Optical interband structure and the low energy plasmon in ScH2

Solid State Communication, Vol. 25, pp. 201—203, 1978.

Pergamon Press.

Printed in Great Britain

OPTICAL INTERBAND STRUCTURE AND THE LOW ENERGY PLASMON IN ScH~ 3. H. Weaver Synchrotron Radiation Center, University o~Wisconsin-Madison Stoughton, Wisconsin 53589 U.S. A. R. Rosei** and D. T. Peterson Ames Laboratory, United States Energy Research and Development Administration Ames, Iowa 50011 U.S.A. (Received 1 October 1977 by G. F. Bassani)

The optical absorptivity of ScH

2 has been measured at 4.2 K between 0.1 and 4.4 eV, and the dielectric functions determined through Kramere-Kronig anniysis. The low energy optical features are shown to be dominated by free-electron-like absorption and a screened plasmon at 1.47 eV. The presence of the low energy plasmon explains the deep blue appearance in ScH2 and the lanthsnide dihydrides. Interband absorption is shown to be dominant above about 1.5 eV.

The transition metal hydrides have been studied1.in A one form or another since at least the large fraction of the published literstore 1890’s reflects the Interest in hydride crystal struc-

and the lowering in energy of those metal states which In have s-character at the thishigh paper, we present the hydrogen results ofsite. optical studies of ScH 2, the first dihydride studied by such techniques. To interpret the optical data, we present a model for the electronic structure of ScH2 which emphasizes free—electron-like behavior at low energy, and significant interband absorption above -1.5 eV. The occurrence a low energy at 1.47 eV accounts for theofwell-known, butplasmon previously unexplained, dark-grey to dark-blue color of the Group BIB and lanthanide dihydrides. The optical absorptivity (A = 1-R where R Is the reflectivity) was measured between 0. 1 and 4.4 eV at near-normal Incidence and 4.2 K using a technique which has been discussed In detail elsewhere’°. Sample preparation involved conventlonal high temperature charging of Sc under

tures, their metallurgical properties, hydrogen embrittlement, superconductivity, and potential uses for hydrogen storage devices. Much less attention has been devoted to their electronic structures, with the exception of electronic apecific heat and magnetic susceptibi]ity studies. 2 Recent (de Haas advances van Alphen include studies those of of mixed Griessen phaseetPdH) al. and Eastman et al.3 (photoelectron spectroscopy, PES, of mixed phase PdH). Select hydrides have been examined by soft x-ray emission spectroscopy4’6 and optical spectroscopy6. Each of these efforts has emphasized the sub-monohydrides, and, to date, there have been no reported investigations of the metal di- or higher- hydrides (e.g. ScH 2, TiH2 lanthanide7 diof nearly or trihydrides), stoichiometric except for PES studies ThH 2 and ThH4H15. sized the Justsub-monohydrides, as the experimentalists so toohave haveemphathe theorists. Several interesting calculations of the Pd-H system have recently appeared8, but only Switendick9 has reported the electronic structure

an atmosphere analysis of the samples of high purity showed H2, them andto subsequent be of ScH151 stoichiometry which is within 1. Sample the compreppositionwill aration range be reported discussedfor later ScH2 in conjunction with reflectance and thermoreflectance studies of ScH 11. 2,The YH2, optical LaH2, absorptLvity and Lull2 of ScH 2 is shown in Fig. 1. Between 0.1 and about 1 eV, A increases steadily but without structure. Near 1 eV, the slope of the absorptivity changes dramatically, and A climbs sharply to a maximum at 1.56 eV. A

for higher hydrides. Those calculations have shown that the formation of the hydrides involves substantial metal- hydrogen hybridization, the development of a metal-hydrogen bonding band, *

**

Work supported in part by the National Science Foundation under Grant No. DMB- 7415089 and in part by the U. S. Energy Research and Development Administration, Division of Physical Research. Permanent address, Istituto di Fisica, Universita degli Studi, Roma, Italy. 201

202

OPTICAL INTERBAND STRUCTURE

comparison of the ScH

2 results of Fig. 1-2 shows 1 withhow the fundamentally analogous spectra different for hop the hydride Sc metalIs from the metal. In particular, low energy optical structures are observed for Sc for both polarizations below about 1 eV, and these can be Interpreted in terms of strong and structured Interband absorption, These features have no counterparts In Sell2 . The dielectric function for a free electron gas can be described by the Drude model as 2 ~ (u)=t ~ i/ T) where -r is the relaxation time (or broadening parameter), c~Is the static dielectric fUZiction, and u is the 2/m, plasma there frequency being N given electrons by of = Ne m per unit volume. In the Drude effective mass model, the reflectivity is large and structureless for ii u <~ u,~,then drops sharply to a minimum; ~ 2 Is large and positive, but decreases monoton-

Vol. 25, No. 4

ttons of analysis Kronig the absorptlvity of the data outside of Fig. the1. range Extrapolaof the measurements were based on the free electron model (below 0.1 eV) and unpublished vacuum ultraviolet data for ScH 2. The absorption coefficient of Sc metal was used to extend the energy range from - 30 to about 250 eV, and a power law was introduced at higher energy. In order to analytically examine the range of validity of the Drude model when applied to SCH2, we have used the dielectric function results of cedure FIg. 2 to discussed plot ~1 by vs.Dletz w -2, et al.Adopting 13 in their theanalproysls of the optical properties of cubic Na0 65W03, we found the plasma frequency to be 4. 1 eV and the static ation timedielectric was subsequently function determined to be 5.6. from The relaxa plot of t 2 ) to be 8. 7 eV- 1 2u . From vs. those E1 (oranalytic c2w vs. examinations w of the dielectric function, It was clear that deviation from the Drude model occurred above 1. 15 eV, as

Ically to zero well above fiwp; a 1 is large and negative, but decreases with frequency and passes through zero at the plasma frequency. 1.0

I

shown quaiitatively by the dashed lines in Fig. 2, and the Interband absorption becomes dominant above about 1.5 eV. C

I

0.8

I

z

£2/10

I

2.~5

0

z >H

‘—1

0.6

_________

I-

________

____

_________

ScH2 4.2K

acc

o 0.4

w

U,

a)

I

ScH2

~,

6-4•

-10.70

~“~NLJ067

0.2

.

