Phys. kondens. Materie 8, 80--86 (1968)

R e f r a c t i v e I n d e x a n d D i s p e r s i o n o f t h e E u r o p i u m - C h a l c o g e n i d e s

P. WACI~TER Laboratorium fiir Festk6rperphysik ETH, Ziirich/Switzerland

Received July 17, 1968

The refractive index of the Europium-Chalcogenides has been measured as a function of wavelength, temperature and magnetic field and compared with dispersion theory. The refractive index increases from EuO to EuTe and with decreasing temperature. Attributing different oscillator strengths to the various substances, classical dispersion theory can account for the observed changes in the refractive index. The optical and static dielectric constant, the l~eststrahlen wavelength and the compressibility have been computed.

L'indice de r6fraetion des ehalcog6nures d'Europium a 6t6 mesur6 en fonction de la longueur d'onde, de la temp6rature et du champ magn6tique, puis compar6 s la th6orie de la dispersion. L'indice de r6fraction augmente de EuO & EuTe et la temp6rature diminuant. En attribuant des forces d'oseillateurs distinctes aux diff6rentes substances, la th6orie classique de la dispersion rend compte des variations observ6es de l'indice de r6fraction. Les constantes di61ectriques optiques et statiques, la longueur d'onde de la rais r6siduelle et la compressi- bilit6 ont 6t6 calcul6es.

Es wurde der Brechungsindex der Europium-Chalkogenide in Abhi~ngigkeit yon der Wellen- lange, der Temperatur and des Magnetfeldes gemessen. Der Brechungsindex nimmt yore EuO zum EuTe zu und ebenfalls mit abnehmender Temperatur. Durch Annahme verschiedener Oszillator-St~rker~ f i it die Europium-Chalkogenide kann man die beobachteten _~nderungen im Brechungsindex mit der klassischen Dispersionstheorie erklaren. Die optische und die statische Dielektrizitatskonstante, die Reststrahlen Wellenliinge und die Kompressibilit~t wurden aus den Messungen bestimmt.

1. Introduction

Since the discovery of the Europium-Chalcogenides as ferromagnetic semi- conductors much effort has been made to evaluate the optical properties of these substances. So far however only measurements to determine the absorption co- efficient or the absorption edge on single crystals, evaporated layers and powders have been reported [1, 2, 3, 4]. To get fur ther information about the electronic transitions it is necessary to investigate another independent optical constant such as, for example, the refractive index in the wavelength range of good trans- parency. I t can be hoped tha t an application of the well known dispersion theory, using the interrelation of the optical constants, will give a bet ter unders tanding and a check of the selfconsistency of the experimental results. The anomalous shift of the absorption edge towards longer wavelengths [1, 2, 3] in the temper- ature range of magnetic ordering is expected to manifest itself also in a change of the refractive index.

2. Method of Measurement

From the m a n y methods to determine the refractive index of a substance the one using a prism yields best results. We have therefore prepared small prisms f rom single crystals with face areas of about 2 x 2 m m and various refractive

Refractive Index and Dispersion of the Europium-Chalcogenides 81

angles. The flatness of the two faces and the refractive angle have been determined by reflection of a laser beam. This method yields a precision in the prism angle of some seconds. A nearly parallel beam of monochromatic light passed through the prisms and the refracted beam was detected by photo-electric means on a large goniometer calibrated in seconds. The laws of refraction for various angles of incidence including the one for minimal deflection were found to hold precisely. For convenience of the measurement, however, the prisms were arranged in such a way that the incident beam was perpendicular to the opposite face. In this case the angle of incidence is equal to the refractive angle of the prism. The prisms were mounted in an atmosphere of lie-exchange gas in a variable temper- ature cryostat which could be brought between the poles of an electromagnet.

3. Experimental Results

The refractive index of the Europium-Chalcogenides is plotted in Fig. 1 as function of the wavelength at room temperature. The refractive index was mea- sured with a precision of • 0.006, which corresponds approximately to the size of the dots in the figures. The arrows indicate the wavelength of the absorption edge which is less steep for EuO than for the other Chalcogenides. This is probably due to a lack in stoichiometry, which is also demonstrated in a smaller dn/d2 for EuO.

2,4

2~

2,2

0,5

t 2,8

2,7

.~ 2,6

2,5

\ \

\ .

~ ~

\ , . !~ .%\ . . . . . . .

