Journal of Low TemperaturePhysics, Vol.2i, Nos, 3/4, 1975
The Impurity Resistivity of ZnFe Alloys E. Babi~* Department of Physics, Imperial College, London, England
M. O~ko Institute of Physics of the University of Zagreb, Zagreb, Yugoslavia
and C. Rizzuto Istituto di Scienze Fisiche, Genova, Italy ( R e c e i v e d M a r c h 10, 1975)
Measurements are presented of the electrical resistivity of several ZnFe alloys with concentrations between 0.04 and 0.05 at % Fe in the temperature interval 0.5-280 K. The low temperature resistivity behavior of even the most dilute alloys is dominated by impurity-impurity interactions leading to fortuitous characteristic temperature 0 ~ 9OK. At higher temperatures (T ~> 15K) the impurity resistivity is dependent mainly on single impurities with much higher 0 values. The estimated characteristic temperature of isolated Fe impurities 01 ~ 350 K is in better agreement with recent magnetic susceptibility and thermopower measurements. 1. I N T R O D U C T I O N If we define as "magnetic" those alloys that show a logarithmic (Kondo) variation of the impu/ity resistivity and a Curie-Weiss behavior of the impurity susceptibility with temperature, we may have the problem of defining the temperature range in which this magnetic behavior is observed, or that of investigating whether alloys that do not show such a behavior at liquid helium temperature do show it at higher temperatures. When transition metal impurities of the 3d row are considered, we know that the AI-3d alloys do not show any magnetic behavior up to above room temperature (see the review by Rizzuto 1 and references therein) while other 3d,alloy systems show a number of alloys with a magnetic behavior as defined above. The appearance of magnetic behavior at low temperatures *On leave o f a b s e n c e f r o m the Physics D e p a r t m e n t , U n i v e r s i t y o f Z a g r e b , Z a g r e b , Y u g o s l a v i a . 243 9 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher.
244
E. Babi~M.O~ko, and C. Rizzuto
is strongly correlated with a decrease of the Fermi energy of a host metal, as was pointed out by Friedel, 2 and it is observed, for example, in an increasing number of alloys in going from Al-based alloys to Zn, Cu, Ag, and Au. The Zn-3d alloy systems, in particular, show a magnetic behavior at temperatures above about 1 K for ZnMn and ZnCr alloys, which is believed to weaken and eventually disappear 3 below about 0.1 K. An indication of the "weakening" of magnetic behavior is normally achieved when the impurity resistivity changes its behavior from logarithmic to quadratic ( - T 2) upon lowering the temperature of measurement. It is still an open question whether all the alloys that show a logarithmic behavior of the resistivity will indeed change over to a quadratic variation of the resistivity at sufficiently lower temperatures, and, conversely, whether alloys that show only a - T 2 dependence will change over to a logarithmic dependence if the temperature interval is extended to sufficiently high values. It is believed that the changeover from quadratic to logarithmic variation takes place over about a decade in temperature around a characteristic temperature 0 which can be defined either by the Curie-Weiss temperature, if such a variation is observed in the susceptibility, or by fitting the quadratic temperature variation of the resistivity to the empirical 4 formula
p(T)=p(O)[1 -(T/O) 2]
(1)
The particular system which we consider in this paper, ZnFe, has been the subject of somewhat contrasting reports about the extent and temperature range of its "magnetic" behavior and is particularly interesting because, as is the case of AlMn, AuV, and CuFe, it may allow us to observe the magnetic weakening 4 effect in a range between helium and room temperature. An earlier superconductivity investigation 5 reported a suppression of the superconducting transition temperature with increasing Fe concentration (below the zinc transition temperature T~0 = 0.85 K) wich compares with that of "nonmagnetic" alloys ("upward" curvature of T~vs. c as in A/Mn). Subsequently Caplin 6 reported a resistivity which varied with temperature in a manner consistent with a logarithmic behavior over the narrow interval (1.5-4.2) investigated. It was of particular interest that this dependence was weaker than that observed for comparable concentrations of solute in other magnetic 3d alloys. Subsequent measurements by Ford and co-workers 7 and Rizzuto et al. 8 over broader temperature intervals (0.4-10 and 1.2-90 K, respectively) resulted in a reported quadratic temperature variation with a characteristic temperature variation with a characteristic temperature 0 of about 80 K. In a second paper approximately linear temperature variation extending between about 50 K and the highest measured temperature (~90 K) was
The Impurity Resistivity of ZnFe Alloys
245
