UO2 : A5f -MAGNETIC SEMICONDUCTOR

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UO2 : A5f -MAGNETIC SEMICONDUCTOR

J. Schoenes

To cite this version:

J. Schoenes. UO2 : A5f -MAGNETIC SEMICONDUCTOR. Journal de Physique Colloques, 1980, 41

(C5), pp.C5-31-C5-38. �10.1051/jphyscol:1980506�. �jpa-00219941�

JOURNAL DE PHYSIQUE Colloque C5, supplbment au n O 6 , Tome 41, juin 1980, page CS-3 1

U02 : AS?-MAGNETIC SEMICONDUCTOR J. Schoenes

Laboratoriwn fUr Festkijrperphysik, ETH, 8093 ZGrich, Switzerland.

RSsum6.- Nous presentons une revue critique de resultats spectroscopiques rQcents et en partie non publies de U02. Les rgsultats experimentaux sont compar6s S des calculs du type Haber-Born et Zi des modsles mol6culaires. La controverse sur la structure electronique de U02 est resolue et la grande similitude entre U02 et les chalcogenures d'europium est dQmontrQe.

Par contre, d'importantes differences apparaissent entre ces composQs 4f et 5f pour les transitions intra f et les excitations S plusieurs phonons.

Abstract.- We present a critical review of recent and partly unpublished spectros- copic data of U02. The experimental results are compared with Haber-Born and molecular cluster calculations. The long existing controversy about the electronic

structure of UO is solved and the strong similarities to the europium chalcogenides are demonstrate8.

On the other hand relevant differences between these 4f and 5f compounds are shown to exist for intra £-transitions and multiphonon excitations.

1. Introduction.- While the electronic structure of 3d and 4f magnetic semiconduc- tors has been widely discussed in the past /1/ rather little is known about 5f magnetic qpmiconductors. This is regretable since the 5f electrons bridge the degree of localiza- tion between 4f and 3d electrons. In fact the s'patial extent normalized to the typical interatomic distance of the 5f wave function lies in between the corresponding values for 4f and 3d materials /2/. Starting from the good knowledge of the strongly localized 4f electrons in the rare earths one can understand many of the electronic properties of actinide semiconductors. On the other hand all physical properties which are affected by crystal field effects will be markedly different from those of the 4f compounds and rather resemble the properties of transition element compounds.

The selection of simple magnetic actinide semiconductors is rather limited.

Monochalcogenides and monopnictides are generally metals or semimetals. From the dichalcogenides only the dioxides form cubic compounds. The radioactivity and the small availability of many of the actinide elements constitute a further handicap for the preparation and the investigation of many of the potential 5f magnetic semicon- ductors. Thus U02 holds a key position

within the 5f-magnetic semiconductors.

Nevertheless its electronic structure has been the subject of controversy for many years. Ackermann et a1./3/ reported the observation of an energy gap around 2eV on thin films. Veal and Lam /4/ using their XPS data interpreted this gap as transition from t,he highest occupied states namely the 5f states to a conduction band. The usual semiconductor gap between the bonding oxygen 2p band and the conduction band was then identifi.ed to occur at -6 eV in agreement with the gap found in Tho2 which has no 5f electron.

On the other hand Naegele et a1./5/

argued from reflectivity measurements that the 5f to conduction band'transition causes the absorption onset at 5 to 6 eV and that the Penn gap (main band to band transition) occurs at only 14 eV. Guided by this more recent work, various authors /6,7/ tried to interpret their own data within similar schemes. However, as we have pointed out recently /8/ the limited photon energy range ( 6 w 4 10 ev) and various interpreta- tional ;7roSlens 9el:e the assignments of Naegele et al. very unlikely. It is the aim of this article to clarify the electro- nic structure of U02 and to show the

striking similarities as well as some relevant differences to a well known class

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980506

JOURNAL DE _PHYSlQUE

of magnetic semiconductors, namely the europium monochalcogenides.

2.0ptical spectroscopy.- Figure 1 shows the near normal incidence reflectivity of UO

2 between 0.0025 and 13 eV (20-105000 cm-l)

.

