ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2008, Vol. 72, No. 4, pp. 443–447. © Allerton Press, Inc., 2008.Original Russian Text © I.N. Shabanova, A.V. Murin, E.A. Naimushina, V.A. Trapeznikov, 2008, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2008,Vol. 72, No. 4, pp. 474–478.

443

Theoretical and Experimental Investigation of the Influence of External Effects on the Electronic Structure

of Ce-Based Heavy-Fermion Systems

I. N. Shabanova

a

, A. V. Murin

a

, E. A. Naimushina

b

, and V. A. Trapeznikov

a

a

Physicotechnical Institute, Ural Division, Russian Academy of Sciences, ul. Kirova 132, Izhevsk, 426000 Russia

b

Udmurt State University, Universitetskaya ul. 1, Izhevsk, 426034 Russiae-mail: XPS@fti.udm.ru

Abstract

—The electronic structure of Ce systems with different degrees of hybridization of

f

electrons withouter-shell electrons and the effect of pressure on the change in the electronic structure has been investigated.A correlation between the parameters of X-ray photoelectron spectra and the magnitude of the heavy-fermionstate is established. The total and partial densities of states of atoms were calculated using the TB LMTO ASAmethod. X-ray photoelectron study of the effect of an X-ray induced vacancy in the inner levels on the shapeof the

Ce3

d

spectra for Ce-based systems with different degrees of covalence has been performed. It is shownthat there is a relationship between the magnitude of the heavy-fermion state and the intensity of the shake-down satellites in X-ray photoelectron spectra and that the magnitude of the heavy-fermion state decreasesunder pressure.

DOI:

10.3103/S1062873808040060

INTRODUCTION

The class of compounds based on

f

elements (in par-ticular, Ce) attracts much attention due to their unusualproperties related to the presence of

f

electrons. Someof these compounds exhibit a heavy-fermion state,which is formed under certain external conditions (tem-perature, pressure, magnetic field, irradiation, etc.).

If mixing of the electron density of free stronglylocalized states with the electron density of delocalizedoccupied states occurs under an external action, thisprocess may lead to a sharp increase in the density ofstates at

E

f

and an increase in the effective mass of con-duction electrons by two to three orders of magnitude,i.e., to the heavy-fermion state.

Heavy-fermion materials have unique properties. Itis known [1] that coating of details of machines andmechanisms with such materials increases the strength

and protective characteristics by more than an order ofmagnitude.

RESULTS AND DISCUSSION

The purpose of this study was to investigate the elec-tronic structure of Ce systems with different degrees ofhybridization of

f

electrons with the outer-shell elec-trons, analyze the effect of pressure on the change in theelectronic structure, and establish a correlation betweenthe parameters of X-ray photoelectron spectra andcharacteristics of the heavy-fermion state.

The electronic structure of a series of heavy-fermionsystems (

CeCu

6

, CePd

3

, CeSi

2

,

and

CeSi

2

Cu

2

) was inves-tigated by X-ray photoelectron spectroscopy (XPS),with calculation of the total and partial densities ofstates of atoms within the tight-binding linear muffin-tin orbital atomic-sphere approximation (TB LMTOASA). The linear muffin-tin orbital atomic-sphere

Table 1.

Parameters of the Ce systems

γ

, MJ/(mol K

2

)

m

*

R

max

f

–

E

F

, eV

∆

4

f

, eV

d

rel

at

E

F

N

f

Lattice

CeCu

6

1600 1000

m

e

0.18 0.07 eV 0.86 0.73

f

0

Orthorhombic

CePd

3

1620 1000

m

e

0.07 0.09 eV 0.54 0.75

f

0

Cubic

CeSi

2

160 100

m

e

0.37 0.2 eV 0.86 0.8

f

0

Body-centered tetragonal

Note:

γ

is the electronic specific heat coefficient,

m

* is the electron effective mass,

R

max

f

–

E

F

is the distance from the resonance peak to

E

F

,

∆

4

f

is the width of the 4

f

-resonance peak in the free-state band,

d

rel

at

E

F

is the relative decrease in the density of states at

E

F

underpressure (

V

/

V

0

= 0.85) with respect to the equilibrium state,

N

f

is the number of

f

electrons under pressure with respect tothe equilibrium state, and

f

0

is the number of

f

electrons in the equilibrium state.

