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Submitted on 1 Jan 1978
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SPECIFIC HEAT OF Cu-0.9 at % Mn BELOW 3 K
Douglas Martin
To cite this version:
Douglas Martin. SPECIFIC HEAT OF Cu-0.9 at % Mn BELOW 3 K. Journal de Physique Colloques,
1978, 39 (C6), pp.C6-903-C6-904. �10.1051/jphyscol:19786401�. �jpa-00217871�
JOURNAL DE PHYSIQUE Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-903
SPECIFIC HEAT OF C u - 0 . 9 a t % Mn BELOW 3 K Douglas L. Martin
Physios Division, National Research Council of Canada, Ottawa K1A 0R6, Canada
Résumé.- La contribution magnétique à la chaleur spécifique de Cu-0,9 at.% Mn présente une courbure positive dans le domaine 0,4 à 3 K, Ce résultat est contraire à de nombreux travaux antérieurs, expérimentaux et théoriques. Toutefois, les résultats sont en accord avec le travail de Ho au-des- sous de 1 K, et celui de Wenger et Keesom au-dessus de 2 K. Il existe également un bon accord avec le modèle de calcul sur ordinateur dû à Walker et Walstedt.
Abstract.- The magnetic contribution to the specific heat of Cu-0.9 at.% Mn shows a positive curva- ture over the region 0.4 to 3 K. This is contrary to much previous experimental and theoretical work. However, the results are consistent with the work of Ho below 1 K and that of Wenger and Keesom above 2 K. There is also good agreement with the computer model calculations of Walkers and Walstedt.
1. INTRODUCTION.- Early measurements /1,2/ of the specific heat of dilute Cu-Mn alloys suggested that, in the low temperature limit, the "spin-glass" or magnetic specific heat contribution (i.e. alloy
specific heat minus pure solvent metal specific heat) was approximately linear in temperature and
independent of the Mn concentration. This was in accord with the Marshall-Klein-Brout /3,4/ theories of impurity-impurity interaction via the Ruderman- Kittel-Kasuya-Yosida mechanism. At higher tempera- tures the magnetic specific heat contribution was found to deviate negatively from the linear increase so that it went through a broad maximum and then decreased. The temperature of the maximum was pro- portional to the Mn content of the alloy /l/. The first measurements below 1 K /5/ were in general agreement with the earlier results and also showed that there was a nuclear specific heat contribution associated with the Mn.
More recent measurements were not in accord accord with this picture. Ho /6/ (quoted in Phillips /7/) made measurements below 1 K which suggested (after subtraction of the nuclear specific heat) that the magnetic specific heat was approximately independent of composition, that the term linear in temperature was about half that found at higher temperatures and that there was a significant con- tribution, perhaps proportional to T , in addition to the term linear in temperature. Most recently Wenger and Keesom /8/ made measurements in the 2 to
40 K. range, covering the temperature of magnetic ordering at T. where the susceptibility shows a
cusp-like peak /9/. Only a broad maximum was obser- ved in the magnetic specific heat. A surprising feature of Wenger and Keesom's /8/ results was that the magnetic specific heat (measured down to 2 K) showed a linear region extrapolating to zero at a positive temperature (^ 1 K) and not at the zero temperature which most earlier work had suggested.
This would be consistent with the marked change of slope which Ho deduced from his results /6/.
2. EXPERIMENTAL.- The present measurements were made on a sample which was prepared by induction melting in an alumina crucible, chill casting, homo^
genising and degassing. Analysis showed the Mn con- tent to be about 0.9 at.% with good homogeneity.
The measurements were made in an apparatus described elsewhere /10/.