£1/10

—

6o

I

I

2

I

3

I

4

5

PHOTON ENERGY Cay) 0

I

0

Fig. 1.

2 3 4 PHOTON ENERGY(eV) The optical absorptivity of ScH2 at 4.2 K. The sharp rise in A near 1.4 eV is inter— preted as being associated with a screened

plasmon. The absorptlvity spectrum of ScH2 shown In Fig. 1 qualitatively resembles that of a free electron gas with an empirical plasma frequency near 1.36 eV (where dA/d w Is a maximum). At higher energies, however, features are clearly seen which have no analog in the Drude model, and these can be interpreted instead in terms of interband absorption. The overlapping character of the Interband and Intraband absorption has the effect of distorting or screening the plasmon assodated with the lrtraband absorption.

The dielectric functions for ScH2 are shown in Fig. 2 and were determined through a Kramers—

Fig. 2.

The real and imaginary parts of the diel— ectric function for ScH2. The behavior below - 1 eV can be approximated by a Drude model. Above — 1.5 eV, interband absorption becomes dominant.

An empirical plasmon frequency can be determined from the absorptivlty spectrum of FIg. 1, but a better measure can be obtained by using the results of Fig. 2 to calculate the volume loss function as defined by Im (- l/~). The strong resonance feature shown In Fig. 3 at 1.47 eV can be identified as a volume plasmon. The dashed curve of Fig. 3 was obtained by subtracting an interband background, and the pluses reflect the shape of a Lorentzlan centered at 1.47 eV with a full-width-at-half-maximum of I’ = 0.21 eV. The agreement between the Lorentzlan lineshape and the experimental lineshape is remarkable in view of the close proximity, and hence interaction, of

]~

Vol. 25, No. 4 0.6

u

OPTICAL INTERBAND STRUCTURE

the plasmon and the interband structures. In order to interpret the interband structures and relate them to optical absorption occurring at well-defined parts of the ScH 2 Brillouin zone, it

I

I

eV

Sc H

0.4

-

-

3

2 0.21eV (FWHM)

F~

~- .~

/ \ t I

-

on the bands calculated along high symmetry lines

t

-

~ I

0.2

-

-

/

-~

-A

-

-

// +, —

C

— —

~

~

I’o

‘-,_~

—

20

-

PHOTON ENERGY (eV) Fig. 3.

a reasonable band structure calculation of the bands of Sell2. Such calculations have not yet been performed. Switendick has, however, reported the bands of YH~, and examination of those bands shows that the onset of interband structures (based

Loss function for ScH2, Im (—1/F). The solid curve is the experimental lineshape. The dashed curve shows the approximate intraband contribution, and the +‘s represent a Lorentzian with FWHM of 0.21 eV.

only) would occur at approximately 1.8 eV. Interpolation would betonecessary the experimental to have, results at the bare for minimum, ScH2 (Fig. 2) Indicates that there Is reasonable agreement between the data for ScH2 and the prelimmary calculations for YH2. Unfortunately, an unambiguous interpretation of the interband struclures In ScH2 cannot be made at this point, and we will not attempt such speculation now. Instead, we urge that further calculations be performed following the model proposed by Switendick. In the meantime, It seems safe to conclude that, based on the results presented here, the low energy optical absorption of the dihydrides is dominated by freeelectron-like absorption, and that, unlike what is found from optical studies of the transition metals, interbandabsorptionplaysasecondaryroleatlow energy. Acknowledgement— The continued support of E. M. Rowe and D. W. Lynch Is gratefully acknowledged.

Expert technical assistance was generously provided by H. H. Baker and A. D. Johnson. 1. 2. 3.

4.

REFERENCES For a general review of transition metal hydrides, see MUELLER, W. M., BLACKLEDGE, J. P., and LIBOWITZ, G. G., Metal Hydrides (Academic Press, 1968). GRIESSEN, R., VENEMA, W. J., JACOBS, J. K., MANCHESTER, F. D., and DE RIBAUPIERBE, 3. Phys. F. (to be published). EASTMAN, D. E., CASKION, J. K., and SWITENDICK, A. C., Phys. Rev. Lett. 27, 35 (1971); see also ANTONANGELI, F., BALZAROTTI, A., BIANCONI, A., and PERFETTI, P., Solid State Comm. 21, 201 (1977). FUKAI, Y., KANZAMA, S., TANAKA, K., and MATSUMOKO, Solid State Comm. 19, 507 (1976).

5. 6.

7. 8.

9. 10. 11. 12. 13.

GILBERG, E., Phys. Stat. Sol. (b)69, 477 (1975). WEAVER, J. H. and PETERSON, D. T., Phys. Left. ~, 433 (1977). Absorptlvity and thermoreflectance measurements have been performed for the ordered and disordered phases of TalL,~ and NbH~(x
203