Four different spectrometers were used to cover these nearly four orders of magnitude of photon energies /9/. The samples were either Ell] or [110] oriented single crys- tals which had been annealed for several hours at temperatures between 1700 and 2000 K in a vacuum of lom7 torr. This treat- ment was shown to reduce U02+x to U02 /lo/

and removes many of the damages introduced at the surface through the optical polishing.

Fig. 1 : The near normal incidence reflec- tivity of U02 at 300 P.

Figure 1 allows to distinguish three out of four regions corresponding to different kinds of optical excitations. On the low energy side we observe a large single oscillator reflecting the phonon absorption in an ionic compound with CaF2 structdre.

Above this one phonon absorption region t'here exists a multiphonon absorption region covering the range of very small reflectivity which is not perceptible in the logarithmic plot of figure 1.

Above 0.15 eV the reflectivity reaches again values above 10 % and shows weak structures. These structures are well resolved in a transmission experiment and

correspond to the excitation of electric dipole forbidden intra 5f-transitions.

Finally, above 2 eV the reflectivity increases strongly and shows a multitude of peaks. This is the fundamental absorption region of U02 on which we will concentrate now.

3. The fundamental absorption.- To discuss the optical properties of a material on a quantitative basis the dielectric function or the optical constants have to be known.

A commonly used method to reach this goal is the Kramers-Kronig analysis of the reflectivity spectrum. However, this method implies theoretically the knowledge of the reflectivity from zero to infinite frequen- cy or in practice at least over that fre- quency range which contributes markedly to the investigated optical excitations. It is evident from figure 1 that a reflectivity measurement extending only up to 10 eV /5/, where the reflectivity increases, misses an important part of the fundamental absorpticm.

Such a measurement should therefore not be used to check sum rules via a Kramers-Kronig relation. On the other hand, at 13 eV the reflectivity decreases strongly (Fig.1).

One can then tentatively extrapolate the spectrum to higher.energies according to a sequence of 1/w2 and l/w4 power laws. If the Kramers-Kronig transformation leads to a number of electrons participating at electronic transitions

in reasonable agreement with the electronic band structure the reduction of the data is selfconsistentand the extrapolation used may be justified. However, if neff is in disagreement with the electronic band structure either the reflectivity measure- ment omits relevant parts of the spectrum and/or the derive4 electronic structure is incorrect.

Figure 2 displays the optical cons:- tants n gnd k as deri&d from the Kramers- Kronig relation of the reflectivity spec- trum in figure 1 using an 1/w2 extrapolation

up to 42 eV and an 1/w4 extrapolation above this energy. We note a good agreement with the direct absorption measurements of Ackermann et a1./5/ supporting the extrapo-

lation as well as the reflectivity measure- ment ifself.

As discussed for and E~ /8/ also n(w) and k(w) are governed by two pairs of transitions. At lower energies n(w) displays two sharp peaks at 2.6 and 5.4 eV corres- ponding to the two smaller structures in k(w) at 3.1 and $ 5 . 8 eV, respectively. At higher energies we find the prominent peaks

in k(w) namely at 8.5 and 11.2 eV corres- ponding now to the two weaker structures in n(w) at 7.5 and 10.3 eV, respectively. Thus the two low energy transitions have rather small oscillator strength f but a large gradient af/aw and are assigned to f ⁺ d transitions.

J

2 4 6 8 10 12

Photon Energy [eV]

Fig. 2 : The optical constants of U02 at 300 K in the fundamental absorption region.

The two transitions at higher energies have large o$cillator strengths f but smaller gradients af/aw and are assigned to p ⁺ d transitions. The occurence of pairs of transitions reflects the crystal field splitting of the final d states which in the atomic notation are called t and e

29 9

states. Contrary to the case of the europium chalcogenides the t levels in U02 are

2 g

higher in energy than the e levels due to 9

the cubic

oh

surrounding of the uranium.

With this exception the gross features of the electronic structure of U02 are identi- cal to the onesof the europium chalcogenides

.

This becomes also evident if we compare the absorption coefficient K = 2kw/c of U02 and EuS /11/ for example (Fig.3).

