Electron spectroscopy and the Kondo Volume Collapse in Ce0.7Th0.3

Journal of Magnetism and Magnetic Matermls 63 & 64 (1987) 515-517 North-Holland, Amsterdam

ELECTRON

SPECTROSCOPY

515

A N D T H E K O N D O V O L U M E C O L L A P S E IN CeoTTho 3

J W ALLEN1", J -S KANGt"* and S -J OH1 "+ f Xerox Palo Alto Research Center, 3333 Coyote Hdl Road, Palo Alto, CA 94304, USA *Insatute for Pure and Apphed Physzcal Sctences, Umversay of Cahfomm at San Diego, La Jolla, CA 92093, USA +Dept of Physics, Seoul Nanonal Umverslty, Seoul 151, South Korea

An electron spectroscopy study of the continuous ~-3' transmon m Ceo 7Tho a has been made for temperatures between 100 and 310 K A rough analysis of the results shows qualltatwe agreement with the Kondo Volume Collapse model, as derived from the Anderson Hamfltoman

In th~s paper we report an electron-spectroscopy study of the o~-~, transition in Ceo 7Tho ~, and a rough analysis of the results in terms of the K o n d o Volume Collapse(KVC) model [1,2], as derived from the Anderson Hamiltonlan [1,3] We relate the electron spectra to the Anderson Hamlltonlan using the results of Gunnarsson and Schonhammer [4], as analyzed in refs [5] and [6] Similar electron-spectroscopy studies of cerium compounds [5-8] and of the a and ~/phases of Ce [9,10] qualitatively support the K V C model Ceo7Tho ~ is an interesting contrast because in this material the transition is continuous as a function of temperature [11,12] The temperature range of our experiment was 100 to 3 0 0 K , the range over which the transition is most rapid Bremsstrahlung isochromat (BIS) and X - r a y photoemlssion (XPS) spectra were taken at a photon energy of 1 4 8 6 6 e V in a V a c u u m Generators E S C A L A B , factory-modified for BIS The BIS sample current was kept low, ~ 5 0 IxA to minimize sample heating and maximize the resolution, which was ~ 0 5 e V T o minimize the data-collection time, Ce 3d XPS spectra were taken with a n o n m o n o c h r o m a t l c Al K c~ source, yielding an overall resolution due to photon and electron resolutions of 1 2 eV Satelhtes due to the Al K,~3,4 lines were removed from the spectra by a standard algorithm [8] The sample was a polycrystalhne ingot of cylindrical shape, about 0 7 cm in diameter and 1 5 cm in length It was tightly fitted into a cylindrical well in a copper block, which replaced

the usual sample holder on the liquld-mtrogen cooled manipulator in the E S C A L A B measurement chamber A thermocouple was fixed to the copper block next to the sample, and the temperature was controlled manually to +2 5 degrees with a heater mounted on the manipulator The sample was scraped with a diamond file to obtain a clean measurement surface, and during datataking the chamber pressure was always below 1 x 10-1° Torr Fig 1 shows the BIS spectrum at four temperatures 310, 150, 135 and 90 K In the energy i

