HAL Id: jpa-00217611
https://hal.archives-ouvertes.fr/jpa-00217611
Submitted on 1 Jan 1978
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
ISOTOPIC EFFECTS IN PdH (D)x(Normal state
phonon resistivity and superconducting tunneling
density of states)
P. Nédellec, L. Dumoulin, C. Arzoumanian, J. Burger
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-432
ISOTOPIC EFFECTS IN PdH ( D )
X(Normal s t a t e phonon r e s i s t i v i t y and superconducting tunneling density of s t a t e s )
P. Ngdellec, h. Dumoulin, C. Arzoumanian, J . P . Burger
Labovatoive de Physique des Solidss, Vnivevsite Paris-Sud, 91405 ORSAI, France
Résumé.- Des mesures de résistivitê électrique de phonons et de densité d'états tunnel à l'état supraconducteur mettent en évidence le rôle fondamental des phonons optiques de l'hydrogène (et du deuterium) dans le couplage électron-phonon des composés PdH(D) . Abstract.- Measurements of normal state phonon resistivity and of superconducting tun-neling density of states point out the essential importance of the H and D optical phonons in the electron-phonon coupling of PdH(D) .
The discovery /l/ of superconductivity in PdH quickly raised the problem of the role played by the H ions and their optical vibration. The simple structure of these compounds, the large mass difference between the Pd and H ions offers the possibility to sort out in this system the elec-tronic (i.e. density of states) and atomic (i.e. acoustical and optical phonons) factors determining T . The striking observation of a positive isotope
c
effect 111 prompted even more the interest in this field. The aim of the present work is to emphasize these points by studying in details the isotope effect when passing from H to D. We use two diffe-rent approaches. First we measure the normal state phonon resistivity'which gives us information on che temperature needed to excite optical phonons and on the strength of the electron-phonon coupling. Secondly, the superconducting tunneling density of states fives us information on the energy location and shape of the phonon modes involves in super-conductivity.
EXPERIMENTAL.- Details on the Pd films and Al-oxyde-Pd junctions have been outlined elsewhere /3/. The H (or D) is introduced afterwards in the Pd lattice by electrolytic charging using a C2H5OH(D) +
112(02)801, mixture. The electrolysis is performed at about 170 K directly inside the cryostat : the sample is fixed on a gold plated copper block en-closed in a teflon cell which receives the elec-trolyte. During the electrolytic charging, we qualitatively control the amount of H ions by mea-suring continuously the resistivity of the Pd films. By this charging procedure, we obtain su-perconducting T ranging between 5.5 K and 9 K.
RESULTS 1.- Resistivity : The experimental phonon resistivity, after subtraction of a constant resi-dual resistivity, is given on figure 1. As a func-tion of temperature for Pd-D films (T = 8.15 K) and one bulk Pd-H sample (T = 9.45 K ) . We will admit in what follows that the phonon resistivity of Pd-H may be split into its acoustical and optical parts : p(T) = p (T) + p (T). Due to the
ac op large value of the ratio of the optical to acous-tical vibration energy, only acousacous-tical thermal phonons are expected to be excited at low enough temperatures (T < 60 K ) , so that in this range, one may consider p(T) = p (T); a T5 lax is
obser-ved for 10 K < T < 20 K and the results up to 50 K' can be fitted by a Griineisen law. To analyse our results up to 120 K (the limiting temperature for stability of our films) we admit that the acousti-cal part of p(T) is described by this Griineisen law at all temperatures for both PdH and PdD (the acoustical Debye temperature is 210 K ) . One obser-ves (Figure 1) that the curobser-ves a (i.e p (T), b
(i.e. Pd-H ) and c (i.e. Pd-D ) tend to coincide x x at low temperature. At higher temperature, the resistivity of Pd-D and Pd-H increases faster
J x x
than the acoustic contribution alone : this indi-cates that the optical phonons, obtained from the difference between curve b or c and a, get ther-mally excited. It is gratifying to observe that in the case of Pd-D the optical contribution to p(T) appears at a lower temperature than for Pd-H in agreement with its lower optical phonon energy. A preliminary analysis of Pd-D films (with T of 8.15 + 0.5 K and 5.1 + 0.5) and of a bulk /4/ Pd-H sample (T = 9.45 K) gives the following
1.5
+
0.15 ( t h e o p t i c a l pho- r e s u l t s : 1) Wop wop (D) E non r e s i s t i v i t y i s f i t t e d on c u r v e s b and c" u s i n g an E i n s t e i n spectrum; a r e t h e c o r r e s p o n d i n g OP e n e r g i e s ) . F i g . 1 : Phonon r e s i s t i v i t y f o r Pd-D ( c u r v e ( c ) ) and X Pd-H ( c u r v e ( b ) ) . Dashed c u r v e s a r e t h e o r e t i c a l : XG r h e i s e n law f o r a c o u s t i c a l phonons (curve ( a ) ) , E i n s t e i n law f o r o p t i c a l phonons ( c u r v e (b*) and
(c*)
1.
The a b s o l u t e v a l u e s of w l i e around 720 K f o r H
OP
and 480 K f o r D i n rough agreement w i t h t h e neutron d i f f r a c t i o n d a t a 151.
2) t h e o p t i c a l phonon c o n t r i b u t i o n t o p(T) i n c r e a s e s w i t h Tc (and s o w i t h t h e hydrogen concen- t r a t i o n x ).
