PHONONS IN MIXED VALENCE COMPOUNDS

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PHONONS IN MIXED VALENCE COMPOUNDS

W. Kress, H. Bilz, G. Güntherodt, A. Jayaraman

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque C6, suppZe'ment au n012, Tome 42, de'cembre 1981 page C6-3

PHONONS I N MIXED VALENCE COMPOUNDS

* X W. Kress, H. B i l z , G. ~ i i n t h e r o d t * and A. Jayaraman

Mux-PZanck-Institut fur FestkBrperforschung, 7000 Stuttgart, F. R. G. * ~ n i v e r s t i t t i t iWZn, F.R.G.

* * ~ e l Z Laboratories, Murray H i Z Z , iVJ, U . S. A.

Abstract.- Several mixed-valence r'JaC1-structure compounds show strong anomalies in the phonon dispersion curves. These anomalies are related to the interaction of localized £-electrons with de- localized band electrons near the Fermi surface and to the isostructural phase transitions characterized by a softening of the bulk modulus. The lattice dynamics of these compounds is revie- wed and the dispersion curves are analyzed in terms of a breathing shell model including various modifications. The relation between the phonon self-energies and the electronic band structure is discussed. In addition, the polarized Raman spectra are interpreted in terms of local cluster deformabilities of breathing and quadrupolar symmetry. Similarities and differences of phonon anomalies, Raman spectra and electronic band structure in semiconducting, superconducting and mixed valence compounds are pointed out.

I. Introduction.- Rare earth atoms are characterized by extremely localized, partly filled 4f shells. In solids most of the rare earth ions are trivalent with the exception of Sm and Eu in the niddle and Tm and Yb at the end of the series. For these ions Hund's rule coup- lings become important and the divalent state is favored. In Sm, Eu, Tm, and Yb as well as in Ce compounds the 4fn(5d6s)" and the 4fn-I (5d6s)"+l states are energetically close and may become nearly degenerate when the external parameters (pressure, temperature) are changed. The same can happen if the composition is changed (e.g. by alloying). In these cases isostructural phase transitions into a homo- geneous intermediate (non integer) valence phase have been observed. Since the screening of the Coulomb attraction of the core is signifi- cantly reduced when a localized 4f electron is promoted to the deloca- lized (5d6s) band large changes in volume occur.

The coexistence of two neighboring, nearly degenerate configura- tions 4fn(5d6s)m and 4fn-I (5d6s)"+l at equivalent rare earth ions leads to valence fluctuations for which the charge relaxation rate may be on the same time scale as the lattice vibrations. It can, therefore, be expected that the valence fluctuations manifest themselves not only in the electronic and magnetic properties of the rare earth compounds but also in the phonon spectra. Due to strong electron-pho-

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C6-4 JOURNAL DE PHYSIQUE

non interactions, pronounced anomalies in the phonon dispersion curves are expected for those modes which are sensitive to the isotropic deformation of the charge density of the rare earth ions.

Experimental investigations of the lattice properties have re-. vealed a number of characteristic features: (i) A soft bulk modulus' due to cI2<o and anomalous mean square sulphur displacements of

_-

Sml-xYxS for x>0.1 5 L , (ii) a softening of the zone boundary phonons in semiconducting and metallic s ~ s ~ ' ~ , (iii) anomalies in the phonon dispersion curves of sm O. 75Y0. 25S5r61 (iv) a softening of the bulk modulus due to c12<o and anomalies in the phonon dispersion curves of T~S&;(V) strong interaction of the 4f multiplet levels with phonons in

9

Sml-xYxSe and Sml-xYxS,and(VI)asoftening of the zone center optic mo- 1

o

des in CePd3

.

Several theoretical approaches have been proposed for the treat- ment of the electron-phonon interactions and the description of the phonon anomalies of Sm0.75Y0.25S 11-15 and SmS4116 ~n . its semiconducting as well as in its metallic phase. Recent calculations of the va- riation of the charge relaxation rates of rare earth ions as a func- tion of their valence have provided a systematic understanding of the occurrence or absence of phonon anomalies in intermediate valence com-

17 pounds

.