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SHABANOVA et al.

approximation allows one to take into account the cova-lent type of bonding; the efficiency and precision of thismethod have been verified for many objects.

The results of the investigation of the electronicstructure of the

CeCu

6

system, having the highestparameters of the heavy-fermion state (Table 1), areshown in Fig. 1. These data demonstrate satisfactoryagreement between the X-ray photoelectron valence-band spectrum and the results of calculations of thetotal density of states.

Figure 2 shows the partial density of electron states.It can be seen that the

f

region has the shape of a doubletdue to the state splitting by the crystal field [2]. It isnoteworthy that the shapes of the curves of the partialdensities of the

f

(Ce)

and

d

(Cu)

states are identical (inthe energy range from 2 to 6 eV with respect to

E

F

); thisfact is related to their hybridization.

It can be seen that the range of free states includes apeak of

4

f

-resonance states, which is adjacent to

E

F

. The

f

,

d

(Ce)

and

s

,

p

(Ce

,Cu) states are located predomi-nantly at

E

F

. As a result of mixing of these states withthe

4

f

-resonance states, the density of states at

E

F

growsand the electron effective mass increases by threeorders of magnitude in comparison with the free elec-tron mass (Table 1).

It is known [3] that a heavy-fermion state can passto an intermediate-valence state under pressure. A nec-essary condition for this effect is strong hybridizationof the outer electron. In this case, electronic transitionsoccur, which lead to a change in filling of electronicstates. Configurations with different numbers of

f

elec-trons turn out to have close energies. This fact is con-firmed by the calculations. Figure 3 shows the changein the partial density of states with a decrease in theunit-cell volume by 15% with respect to the equilib-rium value (

V

/

V

0

= 0.85). The new doublet in the

f

(Ce)

band is shifted by 0.4 eV from the doublet in the

f

(Ce)

band for the equilibrium state (Fig. 2). Application ofpressure (

V

/

V

0

= 0.85) leads to a decrease in the number

–8 –6 0

Energy, eV

Inte

nsity

, rel

. uni

ts

–2–4

X-ray

Density

CeCu

6

Fig. 1.

X-ray photoelectron valence-band spectrum and thetotal density of states of

CeCu

6

.

–8 –6 0

Energy, eV

–2–4

Total

CeCu

6

–7 –5 –3 1–1

d

(Cu)

f

(Ce)

d

(Ce)

p

(Ce)

s

(Ce)

p

(Cu)

s

(Cu)

Fig. 2.

Total and partial densities of states of

CeCu

6

in equi-librium (V/V0 = 1.00).

–8 –6 0Energy, eV

–2–4

Total

CeCu6

–7 –5 –3 1–1

d(Cu)

f(Ce)

d(Ce)

p(Ce)

s(Ce)

p(Cu)

s(Cu)

Fig. 3. Total and partial densities of states of CeCu6 with theunit-cell volume decreased by 15% with respect to the equi-librium value (V/V0 = 0.85).

photoelectronspectrum

of states

BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS Vol. 72 No. 4 2008

THEORETICAL AND EXPERIMENTAL INVESTIGATION 445

of f electrons (Table 1.). Therefore, two configurationswith different numbers of f electrons are superposed.Other partial densities of states are broadened andshifted from EF in comparison with the equilibriumstate. This situation is characteristic of the intermedi-ate-valence state. Localization of the 4f-resonance peakdecreases; it broadens and shifts away from EF (Fig. 3).In addition, as the calculations showed, the density ofstates near EF decreases under pressure (Table 1); thiseffect leads to a decrease in mixing of delocalized and4f-localized electrons.

