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Interaction of d-electron excitations and plasmons in Pd, Ag, Cd, In, Sn and Sb
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.
REFERENCES
/}/o
i/
iv" > 12
t"
1. 2.
3 10
./"
3.
-,/
,!/ 0.2
4.
t,,,,,,,
0.4 0.6 K2/ ~-2
0.8 ,,
1.0
~.~g. 3• Measured energies of collective oscillations vs
5. 6. 7. 8. 9. 10.
E. Zaremba & K. Sturm, Phys. Rev. Lett. 55, 750 (1985). V.D. Gorobchenko, M.V. Zharnikov, E.G. Maksimov & S.N. Rashkeev, Soy. Phys. JETP 61, 398 (1985). H.J. H6hberger, A. Otto & E. Petri, Solid State Commun. 16, 175 (1975). A. Otto & E. Petri, Solid State Commun. 20, 823 (1976). N.E. Christensen, Phys. Rev. B14, 3446 (1976). K. Zeppenfeld, Z. Phys. 223, 32 (1969). B. Bartning, Opt. Comm. 4, 404 (1972). R.C. Vehse & E.T. Arakawa, Phys. Rev. B1, 517 (1970). M. Nishijima, M. Jo, Y. Kuwahara & M. Onchi, Solid State Commun. 58, 75 (1986). J.J. Vuillemin & M.G. Priestley, Phys. Rev. Lett. 14, 307 (1965).
384 11. 12. 13. 14. 15. 16.
PLASMONS IN Pd, Ag, Cd, In, Sn AND Sb D. Pines, Elementary Excitations in Solids, (Edited by W.A. Benjamin), New York (1964). J. Eickmans, H. M611er & A. Otto, Z. Phys. B46, 99 (1982). W. Dieckmann, J. Eickmans & A. Otto, Z. Phys. B65, 39 (1986). K. Sturm, Adv. Phys. 31, 1 (1982). F.P. Netzer & M.M. Gomati, Surf Sci. 124, 26 (1983). T. Aiyama & K. Yada, J. Phys. Soc. Japan 38,
17. 18. 19. 20. 21.
Vol. 65, No. 5
1357 (1974). K.J. Krane, J. Phys. FS, 2133 (1978). R.A. Pollak, S. Kowalczyk, k Ley & D.A. Shirley, Phys. Rev. Lett. 29, 274 (1972). O. Sueoka, J. Phys. Soc. Japan 20, 2203 (1965). P. Bayat-Mokhtari, S.M. Barlow & T.E. Gallon, Surf. Sci. 83, 131 (1979). G. Burns, Introduction to Group Theory with Applications, Academic Press (1977).
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.
REFERENCES
/}/o
i/
iv" > 12
t"
1. 2.
3 10
./"
3.
-,/
,!/ 0.2
4.
t,,,,,,,
0.4 0.6 K2/ ~-2
0.8 ,,
1.0
~.~g. 3• Measured energies of collective oscillations vs
5. 6. 7. 8. 9. 10.
E. Zaremba & K. Sturm, Phys. Rev. Lett. 55, 750 (1985). V.D. Gorobchenko, M.V. Zharnikov, E.G. Maksimov & S.N. Rashkeev, Soy. Phys. JETP 61, 398 (1985). H.J. H6hberger, A. Otto & E. Petri, Solid State Commun. 16, 175 (1975). A. Otto & E. Petri, Solid State Commun. 20, 823 (1976). N.E. Christensen, Phys. Rev. B14, 3446 (1976). K. Zeppenfeld, Z. Phys. 223, 32 (1969). B. Bartning, Opt. Comm. 4, 404 (1972). R.C. Vehse & E.T. Arakawa, Phys. Rev. B1, 517 (1970). M. Nishijima, M. Jo, Y. Kuwahara & M. Onchi, Solid State Commun. 58, 75 (1986). J.J. Vuillemin & M.G. Priestley, Phys. Rev. Lett. 14, 307 (1965).
384 11. 12. 13. 14. 15. 16.
PLASMONS IN Pd, Ag, Cd, In, Sn AND Sb D. Pines, Elementary Excitations in Solids, (Edited by W.A. Benjamin), New York (1964). J. Eickmans, H. M611er & A. Otto, Z. Phys. B46, 99 (1982). W. Dieckmann, J. Eickmans & A. Otto, Z. Phys. B65, 39 (1986). K. Sturm, Adv. Phys. 31, 1 (1982). F.P. Netzer & M.M. Gomati, Surf Sci. 124, 26 (1983). T. Aiyama & K. Yada, J. Phys. Soc. Japan 38,
17. 18. 19. 20. 21.
Vol. 65, No. 5
1357 (1974). K.J. Krane, J. Phys. FS, 2133 (1978). R.A. Pollak, S. Kowalczyk, k Ley & D.A. Shirley, Phys. Rev. Lett. 29, 274 (1972). O. Sueoka, J. Phys. Soc. Japan 20, 2203 (1965). P. Bayat-Mokhtari, S.M. Barlow & T.E. Gallon, Surf. Sci. 83, 131 (1979). G. Burns, Introduction to Group Theory with Applications, Academic Press (1977).