0038-1098/88 $3.00 + .00
Pergamon Journals Ltd.
Solid State Communications, Vol. 65, No. 5, pp. 381-384, 1988.
Printed in Great Britain.
INTERACTION OF d-ELECTRON EXCITATIONS AND PLASMONS IN Pd, Ag, Cd, In, Sn AND Sb
T. Bornemann, J. Eickmans* and A. Otto
Institut fiir Physik der kondensierten Materie, Universit/it Diisseldorf, 4000 Dfisseldorf, FRG
(Received 27 July 1987 by B. Miihlschlegel)
We have measured the dispersion of excitations in polycrystalline Pd,
Ag, Cd and In by electron energy loss spectroscopy (EELS). In Pd a
non-dispersing energy loss structure at 7.2 eV is assigned to a collective
mode of the 4d-valence electrons. The plasmons in Ag (7.8eV
plasmon), Cd and In have quadratic dispersion with a change of slope
at wave vectors k ~ 0.5 A -r. For k ~< 0.5 A -~ the measured dispersion
of Ag, Cd and In agrees with calculated values within the random phase
approximation. The observed plasmon energy in Cd, In, Sn and Sb at
k = 0 is in line with calculations taking into account 4d-core
polarization effects.
COLLECTIVE EXCITATIONS IN Pd, Ag, Cd and
In are of particular interest since the 4d-binding energies in these metals are of the order of the free electron
plasmon energies fitop.0 = fi(4rmoe2/m) 1/2. Consequently 4d -~ 5sp interband transitions considerably
contribute to the dielectric response in the neighbourhood of the plasmon energy leading to characteristic
deviations from free electron behaviour [1, 2]. To
investigate these effects we have measured the plasmon dispersion in the succeeding 4d-metals Pd, Ag,
Cd and In using electron energy loss spectroscopy
(EELS) and related our results to the corresponding
4d-binding energies.
The EELS-spectrometer described in [3] was set to
30 keV primary energy with 0.8 eV energy resolution
and 0.05A -~ wave vector resolution. All samples
(thickness about 30-50 nm) were prepared by evaporation in vacuum (10-6mbar) outside the spectrometer. For Ag, Pd and Cd we used (1 00) NaCI surfaces as substrate whereas In was deposited onto
Formvar foils.
To increase the crystalline size of Pd the NaCI
crystal was heated to 700 K, otherwise it was held at
room temperature during film deposition. After evaporation the films were floated off the NaCI crystal
and transferred to the spectrometer. Electron transmission micrographs showed crystallite sizes of about
18 nm in Pd, 50 nm in Ag, 200 nm in Cd and 60 nm in
In.
Figure 1 shows typical EEL - - spectra of Pd, Ag,
* Present address: Bayer AG, Central Research, 5090
Leverkusen, Federal Republic of Germany.
x64
I
I
I
I
Ag 50nm
t,-,
w0
x2
0
[
I
I
I
10
20
30
energy Ioss(eV)
I
t
40
Fig. 1. Energy loss spectra of Pd, Ag, Cd and In films
at k = 0.
381
382
P L A S M O N S IN Pd, Ag, Cd, In, Sn A N D Sb
Vol. 65, No. 5
Table 1. Measured plasmon energies ficop,exp, theoretical values (ficop,o:free electron approximation, ficop,l" including
core polarization effects) and 4d-binding energies E4d (spin-orbit-splitting neglected) below Fermi energy in e V
Metal
hcop.~xv
Pd
7.2 (this
7.5 [9]
6.6 [15]
7.8 (this
8.0 [4]
9.2 (this
9.07 [2]
9.4 [16]
11.4 (this
11.4 [16]
I1.4 [171
13.7 [6]
13.7 [20]
13.7 [19]
15.3 [7]
15.2 [191
Ag
Cd
In
Sn
Sb
ficop.o
E4d [18]
Ibcop,O~cop,expl
ficop,l [1]
work)
-
0-6
-
-
work)
9.0
4-7
1.2
-
work)
11.3
11
2.1
8.5
work)
12.6
17
1.2
11.5
14.3
24
0.5
13.9
15.1
33
0.2
Cd and In at k = 0. Collective excitations are found
at 7.2 eV in Pd, 3.7 and 7.8 eV in Ag, 9.2 eV in Cd and
11.4 eV in In. The 7.2 eV-loss in Pd cannot be assigned
to a plasmon caused by free 5s-electrons as will be
discussed below. In the energy range above 10 eV the
energy loss spectra of Pd and Ag are very similar and
we assign the loss structures at about 26 and 33 eV to
qasiatomic 4d ~ 4 f transitions which for Ag have
been discussed in detail in [4] and for Pd in [5]. The
measured plasmon energies in Cd and In are strongly
downward shifted with respect to the calculated
homogeneous electron gas values and are in line with
recent calculations of Zaremba and Sturm [1] including core polarization effects (see Table 1).