The investigations of the electronic structure of theCePd3 system gave results similar to those for CeCu6.Figure 4 shows the total and partial densities of statesof Ce and Pd atoms for CePd3 in equilibrium. Here,hybridization of f(Ce)- and d(Pd) electrons is observed.Under pressure, hybridization of f electrons with d, s,and p electrons of Ce and Pd atoms is enhanced. Thedensity-of-states curve shifts by 0.5–1 eV with respectto the equilibrium state, and localization of the 4f-reso-nance peak in the range of free states is reduced(Fig. 5). The density of states at EF decreases by a factorof about 2 (Table 1). Mixing of delocalized and local-ized states decreases (Fig. 5); as a result, the heavy-fer-mion state passes to the intermediate-valence state.

In contrast to the CeCu6 and CePd3 systems, hybrid-ization of the outer-shell electrons in CeSi2 is muchstronger. It can be seen in Fig. 6 that the curves of thetotal and partial (f(Ce), d(Ce), and p, s(Ce,Si)) densitiesof states have an identical shape. Table 1 contains theparameters of the heavy-fermion state (m*, γ) [4]. It canbe seen that these parameters for CeCu6 and CePd3 aremuch larger than for CeSi2. This fact is related to thelarge overlap of the wave functions of electrons of Ceand Si atoms, which decreases localization of the f-res-onance maximum. Under pressure, the CeSi2 systemexhibits the same regularity as CeCu6 and CePd3: a shift ofall curves of the partial density of states by 0.4–0.6 eV anda decrease in the density of states near EF, this behaviorindicates a transition to the intermediate-valence state.

Table 1 contains also the positions and widths ofthe 4f-resonance peaks, the decrease (with respect toequilibrium state) in the density of states at EF underpressure, and the change in the number of f electronswith respect to the equilibrium f0 state for the sys-tems studied.

Thus, as the calculations of the electron density ofstates for atoms in the systems under considerationshowed, the stronger the hybridization of the outer-shell electrons of the neighboring atoms, the weaker thelocalization of the 4f-resonance peak; under pressure,the magnitude of the heavy-fermion state decreases.

We also performed X-ray photoelectron study of theinfluence of an X-ray induced vacancy at the inner lev-els on the change in the shape of the spectra of Ce-based systems with different degrees of covalence. Theformation of a vacancy at the inner levels of an atom is

known to lead to reconstruction of the wave function ofthe outer-shell electron, which is related to the changein the spatial distribution and transition of electronsfrom an occupied shell to a free one. As a result, alongwith the main line of the unrelaxed final state, a satelliteline (shake), corresponding to the relaxed final state,

–8 –6 0Energy, eV

–2–4

Total

CePd3

–7 –5 –3 1–1

d(Pd)

f(Ce)

d(Ce)

p(Ce)

s(Ce)

s(Pd)

p(Pd)

Fig. 4. Total and partial densities of states of CePd3 in equi-librium.

–8 –6 0Energy, eV

–2–4

V/V0= 0.8

CePd3

2 4

V/V0= 0.9

V/V0= 1.0

Fig. 5. Total and partial densities of states of CePd3 in equi-librium and under pressure.

446

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SHABANOVA et al.

may arise in the X-ray photoelectron spectra of theinner levels. The satellite line is strong when there is astrongly localized free state near the occupied states atEF, and reconstruction of the wave function of the outer-shell electron leads to their overlap. This situation canbe implemented for Ce compounds possessing a heavy-fermion state.

We investigated the Ce3d, Ce 4d, and Ce 4p X-rayphotoelectron spectra in systems with different degreesof covalence in chemical bonding. It is known [5, 6]that the ratio of the intensity Is of the satellite line to theintensity I0 of the main line is proportional to the poten-tial formed by the inner vacancy. This potential for theCe3d shell of much higher than for the Ce4d and Ce4pshells, where the relaxed state is not observed. Figure 7shows the Ce3d spectra; they consist of two regionscorresponding to the unrelaxed and relaxed states. Thestructure of these lines is determined by multiplet split-ting due to the exchange 3d–4f interaction and is thesame for systems with the same number of f electrons[7]. The satellite structure, reflecting the relaxed statesof the system, is observed at the low-energy side of themain line; i.e., it is due to the processes of energyrelease (shake-down satellites), which is determined bythe small radius of the 4f shell [2]. Table 2 and Fig. 8present the intensities and positions of the satellite lineswith respect to the main ones for different degrees ofcovalence of chemical bonding in Ce systems [8]. Thesatellite line intensity is maximum for a degree of cova-lence of ~0.5. With a further increase in the degree ofcovalence in chemical bonding, the satellite intensitydecreases. The same effect was revealed by comparisonof the calculated densities of states in the CeCu6 andCeSi2 systems; this comparison showed that, the stron-ger the hybridization of the outer electrons of the com-ponent atoms, the weaker the localization of the 4fstate.