11. Lattice dynamics.- The electronic densities of states 18-20 and the phonon dispersion curves of EUS'~, SmS 22,23 516 and YS 2 4

sm0.75Y0.22S

are shown schematically in Fig. 1. In SmS the filled 3p bands are se- parated by a band gap of about 3eV from the empty 5d and 6s bands. The localized 4f states and the Fermi level lie at the bottom of the con-

duction band. The phonon dispersion curves of SmS look like those of a typical ionic semiconductor. A com- parison between the dispersion cur-

d ves of EuS and SmS reveals, however,

an incipient effect of intermediate

DENSITY OF STATES _{valence in SmS. Compared to EuS the}

LO branch of SmS is lowered and the

> bulk modulus is decreased. The lo-

wering at the r-point and at the L- point is due to an increased dipolar

(r, 5) electronic deformability of

5 El _{the Sm ions and a breathing}

_{( r , )}

₊

Fig. 1. Electronic densities of states deformability of the Sm ions respec-

and phonon dispersion curves.

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modulus by about 15%. These effects are caused by the lowered 4f-5d promotion energy in SmS as compared to EuS.

When we go from SmS to YS we find a considerable change in the dispersion curves. YS is a superconductor with a partly filled 4d-5s band. The metallic screening of the conduction electrons leads to degenerate LO-TO phonons at the r-point. The degeneracy persists all along the h direction. This indicates that the long range Coulomb forces are screened out almost completely and that only nearest neighbor

(nn) overlap forces are important. Therefore a neutral nn approach is a good starting point for the description of phonons in YS and in metallic intermediate valent Sm0.75Y0.25S.

As we have already seen in the discussion of SmS local electronic deformabilities are a very useful concept for understanding the spe- cial features25 and, in particular, the anomalies in the phonon dispersion curves. Assuming radial coupling between nn in a NaCl lattice only three deformabilities are possible for each ion. Fig. 2 illustrates the different symmetry types. In an adiabatic multipole model the dynamical matrix becomes the sum of a rigid ion part and a deformability

I

.

dipole force

t

,,breathingn force

-0

...

--.

t @ A&-Cb6)<0 A i

Q-*

quadrupole force

o-. Tab. 1. Local deformabilities

'..-, _{part which itself contains a sum}

7

AIClz-Cu)>O over all possible symmetries. In

Microscopic origin 4f6+4f5 ( 5 d 1 ) 4 f 6 + 5 d 1 ( 4 f 5 ) 3 d + 3 d XY xy symm. of i e f o r m . .;IS.) I'T5(sm) rT2 ( ~ m ) .:(s) r T 5 ( s ) r f 2 ( s )

Tab. I the effects which result

Fig. 2. Displacement-induced local de-

formabilities in a decrease of the corresponding

+

phonon frequencies are summarized. We have already discussed the TI

-

and TI5 deformabilities of theSmion in SmS. The LA(L) anomaly in YS (the dashed line in Fig. 1 indicates the normal dispersion curve) ex- hibits a breathing deformability of the S ion which may be caused by resonance-like valence d conduction d excitations near EF since

XY XY

YS has not only Y 4d but also S 3d states near EF. 20

XY XY

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C6-6 JOURNAL DE PHYSIQUE

relative to the band edge and a large fraction of the S d states may XY

become depopulated. If we look at the dispersion curves we see that the LA(L) anomaly has in fact disappeared. Instead, a new anomaly in the LA branch is found at smaller q-values where the LA-branch now lies below the TA-branch. At the same time the LO(L) frequency (which in YS was practically degenerate with the TO(L) frequency) is signifi- cantly lowered. Both effects result from a breathing deformability of the Sm ion arising from virtual Sm 4f+ 5d state excitations, which are characteristic of the mixed-valent state. In addition to the splitting of the LO and TO phonons at the L-point we observe a lowering of the optic modes at T. This is consistent with a dipolar deformability at the Sm-ion caused by the hybridization of the Sm 4f-levels with d- states of S , Sm and Y.

Fig. 3 shows the results of our cal-

10 culationsl 3 . Only five parameters

have been used: two nn overlap for-

8

-

ce constants a breathing and a dipo-

-

r-,

2"

2odg

-

lai- Sm deformability (which are as-

G 4

sumed to be equal) and a quadrupolar

m S deformability which lifts the de-

2 _{generacy of the TA(X) and LA(X) and}

0 may be interpreted as a remainder of

the Coulomb interaction. In view of

rather well the phonon dispersion

Fig. 4. Phonon width for longitudinal 2 6

curves of TmSe measured recently

.

The results are given in Fig. 5.

the simplicity of our model the

Fig. 3. Phonon dispersion curves of agreement with experiment is quite

sm0.75Y0.25s' satisfactory.