Energy Gap Eu~O O~o

i i I i

1,0 1,5 2,0 2~5~ Wavelength - w

Fig. 1. Refractive index of the Europium-Chalcogenides at 300~

The temperature dependence of the refractive index has been measured for wavelengths near the respective absorption edges. As seen in Fig. 2, the refractive index increases nearly linearly in the paramagnetie region with decreasing temper- ature for all substances. When magnetic dusters form as short range order commences, the refractive index increases sharply with decreasing temperature and reaches a constant level. Under the influence of a magnetic field measure-

6 Phys. kondens. Materie, Bd. 8

82 P. WAoHT~:

ments in the whole temperature range were possible, while without field good results for the ferromagnets were obtained only above the Curie temperatures. At this temperature ferromagnetic domains come into existence [5] the dimensions of which are smaller than 1 ~ [5, 6] and thus give rise to a strong scattering of light [7, 8]. In the case of EuSe, which is antiferromagnetie between about 3.5 ~ and 4.6~ light scattering is weak because, the domains have dimensions of about 100 ~ [5] thus beeing much larger than the wavelength of light. The curves

I 2 , 6 I

2 , 5

g

2,4

2 ,3

"- --,-- H = 14,5 kOe

" ' --o-- H = 0

EuSe k = 0,66 F

~:"c,-.~. \ ..

�9 "~"-~--_=u,_ EuS X = O,75 F

~. ~'.,.. ~ . "- . EuO X : h40,u.

t I I I I , - . t -

O 20 40 60 80 I00 300~ T e m p e r a t u r e ~-

Fig. 2. Refractive index of the Europium-Chalcogenides for wavelengths near the absorption edge

0,26 -

l 0,22 ~ " " ' ' ' " - - . .

o.,.....~ ~ o.~ - - - o ~ ~ EuS S,6"K H= 14,5 kOe OJ8

0 ~ o EuTe 30()*K H= 0

0,14 I } I I I o o~ ip i,5 2,0 P_~

),'=

Fig. 3. Dispersion relation of EuS and EuTe at 300~ and 6.6~

for the field-flee case of the refractive index below the Curie temperature of the ferromagnets have been inferred from the similarity between the change of the refractive index and the shift of the absorption edge with temperature given elsewhere [2]. The refractive index of EuSe at 4.2 ~ shows as a function of magnet- ic field an intermediate range of partial saturation, due to the well known change in the spin structure.

The refractive index of EuTe does not change on cooling through the NSel temperature nor does the absorption edge show any appreciable shift in this

Refractive Index and Dispersion of the Europium-Chalcogenides 83

temperature range. Light scattering is also weak because the antiferromagnetic domain size is similar to those in EuSe [5].

In t~ig. 3 the refractive index of EuTe and EuS has been plotted in a manner to allow comparison with the classical dispersion relation

1 B n~----~]- = A -- ~ . (I)

Within the entire wavelength range covered by the measurement EuTe is seen to follow closeiy a linear behavior, whereas EuS shows some deviations at longer wavelengths. The refractive indices of EuS and EuSe (not shown) at temperatures both above and below the magnetic transition points follow a dispersion law, as given above. The extrapolated index for infinite wavelenghts is the same in the paramagnetie and in the magnetically ordered state.

4. Discussion and Comparison with Dispersion Theory

Contrary to expectations the refractive index increases from EuO to EuTe. (The refractive index for high purity EuSe and EuTe will be given elsewhere [9].) Moss [10] has derived an empirical relation connecting the refractive index of a substance to the energy gap:

n 4 EQ = constant. (2)

This relation is found to hold for most elementary and compound semiconductors. I t is, however, violated by the Europium-Chalcogenides, assuming that the energy gaps determined by the absorption edge are those given in the Table. The temper- ature dependence of the refractive index, d n / d T , in the paramagnetie region is found to be negative and the temperature dependence of the energy gap is also negative. This constitutes another contradiction to the above stated law. In the temperature range of magnetic ordering, however, the energy gap decreases strongly with decreasing temperature [1, 2, 3] while the refractive index continues to increase in accordance with the empirical relation.

To discuss this behavior we have to indentify the absorption peaks which are responsible for the dispersion of the refractive index. At the absorption edge the absorption constant K is less than 100 cm -1 and i t decreases with increasing wavelength. The absorption index k,

K2 k - - 4Jr (3)

is therefore of the order 10 -a and can be neglected in comparison with n. Under this assumption classical dispersion ~heory yields the following result for wavelengths larger than the resonance wavelength )Lo:

n 2 - - 1 = Ne2] 1 m ~ 0 " ~ o - ~ " ( 4 )