believed to indicate the transition to the weaker logarithmic temperature dependence expected about 80 K. Susceptibility measurements have recently been performed by Bell and Caplin 9 to investigate whether the other feature of a "magnetic" behavior, i.e., a temperature dependence, was observed. This temperature variation should be either Curie-Weiss or quadratic by analogy to the cases of CuFe and AuV, depending on whether we are in a "magnetic" or "weakly magnetic" regime. These measurements 9 show, again, a very weak "magnetic" behavior at lower temperatures, a T-dependent term being superimposed on a larger enhanced Pauli contribution to up 50 K. This behavior has been interpreted as being due to the superposition of a small contribution (the magnetic-like one) due to interacting Fe atoms and a nonmagnetic contribution of the isolated Fe atoms. However, the nonmagnetic contribution does not seem compatible with the reported characteristic temperature of the resistivity, being more characteristic of a localized virtual bound state with an effective width (due to enhancement) of F ,,~ 180 K. Also, thermopower measurements 1~ give results in disagreement with the above reported characteristic temperature 0 deduced from the resistivity measurement. In this paper we report a more accurate and extended investigation of the resistivity of ZnFe alloys, which takes into account the possible contributions to the resistivity of the nonadditivity of the phonon and impurity scattering (deviations from Matthiessen's rule) and of interacting Fe atoms. M6ssbauer effect measurements, which are currently in progress elsewhere, ~ may give additional information in the near future. 2. EXPERIMENTAL As already done previously in a number of other alloys and also in ZnFe, 8 we have used a special rapid-quenching technique 12 to prepare the samples. This technique is used to increase the concentration of the alloys studied, while, we hope, not increasing too much the problems connected with the interactions of solute atoms. It has proved to be successful in many A1-3d alloys 13'14 and in a number of preliminary tests that we have done with ZnFe alloys by comparing their resistivity and the superconducting transition temperatures in bulk and rapidly quenched alloys at lower concentrations as was done in AIFe alloys.15 It must be noted, however, that already above 150 ppm in normally prepared ZnFe alloys reprecipitation may be present, as pointed out by Caplin. 6 The necessity of increasing the concentration is due to the need to increase substantially the impurity-to-phonon resistivity ratio in the tempera-
246
E. Babi~, M. Ofiko, and C. Rizzuto
ture region around the expected characteristic temperature, and this may be done only by reaching concentrations of several tenths of percent, so that the corrections for the phonon resistivity may be made with less uncertainty. Master alloys were prepared as described by Boato et al. 16 and our lowest concentration samples were their original alloys subjected to our rapid quenching technique. The alloys investigated have nominal concentrations of 0.04, 0.08, 0.1, 0.2, 0.3 and 0.5 at % Fe and the measurements have been performed on several samples of each alloy. The concentrations of both master alloys and samples were checked by electron microprobe analysis and quite good agreement was found with the nominal concentrations. All the samples of each alloy were also controlled by checking the residual resistance ratio RRR =
R4.z/(R273
-
R4.2)
which was found to scale well with concentration and in satisfactory agreement with residual resistance ratios of Boato et al. 16 except for the 0.5 at % alloys, which give lower values. Some Z n A g (I, 2, and 3 at % Ag) and Z n C o (0.11 and 0.22 at % Co) alloys prepared by the same method and rapidly quenched were also controlled by the same method. The resistance of the samples that were satisfactory according to the above tests was measured by a potentiometric method similar to that described earlier I v which was modified to allow the simultaneous measurement of two samples. These measurements were performed in a specially designed cryostat between 1.5 and 280 K and the temperatures were monitored by a calibrated germanium thermometer between 1.5 and 100 K and by an Au~).03 at % Fe/chromel thermocouple above 80 K. Some of the samples were measured in a H e 3 cryostat down to 0.5 K against a calibrated thermometer. The resistance accuracy was about one part in l0 s for all samples and the absolute resistivity accuracy was limited by the determination of the geometrical factor to about 1%. Several samples were used for the thermopower measurements referred to above 1~ and some of them (enriched with Fe 5v) are being subjected to M6ssbauer measurements elsewhere.11 3. RESULTS AND DISCUSSION The variation of the RRR with concentration for all alloys, which can be used for approximate residual resistivity determinations (by multiplying with the resistivity of pure zinc at 273 K, pld(273) = 5.45 #~-cm), is reported in Fig. 1.