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

516

J W Allen et al / X P S / B I S / K o n d o volume collapse m Ceo 7Tho

range 2 to 7 eV is a large peak which is a mix of the T h 5f and Ce 4f~---~4f2 spectra Near the Ferret level a small p e a k is evtdent at 310 K and as the temperature is lowered, and the material changes from 3`-hke to ct-llke, the peak grows monotomcally In the framework of the impurity Anderson Hamdtontan, this peak is the K o n d o resonance T h e dlvtslon of weight between that of the resonance, Wb and that of the Ce f2 peak, We, is of interest to determine the 4f occupation ~ , but to deduce this reqmres separating the weight of the Th contribution, WTh, from the higher energy peak We express these weights as W~= (0 7)OrCe[14(1 -- nf) + C], W2 = (0 7)O-ce[13(nr) C], and Wxh = (0 3)trc~[(14)(tr-rh/trc~)], where Cr-rh/trCe = 3 36 IS the ratio of the tabulated [13] 5f and 4f cross secttons at the AI K a energy, and C =/3(14)(1 - nf) is the dynamical correction [4], which ts zero for mfinite C o u l o m b interaction U Using fig 5 of ref [6] we estimate f = W~/(W~ + W2) and nf by the self-consistent procedure of choosing a value for nf, calculating /3 from fig 5, calculating the expected Wrh/We = 3`, using 3' to determine f from the data (using a straighthne b a c k g r o u n d coInctdent wtth the spectrum at 1 2 and 8 5 eV), and requiring that it be the same value of f given from fig 5 for the assumed value of nf Based on the analysis of the 3d spectra given below, we choose the A = 80 m e V curve of fig 5 as most appropriate, and obtain for 3 0 0 K , n ~ = 0 9 6 , f = 0 0 7 5 , and for 90K, nf=092andf=0 14 Fig 2 shows the Ce 3d spectra at 310 and 90K Following the assignments and interpretanons of refs [4] and [5], we focus attenUon on the 3d9/2 4f I and 4f 2 peaks at 884 and 879 eV, respectwely, and on the 3d9/2 4f ° peak at ~ 9 1 3 eV, denoting the first two peaks' areas by A~ and A2, respectively T h e fractional weight of the 4f ° p e a k is proportional to 1 - n ~ , so its modest Increase wtth decreasing t e m p e r a t u r e is quahtatlvely consistent with the BIS results a b o v e We have not attempted to be more quann t a t w e because of the difficulty of separating the peak from the loss structure which underlies it T h e Intensity ratio r - - A e / ( A ~ + A~) is proportional to the hybridization p a r a m e t e r A of the

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BINDING ENERGY (eV) Fig 2 "Ce 3d XPS spectra for CeovTho~ at 310 and 9 0 K , n o r m a h z e d at the 3d~/2 4f ~ shoulder, 879 eV Inset shows detail of the 3dq/2 4f ~ peak

Anderson Hamlltonian, and fig 6 of ref [5] gives the r-A relation o b t a m e d from the theoretical spectra of fig 6 in ref [4] From our data we obtain the results r(310 K) = 0 177 and r(90 K) = 0 193, for which the calibration curve gives A(310 K) = 85 m e V and A(90 K) = 94 m e V Although our peak separatton algorithm reproduces the cahbration curve Itself fairly well, it is obvious that the whole procedure is very rough, and further, the callbraUon curve ts for a particular model density of conduction band states and particular choices of other parameters Thus the absolute values of A have large uncertainty T h e ratio ] = A ( 3 1 0 K ) / A ( 9 0 K ) = 0 9 may be more sigmficant as a measure of the fractional change m A

We next analyze the temperature dependence of the magnetic susceptlbihty Xexp(T), with the aim of deducing the volume dependence of the K o n d o coupling constant J Cox [14] has given the theoretical impurity Anderson Hamlltontan susceptlbdtty for spm 5/2 as a universal curve which is a function of T~ TK For the simplest case of infinite C o u l o m b interaction U and infinite degeneracy Nr, TK is given [4,14] as TK = D e x p ( - 1 / J ) , where D t s the conduction band-

J W Allen et al / XPS/BIS/Kondo volume collapse m Ceo 7Tho ~

w i d t h a n d t h e c o u p l i n g c o n s t a n t is J = NfA/T~Ef, with ef b e i n g t h e 4f b i n d i n g e n e r g y for A = 0 It is u n d e r s t o o d t h a t NfA IS h e l d c o n s t a n t as Nf t e n d s to infinity A s in ref [3] w e a s c r i b e to J a l i n e a r d e p e n d e n c e on n o r m a l i z e d v o l u m e v = V / V o , l e , J = a + by, a n d c h o o s e a a n d b to r e p r o d u c e Xexp(T), using the t h e o r e t i c a l s u s c e p t i b i l i t y [14], w h i c h we h a v e & g l t i z e d , a n d the e x p e r i m e n t a l v o l u m e Vexp(T) W e t a k e for o u r r e f e r e n c e v o l u m e Vo = 3 6 / ~ 3 the a v e r a g e of the v o l u m e s of L a a n d Pr, as u s e d in the K V C c a l c u l a t i o n s of ref [1,3] W e d o n o t k n o w Vexp(T) for C e l - x T h x for x = 0 3 H o w e v e r , b o t h Xexp(T) a n d the t e m p e r a t u r e d e p e n d e n c e of the l a t t i c e c o n s t a n t a ( T ) a r e k n o w n [12] for x = 0 26 a n d the s u s c e p t i b i l i t y c u r v e s for the two v a l u e s of x are i d e n t i c a l within c e r t a i n e x p e r i m e n t a l u n c e r t a i n t i e s set forth b y L a w r e n c e [11] T h e r e f o r e w e h a v e t a k e n as o u r V the q u a n t i t y a 3 ( T ) / 4 for x = 0 26 In so d o i n g , we i n c u r s o m e u n c e r t a i n t y d u e to a small hysteresis of the w e a k l y f i r s t - o r d e r t r a n s i t i o n for x=026 F i g 3 ( l o w e r part) c o m p a r e s X~xp(T) with the x ( T ) c a l c u l a t e d by the a b o v e p r o c e d u r e for D=4eV and J=10553-09487v To obtain this fit it was n e c e s s a r y to shift the V~xp c u r v e b y a b o u t 6 K , a n d in fig 3 ( u p p e r part) we show the /)exp c u r v e , the shifted v c u r v e , a n d the r e s u l t i n g : 0 95