Cu-0.9ot. % Mn ,
§ 3 -
B : «
a*
1 :
O -
I - J
S : r
o y
«_j _ y
"t i i i I » t i i I i i i i I i i i i I i i t i l i i i i
0 ) 2 3
T e m p e r a t u r e / K
Fig. 1 : The specific heat of Cu-0.9 at.% Mn after subtraction of the specific heat of pure copper (1 cal = 4.186J)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786401
p o s s i b l e r e a s o n i s t h e h i g h e r Kondo temperature i n 3. RESULTS.- The r e s u l t s of two experimental r u n s
a r e shown i n t h e preceding f i g u r e a s t h e e x c e s s s p e c i f i c h e a t a s s o c i a t e d w i t h t h e Mn, t h e s p e c i f i c h e a t of p u r e copper / l o / having been s u b t r a c t e d .
(This i s probably a r e a s o n a b l e assumption f o r such a d i l u t e a l l o y a t t h e s e t e m p e r a t u r e s . ) Various f i t s t o t h e e x c e s s s p e c i f i c h e a t were t r i e d , t h e b e s t
being C = H / T ~ +
1
an The f i r s t term i sP n=o
n u c l e a r s p e c i f i c h e a t , t h e magnitude being w i t h i n 10 % of t h a t found by Ho /6/ i n measurements t o much lower temperatures.
4. DISCUSSION.- Reference t o t h e f i g u r e shows t h a t t h e h i g h e r temperature s p e c i f i c h e a t does e x t r a p o - l a t e approximately l i n e a r l y t o z e r o a t a p o s i t i v e temperature o f t h e o r d e r of I K, i n agreement with Wenger and Keesom's 181 o b s e r v a t i o n s . The n u c l e a r
s p e c i f i c h e a t i s a complication i n deciding what happens a t lower t e m p e r a t u r e s b u t i n t h e extreme low temperature l i m i t (below 0.5 K f o r t h e p r e s e n t a l l o y ) t h e r e may be an i n i t i a l v a r i a t i o n l i n e a r i n t e m p e r a t u r e , t h e c o e f f i c i e n t b e i n g about h a l f t h a t deduced from measurements a t h i g h e r temperatures, a s had been suggested e a r l i e r / 5 , 6 / .
The p r e s e n t r e s u l t s appear t o be i n e x c e l l e n t agreement with t h e computer model p r e d i c t i o n s of Walker and Walstedt / ] I / . T h e i r s p e c i f i c h e a t shows marked p o s i t i v e c u r v a t u r e from t h e lowest tempera-
t u r e s and a g r e e s a l s o i n magnitude w i t h t h e p r e s e n t experimental r e s u l t s . Thus r e f e r e n c e / ] I / c a l c u l a - t i o n s a g r e e b e t t e r w i t h experiment than t h e a u t h o r s supposed a f t e r a comparison w i t h Wenger and Keesom's /8/ d a t a a l o n e i n which, a s mentioned above, t h e e x t r a p o l a t e d e x c e s s s p e c i f i c h e a t appeared t o go t o z e r o a t about I K.
Recent work on d i l u t e Cu-Mn a l l o y s t h e r e f o r e shows a d i f f e r e n t v a r i a t i o n of s p e c i f i c h e a t w i t h t e m p e r a t u r e t h a n was observed e a r l i e r . Presumably t h e r e a s o n may be a combination of more a c c u r a t e measurements w i t h b e t t e r samples. It i s c e r t a i n l y
t h e s e o t h e r systems. Cu-Mn i s b e l i e v e d 1141 t o have a v e r y low (* 0.001 K) Kondo temperature and t h e r e - f o r e might be a c l e a n e r "spin-glassf' t h a n many o t h e r systems where t h e r e s u l t s might b e p e r t u r b e d by t h e s i n g l e impurity-conduction e l e c t r o n i n t e r a c t i o n of t h e Kondo e f f e c t 1141. Recent r e s u l t s 1151 on t h e s p i n - g l a s s Pt-Mn show s i m i l a r f e a t u r e s t o t h o s e observed i n t h e p r e s e n t work.
I t i s hoped t h a t measurements on o t h e r com- p o s i t i o n s of t h e Cu-Mn system w i l l be a v a i l a b l e by t h e time of t h e LT15 conference.
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