To illustrate these effects upon 5sp plasma oscillations at k = 0 we have plotted both the 4d-binding
energy with respect to EF (upper edge of the 4d-band
is labeled la, lower edge lb), the measured plasmon
energies (2) and the plasmon energies calculated
within the homogeneous electron gas approximation
(3) vs the corresponding 4d-metal (see Fig. 2). Additionally we have included Sn [6] and Sb [7]. For Sb the
difference hcop,exp-ficop.0is very small combined with a
relatively high 4d-binding energy. Approaching the
"crossing point" of curves 1(a, b) and 3 the deviation
hcop,0Ahcopxxpincreases and finally leads to a splitting of
the bulk plasmon in Ag into two plasmons which
clearly demonstrates the increasing influence of
4d-core polarization on 5sp plasmon excitations (see
also Table 1).
In Pd the condition for collective resonance
(e, (co) = 0 and e2(co) small) is met at about 7.6eV [8].
We assign the 7.2 eV-loss in Pd to a collective excitation of the 4d electrons. In a recent reflection EELS
study of the Pd(1 1 0) surface Nishijima et al. [9] found
a narrow energy loss structure at 7.5 eV which they
attributed to 5s bulk plasmon excitation. Although a
small part of the Pd valence electrons is s-like [5, 10],
we believe that a pronounced dispersion should be
40
I
I
f
I
I
I
P
30
~////
////
//
fizz
- 10
>
OJ
////
//
//
j2o
I
////
....
d
10
///
I.~ /
Pd
I
Ag
I
Cd
I
In
I
Sn
SIb
Fig. 2. Energies of collective excitations (E) and 4dbinding energies (EF-E4d) vs the corresponding metal.
n: upper (curve labeled la) and lower edge (lb) of the
4d band; O: measured energies E of collective oscillations (2); × : plasmon energies E calculated within the
homogeneous electron gas approximation (3). Lines
are guides to the eye, solid lines are drawn to show the
formal correspondence to the no crossing rule [21].
Vol. 65, No. 5
PLASMONS IN Pd, Ag, Cd, In, Sn AND Sb
383
Table 2. Measured dispersion coefficients ~expL for k <<.0.5A -l, ~¢xpHfor k >>.0.5A-l, their difference
A0~: O~exp,H--~exp.L and the corresponding theorettcal values CtRVAcalculated within the random phase approximation
=
Metal
Ctexp,L
Ag
0•39 _ 0.05
1.01
0•40 + 0.09
0•835
0.37 _ 0.03
0.93
0.46 _ 0.02
0.34 _ 0.04
0.52
0.40
0.66
0.54 _ 0.05
0.51 _ 0.05
Cd
In
Sn
Sb
0~exp,H
+ 0.09
_ 0.05
_ 0.05
_ 0.02
observed if the loss were indeed due to a collective
excitation of the free 5s electrons• However no dispersion of the 7.2eV loss in Pd is found in the
0 ~< k ~ 0.9 A - ' regime (see Fig. 3).
In the low wave vector region (0 ~< k ~< 0 . 5 A - ' )
the plasmon dispersion both in Ag (7•8 eV plasmon),
Cd and In follows the formula
~p(k
-+ 0)
=
h
Ogp(0) --1- m ~tl~Ak2'
(1)
CtRpA: = (3/5) (Er/fioJp) (dispersion coefficient), Ee:
Fermi energy calculated within the random phase
approximation (RPA) [11] (see Table 2). At k
I
16
I
I
I
i
I
[
I
I
I
I
o Pd
/
oAg
ACd
• In
,/~/j
14
/
0/
(this work)
[4]
(this work)
[16]
(this work)
[17]
[6]
[7]
/
,'4
A~
O~RpA
0.62
0•37
0.56
0.40
0.18
0.41
0
0.42
0.44
0.5 A-~ the slope of the dispersion curve changes drastically in Ag and Cd and less pronounced in In (Fig.
3). Therefore we have performed additional least
square fits leading to increased dispersion coefficients
aexp,H for k > 0.5A -l (see Table 2).
The difference ~exp,Z--~texp,Ldecreases on going
from Ag to In and completely vanishes in Sb [7] possibly correlating with a decreasing influence of the
4d-electrons.
Deviations from quadratic plasmon dispersion at
k ~ 0.5 A -l are also found for example in AI [12] and
Be [13] and hence are not restricted to 4dometals. A
detailed theoretical investigation of these experimental facts is still missing [14].
The EELS data presented in this work clearly
show a correlation of 4d-binding energies and 5spplasmon excitations on going from Ag to Sb. In Pd the
7.2eV loss is not caused by 5s electrons since no
plasmon dispersion was observable.
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i/
iv"
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PLASMONS IN Pd, Ag, Cd, In, Sn AND Sb
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