PuS, PuSe, PuTe: Relativistic semiconductors

Journal of Magnetism and Magnetic Matermls 63 & 64 (1987) 649-651 North-Holland, Amsterdam

PuS,

PuSe,

PuTe:

RELATIVISTIC

649

SEMICONDUCTORS

M S S BROOKS Commtss~on of the European Commumaes, Joint Research Centre, Karlsruhe Estabhshment, European lnsatute for Transuramum Elements, Postfach 2340, D- 7500 Karlsruhe, Fed Rep Germany

The equations of state of PuS, PuSe and PuTe were calculated from self-consistent energy band calculatmns m a number of ways (1) With 5f electrons treated as localmed and Pu dwalent In thts case insulators were obtained which would have non-magnetic J = 0 ground states, an agreement with experiment However, the calculated lattice constants were far too large (2) With 5f electrons treated as locahzed and Pu tnvalent Metals were obtained, and mvalent Pu systems are normally magneuc In addmon the calculated latuce constants were too large (3) With 5f-electrons treated as mnerant but w~th spm-orblt couphng neglected All three systems were found to be metalhc and the Stoner criterion for ferromagnetism was easily sausfied although experimentally no moment has been observed m these systems The calculated lattice parameters were also too small (4) With 5f-electrons treated as mnerant and fully relatlwstlcally In this case all three systems were found to be semiconductors w~thcalculated lattice constants m agreement w~thexperiment and

band gaps of between 0 2-0 4 eV

Following the discovery some time ago that the 5f derived bands of hght actlnzde metals had a width of several volts [1,2] modern self-consistent band structure and density functional techniques [3] have been used to calculate trends in both lattice constant [4] and cohesive energy [5] quite successfully The rapid decrease in lattice constant as the number of 5f electrons increases is attributed by band theorists to the metallic 5f-5f contribution to the chemical bond The lattice constants of the NaCl-type binary compounds are more of a puzzle T h e y do not decrease slowly and regularly across an A n X series as they do for the corresponding rare earth compounds but are a function of f electron number with a minimum close to the beginning of a series The explanation based upon energy band theory IS that in A n X compounds the cation f-anion p bond makes an additional contribution to the equation of state [6-8] Towards the middle of an A n X series where the calculated 5f-bands are very narrow an explanation based upon single electron theory becomes less tenable Nevertheless we have investigated what single electron theory can contribute to an understanding of the curious properties of the Pu monochalcogenides The prob-

lem may be stated as follows (a) If Pu in the monochalcogenldes is divalent with a localized 5f 6 configuration, as in the analogous rare earth compounds, why are the lattice constants of the Pu monochalcogenides so much smaller than those of the corresponding rare earths 9 (b) A trivalent Pu (5f 5) would be more plausible as the lattice constants are far closer to those of the trlvalent rare earth compounds, although they are too small, especially for PuS But if this were the case, why are the Pu monochaicogenldes observed to have no magnetic order [9] 9 We have therefore made self-consistent energy band calculations for the two cases where the 5f electrons are locahsed (divalent and trlvalent) We have also examined the alternative possibility where the 5f states are treated as band states In all three cases we have calculated the electronic pressure [10] as a function of v o l u m e - t h e equation of s t a t e - a n d determined the theoretical lattice constant The self-consistent energy band calculations were made using the linear muffin tin orbital and relativistic linear muffin tln orbital techniques ( L M T O and R L M T O ) which have been descrlbed in detail elsewhere [11-14] Unless stated otherwise, the results referred to in this paper are from fully relativistic calculations

0304-8853/87/$03 50 © Elsevier Science Publishers B V (North-Holland Physics Publishing Division)