Starting from the low energy side we observe in both compounds first a single maximum with typical values K in the order of lo5 cm-' and which corresponds to a f+d transition. At a little higher energy

-

^{4 e ~}

for EuS, 5.5 eV for U02

-

the absorption coefficient increases again due to the second f + d transition. At nearly the same energy we observe the onset of the p -+ d transitions which cover the rest of the spectrum in figure 3 and which lead to absorption coefficients in the order of 10 cm-I. (The smaller K value of EUS is probably due to scattering losses in the reflectivity measurements on polished samples at high energies.)

Photon Energy [eV]

Fig. 3 : Comparison of the absorption spectra of U02 and EuS.

An other difference between the EuS and UO absorption spectrum merits to be noted.

2

The low energy maximum of U02 is about twice as wide as the one of EuS and seems to consist of two structures separated by -1 eV. This'splitting has been attributed to the spin orbit splitting of the final

JOURNAL DE PHYSIQUE

state of the 5f2 + 5f16de transition /8/.

g

In fact the 5f1 free ion state splits into 2~5,2 and 2~7,2 and this splitting is much larger than the spin orbit splitting of the 4f 6 7 ( F

s

) final state in europium.

The results of this short discussion are summarized in the energy level schemes in figure 4 where again U02 is compared to EuS and also to EuO /13/. To stress the fundamental difference between a one- and a many electron state the band states are shown on the right side and the ldcalized states on the left side of the energy ordinate.

Fig. 4 : Empirical energy level schemes for U02, EuO and EuS.

4. Derivation of an energy level scheme by the thermo-chemical Haber-Born process.- The thermo-chemical Haber-Born process has been applied q u i t e ~ ~ ~ ~ e ~ ~ f ~ l l y to derive energy level schemes for 4f /13,14/ and 3d /15/ magnetic semiconductors. Due to the ionic bond in U02 the Haber-Born process appears particularly suited for U02. However, a certain drawback for the method is the need to know the 4% and 5th ionization energies of U02. No experimental values for these ionization energies have been publi- shed so far and we have to rely on theore- tical results. From the various values published we have chosen the data of Steinhaus et a1./16/ because the latter show the best agreement with the-known experimental values for the first and second ionization energies. In addition these valuesarewithin 0.7 eV of the average

of all other theoretical values.

Figure 5 showa the various steps of the Haber-Born process after four electrons

from the uranium have been transferred to 2

-

the oxygen ions to form

u4+

and 0

.

Fig. 5 : Derivation of an energy level scheme for U02 from the Haber-Born thermo- chemical process.

The ground states are then 5f2 and 2p6 for uranium and oxygen, respectively. The 4th

(5f3 + 5f2

+

e-) and 5th (5f2 + 5f1

+

^e-)

ionization energies of uranium are plotted relative to their respective final state energies which are set zero. Because transition to a 5f3 state from 5f2 or 2p 6 states are dipole forbidden, we are more interested in the position of the 5f 6d 2 state than the 5f state. The energy dif- 3 ference between these two states has been derived by Vander Sluis and Nugent /17/

and is shown in figure 5. Finally the first column contains above the energy origin.the affinity for the second oxygen electron

(zp5 ₊

e- + 2 p 6 ~ .

The second column takes into account the Madelung potential. This electrostatic potential enhances the levels of the

positively charged uranium ions and depresses

the (2p 6 ) level of the negatively charged 02- ion by 39.8 and 21.4 eV, respectively /18/.

The third column considers the pola- rizability of the lattice using the expres- sion of Yost /19/

up

= (eL/2~) (l-cst)

.

Here R is the ionic radius of

u4+

or 0 2- and equals 22 as derived from the far infrared reflectivity.

In the last column we have added some empirically determined splittings. The crystal field splitting of the 6d states is taken from our optical data and the split- ting of the 2p states is inferred from XPS results /4/. The agreement between figures 4 and 5 is remarkable. All transition energies are found within less than 1 ev of the experimental assignments and beautifully corroborate the latter.

The same is true for the molecular cluster calculations of Gubanov et a1./20/.

This calculation for a (U08) 12- octahedral cluster includes the crystal field splitting of the uranium 6d states but not the

splitting of the oxygen 2p states. The latter are split due to the presence of two anions in the minimal fluorite unit cell in states with zone center symmetry

r15

and

ri5.