Here N is the number of molecules/m s, / is the oscillator strength and w0 the resonance frequency in the case of a single resonance line. I t can be seen from Fig. 3 tha t the measured dispersion of n is in good agreement with Eq. (4) and it is therefore possible to extrapolate the refractive index to infinite wavelengths. In the Table the square of this refractive index, i.e. the infrared dielectric con- stant, is given. From this optical dielectric constant, the resonance frequency

6*

84 P. WAc~T~:

of a classical oscillator can be derived, according to the relation

/ (n~o - 1) eom ~ o ~ - N e ~ ( 5 )

I f the absorption cannot be assumed to take place in a single resonance line, the left hand side of Eq. (5) must be replaced by ~ ]z/w~. Usually the longest wave-

z length absorption peak can by itself account for the infrared dielectric constant due to the fact that co~ stands in the denominator in Eq. (5). Considering all the absorption centered in a single line, the resonance wavelength ~0 of this peak has been calculated in the Table, assuming an oscillator strength of unity.

%

15

10

with potorize r

Q.

g~

i I I

2 5 4 Photon Energy

Fig. 4. Refleetivity of EuSe at 300~

with mirror ~:~

I !

5 6 hv

eY

The short wavelength refleetivity spectrum of the Europium-Chalcogenides single crystals has been measured recently. (As an example the reflectivity of EuSe is shown in Fig. 4. A more detailed description of the method of measurement has been given elsewhere [8].) For EuTe the longest wavelength reflectivity peak has been found at 2,12 eV or 5820 A. Considering the fact tha t ,;to is the resonance wavelength for the optical conductivity 2nkco, it can be shown that the corre- sponding maximum in reflectivity occurs at shorter wavelengths than 20 [10]. For EuTe, therefore, it is evident that the absorption with a resonance wavelength ~0 ~ 6400 A and oscillator strength about 1 gives a reflectivity peak at about 5800 A. In EuO, EuS and EuSe, however, the resonance wavelength of a single absorption line with oscillator strength 1 is found at much shorter wavelengths than the longest wavelength reflectivity peak given in the Table. Assuming an absorption spectrum consisting of two resonance lines at ~01 and 20e and using the measured wavelengths (8220 A and 2630 A) of the main peaks for EuO as determined from the reflectivity spectrum, the optical dielectric constant can be obtained only ff the oscillator strength of the long wavelength peak is about ten times smaller than that of the short wavelength peak, assuming the sum of the oscillator strengths to be about unity. Agreement with the optical dielectric

Refractive Index and Dispersion of the Europium-Chalcogenides 85

constant can also be found by taking just one resonance line at the wavelength calculated from the long wavelength reflectivity peak and adjusting the oscillator strength of the transition as given in the Table. Thus EuTe would have an os- cillator strength of about 1 and EuO of about 0.15. These values should not be taken as absolute quantities but rather as an indication of the relative change of [.

I t can be seen from Fig. 3 that, for EuS as an example, the optical dielectric constant is the same at room temperature and below the Curie point. Therefore, according to Eq. (5), [/co~ remains constant. Transmission measurements have shown that the absorption edge moves to longer wavelengths when the substance is cooled below the magnetic ordering temperature [1, 2, 3]. Thus, to0 decreases and, in order to fulfill the above stated condition, the oscillator strength must decrease also. Making use of this change in the oscillator strength and inserting this value in Eq. (4) together with the shift in the resonance frequency, we can compute the change in the refractive index for any frequency o0. Since all the values on the right hand side of Eq. (4) are given by experiment the change of the refractive index for EuO between a temperature of about 100 ~ and 4.2 ~ is found to be 0.18, which agrees fairly well with the measured An shown in Fig. 2. For EuS and EuSe the shift of the absorption edge with temperature is smaller and the change in refractive index is correspondingly smaller. For EuTe no shift of the absorption edge is found, in agreement with no change in n.

In the paramagnetic range the absorption edge shifts towards shorter wave- lengths with decreasing temperature. However, the refractive index increases slightly. We must assume, therefore, according to Eq. (4), tha t the resonance frequency w0 remains constant or becomes even somewhat smaller. On the other hand the long wavelength side of the absorption peak becomes steeper on cooling, in accordance with decreasing phonon interaction.

The optical dielectric constant shown in the Table would also be the static dielectric constant if there were no more long wavelength absorption peaks. For the very ionic Europium-Chalcogenides, however, strong geststrahlen absorption bands must be expected. For EuO the Reststrahlen band has been found at a wavelength of 40 [~ with a peak reflectivity of more than 90% [11]. Assuming that the coupling constant of the Europium-Chalcogenides remains about the same, the geststrahlen wavelengths of the other substances can be calculated from the experimental value of EuO according to Eq. (6).