650

M S S Brooks / PuS, PuSe, PuTe relaawsac sermconductors

In fully relativistic s e l f - c o n s i s t e n t e n e r g y b a n d calculations, w h e r e s p i n - o r b i t c o u p l i n g Is o p e r a t i v e , two partial state densities, Do(E), were c o m p u t e d for each v a l u e of l In the calc u l a t i o n s r e p o r t e d here the c h a r g e d e n s i t y was spherically a v e r a g e d after e a c h i t e r a t i o n T h e i r r e d u c i b l e zone was s a m p l e d at 240 points a n d the v a l e n c e c h a r g e d e n s i t y was c o n v e r g e d to b e t t e r t h a n o n e part in 10 n T h e simplest form of the a t o m i c sphere a p p r o x i m a t i o n [11] ( A S A ) was used with n o c o r r e l a t i o n terms either for the s t r u c t u r e c o n s t a n t s or for the i n t e r c e l l u l a r c o u l o m b i n t e r a c t i o n b e y o n d A S A [15] In the c a l c u l a t i o n for dl- a n d t n v a l e n t P u T e six a n d five 5 f - e l e c t r o n s were p l a c e d m 5f orbltals c o r r e s p o n d i n g in e n e r g y to the 5f b a n d c e n t r e - a t e c h n i q u e a l r e a d y used successfully to r e p r o d u c e the e q u a t i o n of state of U O 2 w h e r e the 5f e l e c t r o n s are also l o c a h s e d [16] T h e s e 5f orbitals are n o t part of the b a n d s t r u c t u r e a n d c o n t r i b u t e essentially zero e l e c t r o n i c pressure T h u s f r o m the p o i n t of view of b a n d t h e o r y these are n o n - b o n d i n g (or locahsed) 5f states In table 1 we show the c a l c u l a t e d lattice c o n s t a n t s for dI a n d t n v a l e n t P u T e , a n d the e x p e r i m e n t a l l y d e t e r m i n e d c o n s t a n t E v i d e n t l y the c a l c u l a t e d lattice c o n s t a n t s are too large In fact they are close to the lattice c o n s t a n t s of c o r r e s p o n d i n g dl a n d t r w a l e n t rare earths T h e c a l c u l a t i o n s also yield that d i v a l e n t P u T e is a n Insulator with a gap of 2 e V , a n d that t r i v a l e n t P u T e is metallic with a d e n s i t y of states at the F e r m i level of 1 7

s t a t e s / e V / f o r m u l a unit T h e sttuatlon is similar for PuS a n d PuSe (table 1) I n table 1 we also show the c a l c u l a t e d lattice c o n s t a n t s of the three P u m o n o c h a l c o g e n i d e s w h e n the 5f states were t r e a t e d as b a n d states in R L M T O c a l c u l a t i o n s I n th~s case the results are in a g r e e m e n t with the e x p e r i m e n t a l l y d e t e r m i n e d lattice c o n s t a n t s T h e 5f c o n t r i b u t i o n to the e l e c t r o n i c pressure Is also s h o w n m the table a n d it m a y be seen that the 5f e l e c t r o n s are b o n d i n g - a l t h o u g h far less t h a n in c o m p a r a b l e u r a n i u m c o m p o u n d s I-7] T h e total d e n s m e s of states for the three c o m p o u n d s from these fully r e l a t w i s h c c a l c u l a t i o n s are s h o w n in fig l T h e three c o m p o u n d s are, p e r h a p s surprisingly, e x t r e m e l y small gap s e m i c o n d u c t o r s It r e m a i n s to discuss exactly why PuS, PuSe a n d P u T e are c a l c u l a t e d to be s e m i c o n d u c t o r s Some insight m a y be o b t a i n e d by t a k i n g away the s p i n - o r b i t c o u p l i n g T h i s is d o n e by r e v e r t lng to the L M T O c a l c u l a t i o n s T h e effect u p o n the c a l c u l a t e d lattice c o n s t a n t s a n d partial 5f e l e c t r o n i c pressures of PuS, PuSe a n d P u T e are s h o w n In table 1 T h e a g r e e m e n t with experim e n t IS c o n s i d e r a b l y w o r s e n e d as the m a g n i t u d e of (negative) 5f e l e c t r o n i c pressure is i n c r e a s e d , a n d c a l c u l a t e d lattice c o n s t a n t c o r r e s p o n d i n g l y decreased T h e r e a s o n for this is that the m a g n i t u d e of the e l e c t r o n i c p r e s s u r e is a m a x i m u m for a halffilled b a n d a n d zero for filled or e m p t y b a n d s [5]

Table 1 Summary of some calculated quantmes for plutonmm monochalcogemdes n, are the occupation numbers, a the lattice parameter m /~, and B the bulk modulus m kbar DI is the partial I density of states at the Fermi level m states/eV/formula unit

a(expt) a(theory) n~ Pf

PuTe dw

PuTe tnv

PuS

PuSe (relativistic)