Optical transitions to the empty 6d states with symmetry T12(=e ) and

9

(=t ) are only dipole allowed from T15 2g

but not from

r25.

The inclusion of this splitting of the 2p states should move up the

r15

state and thus reduce the energy of the only observable 2p(T15) + 6d(T12,

ri5)

transitions. Gubanov et a1./20/ find

between the center of gravity of the oxygen 2p states and the 6de level an energy sepa-

g

ration of 9 eV. Including the cited p state splitting a nearly perfect agreement to the experimental value of 8 eV should result.

5. Intra 5f-trensitions.- All the physical properties of U02 discussed up to this point are very similar to the corresponding properties of the europium chalcogenides.

This is no longer the case if the photon

energy is decreased to values below the energy gap of 2 eV. Figure 6 displays the absorption coefficient of U02 below 2 eV for various temperatures.

Fig. 6 : The absorption coefficient of U02 in the spectral range between one phonon absorption and interband transitions.

We observe a multitude of peaks while in the europium chalcogenides no such peak occurs. The relatively low absorption coef- ficient of lo3 cm-' indicates that these peaks are not due to dipole allowed inter- band transitions but rather to intra 5f- transitions. The complexity of the spectra reflects the importance of both crystal field effects'and spineorbit splitting in the 5f electronic system. In 4f compounds the crystal field splitting is in the order of 1 0 - ~ e ~ and can be neglected compared to the spin-orbit splitting gf some 10-I eV.

In the 3d compounds it is the crystal field splitting of a few eV which largely domi- nates the spin-orbit splitting of only 10-I eV. However, in the actinides both split- tings are'of the same size of some tenth to 1 eV. Table I compares the energy of the absorption peaks of figure'6 at 300 K with values computed by Rahman and Runciman /21/

using realistic spin-orbit and crystal fieid parameters to obtain an effective magnetic moment of 1 . 8 ~ ~ per uranium. The agreement

is throughout good and constitutes the first experimental verif Lsation of the data

JOURNAL DE PHYSIQUE

proposed by Rahman and Runciman /22/.

Table I.- Comparison of calculated /21/ and measured energy levels of the 5f2 configu- ration of U02 below 1.3 eV. All experimental values are for 300 K except the values in bracketswhich have been determined at 60 K.

E [e~]

:

^{E CevI}

:

State

:

Theory /21/

:

Exp. (300K) :

6. Order induced optical effects.- On lowe- ring the temperature from 300K the peaks of figure 6 become better resolved first (60K) and finally split below TN. This splitting of the absorption lines reflects the split- ting of the cubic crystal field levels below TN when a local rearrangement of the oxygen sublattice occurs /23/.

The phase transition to the antiferro- magnetic state isof first order as manifes- ted in the step of the red shift of the absorption edge.in figure 7. A quantitative analysis of the size of this step /24/

shows that it is much larger than expected from the lattice contraction of U02.

Obviously, the largest part of the red shift is due to an exchange induced splitting of the initial and/or the final state of the 5f + 5f '6de transition.

The antiferromagnetic state of U02 g also generates striking changes in the two phonon spectrum as can be seen around 0.15 eV in figure 6. A discussion of this interesting phenomena .is beyond the scope

of the present paper and will be reserved to a further article covering more general- ly phonon properties of U02.

Fig. 7 : Shift of the absorption edge of UO as function of temperature. The photon engrgy corresponds to an absorption

coefficient of 1960 cm-1.

7. Conclusion.- It has been shown that UO is a magnetic semiconductor whose 2 electronic structure is very similar to the one of the europium chalcogenides. The optical gap found at 2 eV is due to an 5f2 + 5f '6de transition. The 5f2 state is localized as evidenced by the observation 9 of many narrow lines corresponding to intra 5f-transitions. But also photoemission, Faraday rotation / 2 4 / and neff support a localized description of the 5f state in

uo2.

The transition from the bonding p valence to the d conduction band starts at 5.5 to 6 eV and peaks at 8 and 10.8 eV.