The Impurity Resistivity of ZnFe Alloys
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We must note that, while the linearity of the RRR vs. c excludes sizable precipitation, it does not exclude the possibility of interactions between impurities, since the residual resistivity is not very sensitive to these interactions) A moresensitive test for the interactions is ~ven by a detailed analysis of the temperature variation of the resistivity at sufficiently low temperatures. We therefore start by considering the data obtained in lower temperature range. Figure 2 displays the resistivity data between 1.2 and l0 K for a representative sample of each alloy (except Zn-0.04 at % Fe alloy) and Fig. 3 shows the data between 0.5 and 8 K for two alloys with 0.04 and 0.11 at % Fe, respectively. Note the slight variation in resistivity of the different samples due to minor differences in metallurgical treatment or evaluation of the geometrical factor. The behavior of the Zn-0.04 % Fe alloy is very similar to that previously observed by Ford et al. ~ for samples of a 0.03 % Fe atloy prepared by normal quenching. We note that the impurity part (i.e., the decreasing part) of the resistivity is quite similar for all alloys. An increase in the concentration of the impurities only moves the resistivity minimum to higher temperatures
248
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and increases its depth. The variation of Train with concentration is rather weak, as shown in the inset of Fig. 3. The overall behavior of the resistivity curves confirms that which was observed previously 7'8 and suggests a - T 2 behavior at lowest temperatures. We verify this by plotting the data of three of the alloys (the two measured down to 0.5 K and one of the more concentrated ones, Zn-0.2 at ~o Fe) as a function of T 2 (Fig. 4). In this figure we also report the data corrected by subtracting the p h o n o n contribution to the resistivity, as explained later. We observe that an approximately - T 2 behavior seems to extend between a b o u t 0.5 and 2.2 K, above which temperature a deviation occurs to a weaker temperature dependence: The fit of this part of the data to formula (1) yields a value 0 = 9 0 - t - 2 0 K, in agreement with previous results. 7'8 However the limited temperature interval (less than one decade) in which this fit is valid casts some doubts on a simple effective - T 2 variation. It is, in any case, surprising to find that the deviation away from the T 2 behavior takes place at temperatures of the order of 0.020, while in most other alloys 1'8 the - T 2 behavior is observed up to at least 0.10. We must also note that in the same temperature range (below 10 K) a slight temperature variation of the susceptibility referred to above 9 and -
The Impurity Resistivity of ZnFe Alloys
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believed to be due to coupling between Fe atoms was observed. Moreover, the depths of the resistivity minima are found to vary as c z, which is again an indication of coupling effects. The detailed analysis of the low temperature interactions is left to another paper. In this paper we want to define only the one-impurity effects. We need therefore to extend the detailed analysis of the impurity resistivity data to higher temperatures and to do this, we must subtract the phonon contribution to the resistivity. It has in fact been found earlier 18 that if a spurious effect due to coupling between atoms exists in the resistivity, this may become smaller and does not give a sizable contribution at higher temperatures 1. ~3 (see also Star ~9).
250
E. Babi~, M. O~ko, and C. Rizzuto
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Fig. 4. The resistivities (solid symbols) and impurity resistivities (open symbols) for three ZnFe alloys at lowest temperatures plotted against the square of the temperature. Note the deviations from - T 2 behavior around 5 K 2 in all alloys.
