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Critical behaviour of the electrical resistivity and thermopower in ferromagnetic Tb-Gd alloys
J. Sousa, M. Amado, R. Pinto, J. Moreira, M. Braga, D. Hukin, G. Garton
To cite this version:
J. Sousa, M. Amado, R. Pinto, J. Moreira, M. Braga, et al.. Critical behaviour of the electrical resistivity and thermopower in ferromagnetic Tb-Gd alloys. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-44-C5-45. �10.1051/jphyscol:1979517�. �jpa-00218934�
JOURNAL DE PHYSIQUE Colloque C5, supplkment au no 5, Tome 40, Mai 1979, page C5-44
Critical behaviour of the electrical resistivity and thermopower in ferro- magnetic Tb-Gd alloys (*)
J. B. Sousa, M. M. Amado, R. P. Pinto, J. M. Moreira, M. E. Braga (") Centro de Fisica da Universidade do Porto, Portugal
and D. Hukin, G . Garton ( b )
Clarendon Laboratory, University of Oxford, England
Rbsumb. - Le comportement critique de la rbistivitk tlectrique (p) a ett Ctudie dans une serie d'alliages ferro- magnktiques de Tb-Gd (hcp). Pour une direction basale on obtient pour Tb7,Gd2, au voisinage du point critique : dp/dT = A ( E
I-" +
B, avec 1 E 0 pour < 0,8 x et 1 = 112 pour 8 > lo-' : dans la direction axiale le comportement est complexe. Au dehors de la region critique nos rtsultats indiquent un comportement anormal.De plus on a ttudiC le comportement critique du pouvoir thermoelectrique ( S ) dans Tb7,Gd2,. La forte ressem- blance entre dS/dT et dp/dT au voisinage de T,, suggbre le mCme comportement critique pour les deux proprietes de transport.
Abstract. - The critical behaviour of the electrical resistivity (p) has been investigated on a set of hcp Tb-Gd alloys. Quantitative analysis (Tb,,Gd,,) shows for a basal direction : dp/dT = A 1 E I-"
+
B, with 1--
0 forE < 0.8 x lo-' and ,I= 112 for E > lo-' : along the c-axis, the behaviour is rather complex. Outside the critical region ( T < T,), the very anomalous behaviour of dp/dT is discussed. In addition, the behaviour of the thermo- electric power (S) is studied near T,. Striking similarities appear between dS/dTand dpldT, suggesting an intimate connection between both properties near T,.
In a previous paper [I] we have investigated the qualitative behaviour of the temperature derivative of the electrical resistivity (dp/dT) near the Curie point of monocrystalline hcp Tb-Gd alloys : drastic differences appear when the current flows along a basal (a, b) or axial direction. The results have been interpreted in terms of the high anisotropy of the Fermi surface [I]. For a basal direction the electron wavelength (&) is expected to be small [2], so that its motion is very sensitive to short-range effects.
A specific heat anomaly in dp/dT then results (Fisher- Langer behaviour [3]). Along the c-axis
&
is large [2], so that long-range effects become important and produce a maximum in p at T,. Then'dpldT changes sign when the sample enters the paramagnetic state, as shown in the inset of figure j (De Gennes-Friedel behaviour [4]).Here we present a quantitative analysis of the critical behaviour of dpldT for a basal direction. The c-axis analysis is complex and will be given in a forth- coming paper. The previous information on the basal resistivity is also extended here to a wider range of compositions. Finally we investigate the critical behaviour of the thermoelectric power and its tempe- rature derivative (dSldT).
(*) Supported by INIC, Portugal (") and NATO Res. Grant 1481 (") ( b ) .
Fig. 1. -Temperature dependence of (llp3 (dp/dT) in single crystals of Tb7,Gd,,, Tb,,Gd,,, Tb,,Gd,, (b-axis). Inset : c-axis behaviour
.
Figure 1 shows dpldT along a basal direction in single crystals of Tb7,Gd2,, Tb,,Gd,, and Tb,,Gd,, (at
%).
The general behaviour of dp/dT is remarkablyArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979517
CRITICAL BEHAVIOUR OF THE ELECTRICAL RESISTIVITY A N D THERMOPOWER IN Tb-Gd ALLOYS C5-45
similar in all these samples, and very different from that along the c-axis (see inset). The anomalous behaviour of dpld Tin the ferromagnetic phase should be emphasized here. Usually (e.g., Ni, Fe, ...), as T is lowered, the increasing magnetic order in the system considerably reduces dp/dT, whereas the opposite happens in Tb-Gd. This anomalous behaviour was also found by us in Gd and TbZn, and it might be a common feature in many rare earth systems.
Figure 2 summarizes the quantitative analysis of the b-axis behaviour for Tb,,Gd,, and T > T,.
In the vicinity of the Curie point the results are accurately described by a log-type dependence :
with A = 2.88 x k - ' , B = 3.48 x k-', p, = p(T,) and Tc = 242.85 K. This particular value of T, ensures the best least squares fit (o = 0.96) to the above expression over a wide range of reduced (E) temperature : 5 x l o p 4 5 E 5 1.2 x It is also fairly close to the temperature where dp/dT is maximum (z 242.6 K), the difference being attribu- table to unavoidable rounding effects near T,.
Fig. 2. - (lip,). (dp/dT) vs. log (T - T,) for Tb,,Gd,, (b-axis) near T,(5 x 5 8 5 1 . 2 ' ~ 1 V 2 ; T > T,). Fore 2 1.2 x a classical c-lI2 dependence is observed, as shown in the inset.
For E 2 10- the log-fit breaks down and a classical (T - T,)- ' I 2 dependence appears in dp/dT. The interesting crossover between both regimes is shown in the inset of figure 2. These findings are consistent with recent theoretical treatments [ 5 ] , which give a specific heat anomaly &-'I2 for T
2
TG, where T, is the Ginsburg temperature. From the data we estimate TG = 246 K in our case.Finally we have investigated the thermoelectric power (S, dS/dT) in a polycrystal of Tb,,Gd,,.
The critical behaviour of dS/dT is remarkably similar to that in dp/dT, as shown in figure 3. This strongly suggests that both properties might be governed by the same critical exponents [6]. In the paramagnetic phase there is a minimum in dS/dT, in the same manner as for dp/dT in the same sample. As shown elsewhere [I] this minimum is reminiscent from that found along the c-axis. Work is in progress to study S and dS/dT in Tb-Gd single crystals. A full account of our thermoelectric power work will be given elsewhere.
Fig. 3. - Temperature derivatives of the electrical resistivity (dp/dT) and thermoelectric power (dS/dT) in the vicinity of T,.
Acknowledgements. - The authors wish to thank Dr. D. Bagguley for the loan of samples, and to Eng. J. Bessa for technical assistance.
References
[I] SOUSA, J. B., AMADO, M. M., PINTO, R. P., MOREIRA, J. M., HUKIN, D., Commun. Phys. 2 (1977) 95.
[2] GELDART, D. J., RICHARD, T. G., Phys. Rev. B 12 (1975) 5175.
[3] FISHER, M. E., LANGER, J. S., Phys. Rev. Lett. 20 (1968) 665.
[4] DE GENNES, P. G., FRIEDEL, J., J. Phys. Chem. Solids 4 (1958) 71.
[5] ALEXANDER, S., HELMAN, J. S., BALBERG, I., Phys. Rev. B 13 (1976) 304.
[6] Aus~oos, M., J. Phys. A (To be published).