This empirically derived scheme is shown to be consistent with the ones obtained from a thermo-chemical Haber-Born process and a molecular cluster calculation. However, it disagrees markedly from the empirical scheme of Naegele et a1./5/. Besides the insufficient spectral range of measurement the latter authors misinterpret the sum rule. In fact the 5f2 + 5f 6d transition 1 involving localized states should only

contribute one electron to neff and not two. Because of parity conservation the p + d,s transitions should contribute about 6 electrons per formula unit and not 12 electrons as has been claimed. Figure 8 shows neff as derived from our measurements.

and exchange splitting of states.

Acknowledgement.- The author thanks Prof.

P. Wachter for his support and many valuable discussions. The technical assistance of Mr. B. Naef is gratefully acknowledged.

References

Photon Energy Lev]

Fig. 8 : Effective number of electrons per formula unit contributing to optical tran- sition as a function of photon energy.

We observe at 5 eV 0.2 el./f.u. correspon- ding to the 5f2 + 5f16de transition. Above -6 eV the onset of the p 4 + d transition manifests itself in a strong increase of n leading to 6 el./f.u. at 13 eV and

eff

to the theoretically expected value of 7 el./f.u. at 15 eV. Thus neff is consistent with the assignments of electronic transi- tions as required for selfconsistency.

Below the energy gap the optical properties of U02 are qualitatively

different from those of the europium chalco- genides. The nearly equal size of crystal field and spin-orbit splittings of the 5f states lead to a variety of phenomena not present in the europium chalcogenides. The unique power of optical spectroscopy is shown to allow a profound insight into many of these phenomena like the first order phase transition, changes in the symmetry

/I/ See Proc. Discussion Meeting Magnetic Semiconductors, W. Zinn, Ed., (North Holland; 1976.

/2/ Freeman, A.J. and Koelling, D.D.,

"The Actinides", A.J. Freeman and J.B. Darby, Jr. Eds., (Academic Press)

1974.

/3/ Ackermann, R.J., Thorn, R.J. and Winslow, G.H., J. Opt. Soc. Am.

49

(1959) 1107.

/4/ Veal, B.W. and Lam, D.J., Phys. Rev.

B

10

(1974) 4902.

/5/ Naegele, J., Manes, L. and Birkholz, U., "Plutonium and other Actinides"

H. Blank and R. Lindner, Eds. (North Holland) 1976, p.393.

/6/ Pireaux, J.J., Riga, J., Thibaut, E., Tenret-Noel, C., Caudano, R. and Verbist, J.J., Chem. Phys.

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113.

/7/ Kelly, P.J., Brooks, M.S.S. and Allen, R., J. Physique Colloq. C 4 (1979)184

.

/8/ '~choenes, J., J. Appl. Phys.

49

⁽¹⁹⁷⁸⁾

1463.

/9/ The measurements from 0.0025 to 0.03 eV were performed by Dr. P. Bruesch to whom the author expresses his gratitude.

/lo/ Edwards, R.K., Chandrasekhardish, S.W.

and Davidson, P.M., High Temp. Sci.

1 (1969) 98.

-

/11/ Giintherodt, G., Phys. Condens. Matter 18 (1974) 37

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/12/ Wachter, P., Handbook on the Physics and Chemistry of Rare Earth, Vol. 2, K.A. Gschneidner, Jr. and L. Eyring eds., (North Holland) 1979, p.507.

/13/ Wachter, P., Crit. Rev. Solid State Sci.

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/14/ Kasuya, T., J. Appl. Phys.

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/15/ Van Houte~s., J. Phys. Chem. Solids 17 (1960) 7.

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/16/ Steinhaus, D.W., Radziemski, L.J., Jr. and Cowan, R.D., NASA- Spec. Publ.

236 (1970) 151.

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/17/ Vander Sluis, K.L. and Nugent, L.J., J. Opt

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^{Soc. Am.}

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/l8/ Hodby, J.W. "Crystals with the fluorite structure", W. Hayes Ed.,

(Clarendon Press Oxford) 1974

JOURNAL DE PHYSIQUE

/19/ Y o s t , W., J. Chem. Phys.

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(1933) /22/ S c h o e n e s , J . , Nagn. Magn. Mat.

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