In a previous publication s the impurity resistivity of two alloys of ZnFe was evaluated by subtracting the values of the phonon resistivity for Zn alloys of the same residual resistivity by extrapolating existing data 2~ on ZnAl and ZnAg alloys of lower resistivity. This extrapolation was based on the experimentally observed relationship between the impurity resistivity and the total phonon resistivity 21 (including deviations from Matthiessen's rule). However, due to the limited amount of data, this evaluation was not very satisfactory, although the criterion followed was later confirmed by more detailed data on nonmagnetic Zn alloys. 22 In this work we have improved on the accuracy of the phonon subtraction by measuring, simultaneously with the ten ZnFe samples considered, ZnAg or ZnCo alloys having a residual resistivity similar to that of the ZnFe alloys. Two examples of the low temperature resistivity variation of the alloys used for the subtraction of phonon resistivity are shown in Fig. 2. In some cases the measurements have been repeated by measuring the same ZnFe alloy against both a ZnAg and a ZnCo alloy, to avoid possible effects due to the high concentration of Ag (the specific resistivities, Ap/c, of Fe and Ag in Zn differ by a factor of more than ten, while Ap/c for Fe and Co differ by about a factor of t w o 16) needed to match the resistivity produced by a given concentration of Fe. Also, we noted that samples with different impurity concentrations prepared by rapid quenching showed somewhat different degrees of texture
The Impurity Resistivity of ZnFe Alloys
251
(i.e., crystalline orientation) and this might have some effect due to anisotropy of the resistivity. A comparison between the different ways of subtracting the phonon resistivity (ZnAg or ZnCo) does not give any sizable and systematic effect of either concentration (as long as the residual resistivities are.about the same) or texture. 23 Figure 5 shows the impurity resistivities of three samples (0.04, 0.11, and 0.2 at % Fe, respectively) between 1.5 and 270 K. The data for the lowest concentration show a residual contribution from deviations from Matthiessen's rule which alters the impurity resistivity behavior up to above 50 K; this effect decreases strongly in the 0.11% Fe alloy and seems negligible in the 0.2 % alloy. In zinc-based alloys 22 deviations from Matthiessen's rule scale in fact with the logarithm of concentration, while the impurity resistivity is scaling linearly, as our data show. The reason, however, why the phonon resistivities of a Zn-0.04 at % Fe alloy and corresponding ZnAg or ZnCo alloys differ so much at low temperatures is not yet clear to us. There may be several factors acting simultaneously, but even the different degrees of anisotropy between these samples might suffice to give the observed effects. At higher temperatures the effect of deviations from Matthiessen's rule should not affect the temperature dependence of the impurity resistivity
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Fig. 5. The impurity resistivities of three representative ZnFe alloys between 1.5 and 270 IC The error bars at 250 and 100 K show the maximum error due to uncertainty in the geometrical factor evaluation (see text). In the inset the temperature coefficients of the resistivity at 273 K vs. concentration are shown for all alloys investigated,
252
E. Babi~, M. O~ko, and C. Rizzuto
which we obtain. A residual systematic error, however, may be due to uncertainties in the determination of the geometrical factors, which may affect our results by giving a contribution linear with temperature. The estimated maximum contribution is indicated on Fig. 5 by two error bars at different temperatures. Therefore by considering the highest concentration samples in the intermediate temperature range, and all samples at the higher temperatures, we should be able to get significant information on the impurity resistivity behavior. If we plot the data for the two highest concentration alloys below 45 K as a function of T 2 (Fig. 6), we observe that there is a superposition of the low temperature part already discussed, whose fit to a T 2 law yields a value of 0 ,~ 80 K, and a higher temperature part, again with a - T 2 dependence but with characteristic temperature which for the alloys shown is 0 -~ 350 ___ 50 K. The uncertainty quoted is due to the difference observed between several alloys. A slight decrease of the 0 value with increasing concentration may be due to a residual contribution of coupling or to the deviations from Matthiessen's rule in the lowest concentration alloys. Above about 40 K the impurity resistivity deviates away from the - T 2 behavior; this is a temperature of ~ 0.10, in agreement with the systematics found in other alloys. 8 If we consider the two more concentrated samples
A
i ~',
3"1
9 Zn'2Fe .
IN
1"66 3"06
1000
T 2 (K 2)
2000
Fig. 6. The impurity resistivities of Zn-0.11 at ~ Fe and Zn-0.2 at 7o Fe alloys below 45 K vs. square of the temperature. Note superimposed interaction effects below about 10 K in both alloys.