~est ~ #1/2 , (6)

where ~ is the reduced mass of the oscillating system. These reduced masses and the computed Reststrahlen wavelengths are given in the Table.

SZIGWTTI [12] has derived a relation which gives the increase of the dielectric constant due to the geststrahlen absorption,

Here N is the number of absorbing molecules/m 3, e* an effective charge, [ the oscillator strength and # the reduced mass. Assuming an effective charge equal to the charge of one electron and an oscillator strength of 1 the static dielectric constants have been computed and compiled in the Table.

86 R. W&OHTER: Refractive Index and Dispersion of the Europium-Chalcogenides

EuO

EuS

EuSe

EuTe

Tc *TN [~

Table. Observed and calculated optical data/or the Eum

n~ N~ 2, 10 ~s ~o~t. [m ~]

3,85

EG [m~]

69

16,3

*4,6

*9,8

~,ma• Refl. [mt~]

1105 825

750 650

690 608

620 I 582

4,9

5,3

5,92

2,95

1,89

1,69

1,42

(~q---- 1 ) ] ] /~ 10-~s (ko from] [kg]

[m~] !Zefl.)

I

340 0,15 2,42

500 0,52 4,38

550 0,74 8,7

640 1,14 11,5

)ium- Chalcogenides

~Rest gstat

] u 10-6 I :d0-* calc. ] obs.

40

54

76

88

9,8

10,2

10,5

11,2

1,4

1,8

2,0

2,2

1,0 [14] 1,0 [15] 4,3 [16]

4,79 [17]

I n ionic mate r ia l s t he connect ion be tween the compressibi l i ty , the opt ica l and the s ta t ic dielectr ic cons tan t is given, according to SZIG~TTI [13], b y

1 ~ N ( ~ , + 2 /

where R is the nex t neares t ne ighbour distance. Using this formula , the com- pressibi l i t ies of the Europium-Chalcogenides have been de te rmined and compared wi th the expe r imen ta l ly known values [14, 15, 16, 17]. Considering the large sca t te r ing in the exper imenta l resul ts and the m a n y assumpt ions in our calculat ion, the agreement is sa t i s fac tory .

The author is obliged to ProL G. Busch director of the Laboratory for Solid State Physics at ETH for his continued encouragement and to the ,,Schweizerischer Nationalfonds zur F6r- derung der wissenschaftIichen Forschung" and to the ,,Verein zur FSrderung der FestkSrper- physik an der ETH" for financial support. The crystals were supplied by Dr. O. VOGT of this laboratory and the measurements were carried out by Mr. H. P. STA~B to whom the author expresses his gratitude.

R e l e r e n e e s 1. BvscH, G., P. JvNov, and P. WAe~TEa: Phys. Letters 12, 11 (1964). 2. -- , and P. WACETnR: Phys. kondens. Materie 5, 232 (1966). 3. A~OYLE, B. E., J. C. SUITS, and M. J. FR]~IsE~: Phys. Rev. Letters 15, 822 (1965). 4. METHFESSEL, S.: Z. angew. Phys. 18, 414 (1965). 5. WACHWV, g, P. : Phys. kondens. Materie 7, 1 (1968). 6. K~EEn, G., and W. ZINN: Arbeitsgemeinschaft Magnetismus, Miinster 1968. 7. SUITS, J. C. : J. appl. Phys. 38, 1498 (1967). 8. Busca, G., and P. WAe~WEg: Arbeitsgemeinschaft Magnetismus, Miinster 1968, in print

Z. angew. Phys. 9. -- , and R. VERREAVLT: tO be published.

10. Moss, T. S. : Optical properties of semiconductors. London: Butterworth 1959. l l . BALTES, H. : Private communication, Labor ffir FestkSrperphysik ETH Ziirich. 12. SZmXTTI, B.: Trans. Faraday Soc. 45, 155 (1949). 13. -- Proc. Roy. Soc. A 204, 51 (1950). 14. SOKOLOVA, G. K. , K. M. DEMCHUK, K. P. I~ADIONOV, and A. A. S~OKm~LOV: Soviet

Phys. JETP (USA) 22, 317 (1966). 15. McWm~N, D.B., P. C. SVOE~S, and G. Jv~).: Phys. Rev. 143/11, 385 (1966). 16. STeVENSOn, R., and M. C. Ro~IxSON: Canad. J. Phys. 43, 1744 (1965). 17. -- Canad. J. Phys. 44, 281 (1966).

Dr. PETER WACkiER Laboratorium fiir FestkSrperlohysik der ETH Ctt-8006 Ziirich, Gloriastr. 35