width of 2-phonon bands. Raman scatterinn. Solid
-
lines, electrons; dashed lines, photons; wiggly lines dressed phonons. (Refs. 3,7,8)
This work was supported by the NSF through the MRL grant DMR-80-20250. References
1. C. M. Varma and W. Weber, Phys. Rev.
Bx,
6142 (1979).2. P. F. Xaldague and J. C. Tsang, in Proc. Int. Conf. Lattice Dynamics, ed. by M. Balkanski (Flammarion Sciences, Paris, 1978).
3. M. V. Klein, Phys. Rev. B, to be published.
4. R. Sooryakumar, M. V. Klein and R. F. Frindt, Phys. REV. B E , 3222 (1981).
5. H. Wipf, M. V. Klein and W. S. Williams, unpublished. 6. .H. Wipf, et al., Phys. Rev. Lett.
1,
1752 (1978).7. M. V. Klein, in Light Scattering in Solids, ed. by M. Cardona and G. Giintherodt, to be published by Springer-Verlag.
8. A. Kawabata, J. Phys. Soc. Japanz, 68 (1971).