3) t h e o p t i c a l electron-phonon c o u p l i n g c o n s t a n t i s 2.5 t o 3 t i m e s l a r g e r t h a n A a c ( t h i s l a s t r e s u l t stems from t h e h i g h t e m p e r a t u r e e x t r a - p o l a t i o n of p .
(T)
=
A .T, i = a c , op).
2.- Tunneling : Tunneling e x p e r i m e n t s on Pd-D and
X
Pd-Hx f i l m s have been performed and g i v e r i s e t o a p p r e c i a b l e v o l t a g e dependent s t r u c t u r e s i n t h e t u n n e l i n g c u r r e n t . Our main r e s u l t s a r e d i s p l a y e d on t h e second d e r i v a t i v e s of t h e t u n n e l i n g c u r r e n t I v e r s u s b i a s v o l t a g e , i . e .
&
(V). They a r e dv2 g i v e n i n F i g u r e 2 f o r Pd-H (T = 5.3K)
and Pd-Dx X C (Tc = 7.7 K). d2v F i g . 2 : Experimental-
(V) d a t a a t 1.7 K f o r d12 a d e u t e r a t e d (Tc = 7.7 K) and an hydrogenated (T = 5 . 3 K) t u n n e l i n g j u n c t i o n . The arrow i n d i c a - te; t h e p o s i t i o n of t h e o p t i c a l phonon induced anomaly.O u t s i d e of t h e s u p e r c o n d u c t i n g gap t h e s t r u c t u r e d21
on t h e
7
(V) c u r v e r e f l e c t s t h e phonon d e n s i t y dVof s t a t e s . For Pd-Dx f i l m s , a w e l l pronounced mini- mum around 35 meV i s shown o n F i g u r e 2. T h i s s t r u c t u r e , f i r s t observed by E i c h l e r e t a 1 161, h a s been a t t r i b u t e d t o t h e o p t i c a l phonon mode i n agreement w i t h n e u t r o n d i f f r a c t i o n r e s u l t s . T h i s s t r u c t u r e i s m i s s i n g i n Pd-H and i s r e p l a c e d b y t h e somewhat weaker and broader anomaly n e a r 52 mV. T h i s i s t h e behaviour one e x p e c t s f o r b o t h t h e p o s i t i o n and t h e w i d t h of t h e o p t i c a l phonon induced ano- m a l i e s ; f o r i n s t a n c e , t h e observed v a r i a t i o n i n t h e t u n n e l i n g conductance n e a r t h e phonon peak,
aa
(%8x10-~ f o r D) i s i n good agreement w i t h t h e Aexpected v a l u e (A
=
1 meV and fiwo = 35 mev) Other anomalies a r e observed b o t h i n Pd-H and Pd-D a t e n e r g i e s between 10 and 24 meV which may b e r e l a t e d t o t h e a c o u s t i c phonons of t h e Pd l a t t i c e . By s u b s t r a c t i n g t h e normal s t a t e c o n t r i b u t i o n t o d21-
(V),
a q u a n t i t a t i v e d e t e r m i n a t i o n of t h e ener- d v2 gy p o s i t i o n of t h e s t r u c t u r e s i s o b t a i n e d . I f we d21 assume t h a t t h e p o s i t i o n of t h e minima i n-
a r e dV2 r e p r e s e n t a t i v e o f t h e energy w (H o r D) of t h e OP o p t i c a l phononmodes, we f i n d w (D)= 34.72
0 . 5 OPT h i s d i f f e r e n c e i s p r o b a b l y r e l a t e d t o d i f f e r e n t v i b r a t i o n amplitude of H and D g i v i n g r i s e t o an e f f e c t i v e , mass dependent ( o r anharmonic) f o r c e c o n s t a n t . From o u r r e s u l t s we f i n d t h i s f o r c e cons- t a n t t o be 14 % l a r g e r f o r H. T h i s i n c r e a s e i s s m a l l e r , b u t of t h e same o r d e r of magnitude, a s observed by n e u t r o n d i f f r a c t i o n i n non s t o e c h i o - m e t r i c Pd h y b r i d e s and d e u t e r i d e s 171. It can ex- p l a i n q u a n t i t a t i v e l y / 8 , 9 / t h e p o s i t i v e i s o t o p e e f f e c t observed f o r T
.
R e f e r e n c e s
/ I / S t o s k i e w i c z , T., Phys. S t . S o l . (1972) 123. / 2 / S t r i t z k e r , B. and Biickel, W.,Zeits. f. Phys.
257 (1972) I .
-
/ 3 / Dumoulin, L., Guyon, E. and N g d e l l e c , P . , Phys. Rev.
B16
(1977) 1086./ 4 / McLachlan, D.S., B u r g e r , J . P . , M a i l f e r t , R.and SouffachG, B . , S o l . St.Commun
17
(1975) 281. / 5 / Rowe, J . M . , Rush, J . J . , Smith, H.G. M o s t o l l e r ,M. and Flotow, H.E., Phys. Rev. L e t t .
33
(1974) 1297./ 6 / E i c h l e r , A . , Wiihl, H. and S t r i t z k e r , B., S o l . S t . Commun
17
(1975) 213./ 7 / Rohman, A., S k g l d , K . , P e t i z z a r i , C. and S i n h a , S.K., Phys. Rev.
B
(1970) 3630./8/ Ganguly, B.W., Z e i t , f . Phys.