Recent calculations of Wakabay- ashi15 show that the model can also account for the wave vector depen- dent lifetimes of the longitudinal

1 1 1 1 I I I I 1 1 1 1 phonons if the relaxation of the

electronic system is taken into account. Fig. 4 shows that the line

$

-

/

-

widths calculated15 with a relaxa-

I \

tion time of 4.10-I 4s compare well with the experimental

Using essentially the same

0 02 0 4 a6 a8 (0 a8 0.6 0.4 0.2 0 02 a4

C. R U X h E O WAVE VEtXII model we have been able to reproduce

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It is seen from the splitting of the LO (A) and TO (A) bran- ches that for shorter wave- lengths the Coulomb contributions play an important ro- le and have to be included in the calculation. In addition to the parameters used for the calculation of

Sm0.75Y0.25S we take into account screened Coulomb and weak Tm-Tm interactions.

Fig. 5. Phonon dispersion curves of TmSe.

111. Raman Scattering.- So far we have parametrized the electron-lattice interaction in terms of local cluster deformabilities and found that three deformabilities ( breathing, quadrupolar and dipolar) were sufficient to describe the anomalous part of the phonon dispersion curves. We show now that the relevant features of the polarized Raman spectra are due to the same deformabilities which cause the strong anomalies in the phonon dispersion curves. For this purpose we expand the polarization operators PaB(t) into normal coordinates A(q,j ) and im- purity-induced distortions B ( ~ , K ) at lattice site K . The first-order terms read as follows

,"

CPaB (q'j~) B ( - ~ , K ) A(q,j) = PaB (qj) A(gj)

K

This equation describes the symmetry breaking effect of the impurities with respect to the q selection rule, so that gaB(q,j)

+

o for q = o. Instead of using a many parameter fit of the expansion coeffi- cients of PaB(q,j) in ordinary space we use cluster related projec- tion operators to calculate the components of the Xaman spectra which correspond to the different cluster deformabilities. The scaling fac- tors for the partial spectra related to the cluster deformability of symmetry

ri

at the central cluster ion K are taken as parameters.

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JOURNAL DE PHYSIQUE

spectra.However, taking into account the impending valence instability

+

Sm by a breathing response (rl) of the charge density around the Sm ion, we obtain the shaded curve, which explains nicely the

i-

strong

rl

Raman scattering near 200 cm-l

.

An effect of a quadru-

+

polar

rI2

deformability of the Sm-ion has been detected neither in the Raman spectra nor in the phonon dispersion curves. The effect of such a deformability would lead to the spectrum repre-

sented by thin lines in the lower part of Fig. 6. A qualitative

+

analysis of the

rz5

contribution near 60cm-I shows that it is consistent with S-S interactions.

The most interesting spectrum F i g . 6. P o l a r i z e d Raman s p e ~ t r a ~ ~ o f is of course the mixed valent SKS (upper art). Lower p a r t ; weigthed

Smo.75Yo.25S27 (Fig. 7) which is one phonon d e n s i t y : b o l d l i n e ; brea-

t h i n g c o n t r i b u t i o n : hatched a r e a ; qua- clearly dominated by the promi- d r u p o l a r c o n t r i b u t i o n : t h i n l i n e . _{nent T, scattering intensity near}

+

245 cm-I and the weaker one near 85cm-l.

h he

results of the calculat- tion (shaded curve) show that these structures are caused by the breathing deformability of the Sm-ions.

From our lattice dynamical analysis we expect a strong

I'i

deformability of S in YS. The Raman scattering data27 confirm this inter- pretation (Fig. 8). The intensity near 210cm-' arises from second order acoustic phonon scattering which is not included in our calculations.

Our analysis of TiN shows that the Raman spectrum28 is made out of two nearly equal contributions from the breathing and quadrupolar deformabilities at the N site which are represented in Fig. 9 by shaded spectra enclosed by full and dashed lines, respectively. This is again in agreement with the analysis of the phonon dispersion curves

+

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W E NJMBER (cm-1) WAVE NUMBER (cm-1)

F i g . 7 . P o l a r i z e d Raman s p e c t r a z 7 o f Fig.8. P o l a r i z e d Raman spectrum27 o f Sm0.75Y0.25S. N o t a t i o n a s i n F i g . 6. YS. N o t a t i o n a s i n F i g . 6.

shells of Ti and N, respectively. The symmetr:~ of purely radial charge de- formations of the (pdn)-overlap leads, in a first approximation, to equal strength of the breathing and the quadrupolar deformability of the N site. In YS the pd coupling is less effecti- ve and largely replaced by dxy-dxy

0 (1

WAVE W B E R I c m l) excitations which lead to a breathing

F i g . 9. Raman spectrum o f TIN

0.95' deformation only. In Sm0.75Y0.25S

the local symmetry of the Sm site imposed by the Y impurities is consistent with radial

r i

and

r I 5

de-

f

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C6-10 JOURNAL DE PiIYSIQUE

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