PuTe

PuS

6 18 6 63 60 -

6 18 6 46 50 -

5 53 5 51 50 -125

5 79 5 76 49 -88

6 18 6 21 53 -61

5 53 5 38 50 -1_65

nf,~2

-

-

nf7/2

00

17

Pf,/2 Pf~/2 B D(EF)

PuSe PuTe (semlrelatlvlsUc) 5 79 5 57 49 -125

6 18 5 95 54 -99

4 7

4 6

5 1

-

-

-

03 -53 -73 1030 00

03 -41 -48 390 00

02 -26 -35 230 00

36

28

27

M S S Brooks/PuS, PuSe, PuTe relat~mstlc semiconductors

In the semlrelatlvistlc calculations the n u m b e r of electrons with 5f character IS about 5 (table 1), would approximately half-fill pure (unhybrIdlzed) 5f bands, and the magnitude of the 5f electronic pressure is large In the fully relativistic calculations the n u m b e r of electrons wzth 5f5/2 character (table 1), m e g PuTe, Is 5 1 and of the 5 f 7 / 2 character is 0 2 Thus pure 5f5/2 bands would be almost filled, and 5f7/2 bands almost e m p t y and their partial pressures m u c h reduced T h e hybrizatlon with other states is what al- 7 O0 I

g

- 5 O0 I

- 3 O0 I

651

lows the semlconductlng gap to appear E v e n if spin-orbit coupling splits pure 5f-bands, the 5f5/2 bands are not filled unless the n u m b e r of electrons with 5f5/2 character IS s ~ x - w h m h It is not In any case, m the absence of hybridlzaUon between 5f and other conduction electrons, the state density at the Fermi energy would remain fimte irrespectwe of what happened to the 5f levels or bands H o w e v e r , m the presence of hybridization, the 5f5/2 derived bands are filled and since they are split from the 5f7/2 derived bands they create a gap in the entire conduction band spectrum, albeit small

- I O0 I

References J

pute

g

W=P

w pe'r o1-oU')

W

/ puse

J

pus

~

/

-I

O0

E N E R G T tEVI

Fig 1 State densltms of the plutonmm monochalcogemdes from self-consistent fully relatlwstlc RLMTO calculatmns The zero on the energy scale Is the Fermi energy

[1] A J Freeman and D D Koelhng, m The Actlnldes Eiectromc Structure and Related Properties, vol 1, eds A J Freeman and J B Darby (Academic Press, New York, London) p 51 [2] D D Koelhng and A J Freeman, Phys Rev B12 (1975) 5622 [3] See e g A R Mackantosh and O K Andersen, in Electrons at the Fermi Surface, ed M Sprmgford (Cambridge Univ, Press, Cambridge, 1979) [4] H L Skrlver, O K Andersen and B Johansson, Phys Rev Lett 41 (1978)42, Phys Rev Lett 44 (1980) 1230 [5] M S S Brooks, J Phys F14 (1984)1157 [6] M S S Brooks and D Glotzel, Physica 102B (1980) 51 [7] M S S Brooks, J Phys F14 (1984) 653 (1984) 857 [8] M S S Brooks, B Johansson and H L Skrwer, m Handbook on the Physics and Chemistry of Actmides, vol 1, eds A J Freeman and G H Lander (NorthHolland, Amsterdam, 1984) p 153 [9] D J Lam and A T Aldred, m The Actlmdes Electromc Structure and Related ProperUes, vol 1, eds A J Freeman and J B Darby (Academic Press, New York and London) p 110 [10] D G Pettdor, J Phys F7 (1978) 613, (1978) 1009, 7 (1978) 209 D G Pettifor, Commun Phys 1 (1976) 141 [11] O K Andersen, Phys Rev B12 (1975) 3060 [12] H L Sknver, The LMTO Method (Springer, Berhn, 1984) [13] M S S Brooks, J Phys F14 (1983) 639 [14] C Godreche, J Magn Magn Mat 29 (1982)262 [15] D Glotzel and A K McMahon, Phys Rev B20 (1979) 3210 [16] R J Kelly and M S S Brooks, J Phys C13 (1980) L939, M S S Brooks and P J Kelly Sohd State Commun 45 (1983) 689