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Fig 3 Temperature dependence of experimental and shifted volume curves, Kondo temperature TK, and experimental and calculated suscephblhtles as described m text

517

T K ( T ) c u r v e w h i c h t o g e t h e r yield the c a l c u l a t e d x ( T ) of fig 3 ( l o w e r part) T h e two X c u r v e s a g r e e v e r y well F r o m t h e s e results we c a n d e d u c e the v a l u e s of J at the t e m p e r a t u r e s of the s p e c t r a of figs l a n d 2 W e find J ( 3 1 0 K ) / J ( 9 0 K ) = 0 172/0 2 4 5 - 0 70 Since J is p r o p o r t i o n a l to A, we c o m p a r e to the r a t i o 1 = 0 9 d e d u c e d a b o v e f r o m the 3d s p e c t r a , finding q u a l i t a t i v e a g r e e m e n t

W e a r e d e e p l y I n d e b t e d to J L L a w r e n c e for p r o v i d i n g the s a m p l e of Co 7Th0 3 a n d his u n p u b h s h e d s u s c e p t l b l h t y d a t a W e also t h a n k him, as well as J C F u g g l e , O G u n n a r s s o n , a n d M B M a p l e for helpful d i s c u s s i o n s R e s e a r c h s u p p o r t by the U S N a t i o n a l S c i e n c e F o u n d a t i o n - L o w Temperature Physics-grant DMR-8411839 ( J W A , J S K ) is g r a t e f u l l y a c k n o w l e d g e d References

[1] J W Allen and R M Martin, Phys Rev Lett 49 (1982) 1106 [2] M Lavagna, C Lacrolx and M Cyrot, Phys Lett 90A (1982) 210 [3] R M Martin and J W Allen, J Magn Magn Mat 47&48 (1985) 257 [4] O Gunnarsson and K Schonhammer, Phys Rev B 28 (1983) 4315 [5] J C Fuggle, F U Hdlebrecht, Z Zolmerek, R Lasser, Ch Frelburg, O Gunnarsson and K Schonhammer, Phys Rev B 27 (1983) 7330 [6] F U Hlllebrecbt, J C Fuggle, G A Sawatzky, M Campagna, O Gunnarsson and K Schonhammer, Phys Rev B 30 (1984) 1777 [7] J W Allen, S -J Oh, M B Maple and M S Tonkachvdl, Phys B 28 (1983) 5347 [8] J W Allen, S -J Oh, O Gunnarsson, K Schonhammer, M B Maple, M S Tonkachvd] and I Lmdau, Advan Phys, to be pubhshed [9] E Wullloud, H R Moser, W -D Schneider and Y Baer, Phys Rev B 28 (1983) 7354 W - D Schneider, B Delley, E Wullloud, J -MImer and Y Baer, Phys Rev B 32 (1985) 6819 [10] F Patthey, B Delley, W - D Schneider and Y Baer, Phys Rev Lett 55 (1985)1518 [11] J M Lawrence and R D Parks J de Phys 37 (1976) C4-249 [12] S M Shapiro, J D Axe, R J Birgeneau, J M Lawrence and R D Parks, Phys Rev B 16 (1977) 2225 [13] J J Yeh and I Lmdau, Atomic Data and Nuclear Data Tables 32 (1985) 1 [14] D L Cox, Ph D Thesis, Cornell Umverslty, U S (1986)