–8 –6 0Energy, eV

–2–4

Total

CeSi2

–7 –5 –3 1–1

d(Ce)

f(Ce)

p(Si)

p(Ce)

s(Ce)

Fig. 6. Total and partial densities of states of CeSi2 in equi-librium.

873 876 885Binding energy, eV

Int

ensi

ty, r

el. u

nits

882879

Ce3d

888 891 894

CeCu6

CeCu2Si2

CeS3

CeCl

CeF3

Fig. 7. Ce3d X-ray photoelectron spectra.

Table 2. Relative intensities and positions of satellite linesfor different degrees of covalence of Ce systems

Compound ∆s, eV Is/I0, ∆ = 5% k

CeCl 3.7 0.5 0.38

CeS3 3.7 0.4 0.60

KCe(PO3)4 3.5 0.6 –

Ce 4.1 0.25 –

CeBr3 3.8 0.5 0.48

CeN 4.1 0.3 0.38

CeSb 4.3 0.17 0.87

CeF3 3.7 0.03 0.13

CeCu2Si2 3 0.7 –

CeCu6 3.8 1.2 –

Note: k is the degree of covalence, ∆s is the spacing betweenthe peaks of the satellite and main spectra, Is is the intensity ofshake-down satellites, and I0 is the intensity of the main line.

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THEORETICAL AND EXPERIMENTAL INVESTIGATION 447

The relative satellite intensity for heavy-fermionsystems greatly exceeds the satellite intensity for otherCe compounds.

Thus, there is a correlation between the intensity ofthe shake-down satellites in X-ray photoelectron spec-tra of the inner Ce levels and the characteristics of theheavy-fermion state in the compounds studied. On thebasis of the satellite intensity, one can draw conclusionsabout the existence of the heavy-fermion state in Cesystems. The same satellites are observed in Nd sys-

tems. Further filling of the f shell does not reveal anyshake-down satellites [9].

REFERENCES

1. Trapeznikov, V.A., Shabanova, I.N., and Zhurav-lev, V.A., RF Patent 2296185, 2007.

2. Moshchalkov, V.V. and Brandt, N.B., Usp. Fiz. Nauk,1986, vol. 149, no. 4, p. 585.

3. Khomskii, D.I., Usp. Fiz. Nauk, 1979, vol. 129, no. 3,p. 443.

4. Stewart, G.R., Rev. Mod. Phys., 1984, vol. 56, no. 4.

5. Larsson, S., J. Electron. Spectrosc., 1976, vol. 8, p. 171.

6. Asada, S. and Sugano, S., J. Phys. Soc. Jpn., 1976,vol. 41, p. 1291.

7. Demekhin, V.F., X-ray Spectra of Elements with anUnoccupied Shell, Extended Abstract of Doctoral(Phys.–Math.) Dissertation, Rostov-on-Don: RGU,1974.

8. Siegbahn, K., Nordling, C., Fahlman, A., et al., ESCA:Atomic, Molecular, and Solid State Structure Studied byMeans of Electron Spectroscopy, Amsterdam: NorthHolland, 1967. Translated under the title ElectronnayaSpectroskopiya, Moscow: Mir, 1979.

9. Shabanova, I.N., X-ray Photoelectron Spectroscopy ofDisordered Systems Based on of Transition Metals,Extended Abstract of Doctoral (Phys.–Math.) Disserta-tion, Izhevsk: FTI UrO RAN, 1990.

0.6

0 0.2 0.4k

Is/I0

0.4

0.2

0.6 0.8 1.0

CeF3

CeCl CeBr3

CeS3

CeSb

CeN

Fig. 8. Dependence of the relative intensities of the satellitelines on the degree of covalence of Ce systems.