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CRITICAL FIELD EFFECTS OF THE Gd IN
GdxEr1-xRh4B4
R. Wang, C. Huang, J. Smith
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supp1Pment au no 8, Tome 39, aotit 1978, page C6-373
CRITICAL FIELD EFFECTS
OF
THE
GdIN
GdxEr1-xRh4B4 ( * >R.H. Wang, C.Y. Huang and J .L. Smith
Los A L M O S Scientific Laboratory, Lo8 AZaflos, NM 87545, U.S.A.
Rdsum6.- Nous avons Btudie l'influence des ions Gd sur la temp6rature de transition supraconductrice, le champ critique supgrieur et la tempdrature de transition magn6tique du systhme Gd Erl-xRh4B4 pour
x
0 6 x & 1. Les courbes r6entrantes mesurges sont en accord raisonnable avec la th6orle de Fulde et Maki.Abstract.- The effects of Gd ions on the superconducting cransition temperature, the upper critical field, and the magnetic transition temperature of the GdxErl-,Rh4B4 system were investigated for x = 0 to 1 . The measured reentrant upper critical field curves are in reasonably good agreement with the theory of Fulde and Maki.
1. INTRODUCTION.- Recently the compound ErRh4B4 was found to become superconducting at T = 8.7 K follo- wed by a return to the normal state at Tm = 0.9 K due to the onset of long-range magnetic ordering of Er ions /I /. In contrast to ErRh4B4, GdRh4B4 under- goes a ferromagnetic transition at 5.6 K. In order to study the nature of the reentrant superconducti- vity in ErRh4B4, we recently measured the variations of the superconducting critical temperature Tc, the magnetic ordering temperature Tm, and the upper critical field Hc2, of a series of pseudoternary compounds GdxEr,-xRh4B4 121. On the basis of the theories by Fulde and Maki, and by Werthamer, Helfand, and Hohenberg 1 3 1 , we calculated the dependencies of Hc2 on the temperature and Gd concentrations. Over the entire measured range, our data can be explained reasonably well by the theories.
2. ANALYSIS AND DISCUSSIONS.- The samples were pre- pared following the work of Fertig et al.
111.
The upper critical field Hc2 was defined as the applied field for which the sample resistance was half the normal resistance. The measured upper critical field H (T,x) as a function of various impurityc2
concentrations for x = 0 to 0.24 is shown in fig. 1 . All of the samples (including x
"
0.26, not shown) are reentrant magnetic superconductors in that they undergo a second order transition into the magnetic state at temperatures Tm(cTc) with a concurrent disappearance of superconductivity. The maximum upper critical field increases then decreases with increasing x, exhibiting a maximum near x = 0.02.(*) Work performed under the auspices of the US Department of Energy.
Fig. 1 : Upper critical field Hc2 versus temperature for seven GdxErl.-xRh4B4 samples with x ranging from 0 to 0.24. Calculated values of Hc2 are given by the solid and dashed curves.
Such nonmonotonic concentration dependence of H c 2 may be due to compensation of the orbital critical field H~~~ by the mean exchange field H. between the
J
conduction electrons and the localized moments 141. In order to make a quantitative analysis of our data, we use the multiple pair breaking theory and the extreme Type-I1 strong spin-orbit theory of Fulde and Maki 1 3 1 . Since the procedure of the ana-
lysis follows closely that of Ishikawa and Fischer / 5 / , we only give its main features. The total de- pairing parameter equation can be written as /5/
The notations adopted in this paper are identical to those used in Ref. 5. To calculate Hc2, we assume /5/ H. (T,H) = ( g - 1 ) I H X /(Ng 1-1;)
,
3 (2)
where g is the Lande g-factor, N the total number of atoms per unit volume, I the exchange constant bet- ween the conduction electrons and the magnetic mo-
m e n t s , ~ the magnetic susceptibility, and
%
the Bohrmagneton. For
x
we use the Curie-Weiss lawwhere J is the total angular momentum. For ErRh4B4
we assumed Pscat = 0 corresponding to Tco = Tc. For
x # 0, pscat was deduced from the AG curve correspon-
ding to Tc/Tco. Even in the worst case of x = 0.24,
the fitting of Hc2(T) with pscat = 0 is only about
4% off from that with pscat# 0
.
The parameter/ A S o 2
,
determined by fitting Hc2 at one tempera-ture using Eqs. (I)-(3), varies from I x I O - ~ ~ O 3x10-~ eV with increasing x. The corresponding Pscat ranges from 0 to 0.021 at x = 0.24.
The calculated upper critical fields for seven different Gd concentrations are shown by the solid and
dashed curves in fig. 1. Considering the questionable
validity of the Curie-Weiss law near the magnetic transition temperatures Tm, the fit is excellent away from Tm. The experimentally observed reentrant beha- vior can be adequately explained by the theory of Fulde and Maki over the entire range of Gd concentra-
tions of interest. A more detailed account and dis- cussion of this work will be published elsewhere.
In conclusion, the spin polarization effect can successfully account for our measured reentrant upper critical field in the GdxEr,,xRh4B4 system from
x
= 0 up to the critical concentration xc=
0.28 forthe entire superconducting regime.
References
/ I / Fertig, W.A., Johnston, D.C., Delong, L.E., McCallum, R.W., Maple, M.B., and Matthias, B.T.
Phys.Rev.Lett.
38
(1977) 987/2/ Wang, R.H., Laskowski, R.J., Huang, C.Y., Smith, J.L. and Chu, C.W., accepted for publi- cation in J. Appl. Phys.
131 Fulde, P., and Maki, K , , Phys.Rev.
141
(1966)275
Werthamer, N.R., Helfand, E., and Hohenberg,P.C.
Phys. Rev.
147
(1966) 295/41 Fischer, O.H., Helv. Phys. Acta
45
(1972) 331/ 5 / Ishikawa, M. and Fischer, O., Solid State
Commun.
3
(1977) 747ACKNOWLEDGEMENT.- We are grareruL to Dr. M. Ishikawa for providing detailed information on his calculation,
and Dr. S. Kohn for showing us his preliminary results