The Impurity Resistivity of ZnFe Alloys
253
above ~ 60 K, we observe that instead of the gradual transition from a - T 2 law to a linear and then to a slower than linear variation, as expected by comparison with other alloy systems, a'" there is a behavior similar to that found in other alloys up to about 130 K and then a fairly well-defined transition to a linear behavior at higher temperatures. According to the systematics referred to above, a slower than linear behavior above approximately 200 K would be expected. (At these temperatures, T > 0D/2, we may relay on the fact that the phonon resistivity and residual variation of the deviations from Matthiessen's rule are linear in temperature.) We believe that, as in the case of A/Mr, 24 and AuV, 25 the behavior of ZnFe data above about 130 K is affected by the thermal expansion and consequent change in the characteristic temperature. 26 We have noted before that the absolute value of the resistivity for our samples is influenced by the uncertainty in the geometrical factor and affects the determination of Pimp and dp/dTat 273 K. In the inset of Fig. 5 we report the averages between the values of (dp/dT)~73 obtained for all specimens and the mean square deviation observed. We note that the deviation observed is less than the maximum (estimated) limit given in the same figure. If we extrapolate the average data of (clp/dT)273 to zero concentration we obtain a temperature coefficient of the resistivity which agrees with values quoted in the literature z6 for pure Zn. This value is 22.5 _+ 0.5 nflcm/K. Although the fairly linear variation of(dp/dT)273 with concentration indicates an effect due to isolated impurities, its values are not directly indicative of the behavior of the Fe impurities, because of the possible effect of thermal expansion. 4. C O N C L U S I O N S The new measurements of the impurity resistivity presented in this paper show that the characteristic temperature of the - T 2 variation due to isolated Fe atoms in zinc is higher than reported before %8 and has a value of 350 _+ 50 K. The disagreement with previously reported values is due to the fact that those were affected by interaction effects between Fe atoms which are present even in the lowest concentration alloys considered in the literature 6'7'9 and important up to about 10-20 K. These effects can be observed and taken into account by extending the measurements to alloys of concentrations in the range of c > 0.1 at % Fe and to higher temperatures. The single-impurity behavior varies as - T 2 up to about 40 K (i.e., --~0.10), in agreement what is observed in other alloy systems. 1 Therefore our measurements will scale with measurements in other alloys 8 containing Fe by considering a reduced temperature T/O.
254
E. Babi~, M. O~ko, and C. Rizzuto
At higher temperatures the resistivity behavior is probably affected by thermal expansion as observed in other alloys 24'25 and a detailed determination of the impurity resistivity behavior is therefore subject to further corrections. In the intermediate temperature range (~ 50 K) there are indications of small differences between the phonon contributions of different alloys having approximately equal impurity resistivity: This may indicate some differences in the deviations from Matthiessen's rule for different impurities. The above findings do not allow us to conclude whether the Z n F e alloys show a magnetic behavior at higher temperatures, due to very strong complications in the separation of host and impurity effects. On the other hand, we have been able to correct the reported value of 0 and to find that the behavior at lower temperatures is in agreement with other alloys in the "weakly magnetic" regime. ACKNOWLEDGMENTS We particularly acknowledge Prof. B. R. Coles for useful discussions and comments. Thanks are also due to Dr. R. Vaccarone for his help in some measurements and to Dr. J. R. Cooper for a helpful criticism. We also acknowledge a continuous support of Prof. B. Leonti6. This work was completed at Imperial College, where one of the authors (E.B.) held an SRC fellowship.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
C. Rizzuto, Rep. Prog. Phys. 37, 147 (1974). J. Friedel, Nuovo Cim. SuppL 7, 287 (1958). A. Pilot, R. Vaccarone, and C. Rizzuto, Phys. Left. 40A, 405 (1972). A. D. Caplin and C. Rizzuto, Phys. Rev. Lett. 21, 746 (1968). G. Boato, G. Gallinaro, and C. Rizzuto, Phys. Rev. 148, 353 (1966). A. D. Caplin, Phys. Lett. 26A, 46 (1967). P. J. Ford, C. Rizzuto, and E. Salamoni, Phys. Rev. B 6, 1851 (1972). C. Rizzuto, E. Babi6, and A. M. Stewart, J. Phys. F: Metal Phys. 3, 825 (1973). A. E. Bell and A. D. Caplin, J. Phys. F: Metal Phys. 5, 143 (1975). J. R. Cooper and E. Babi6, unpublished data. J. W. Williams and J. B. Dunlop, private communication. E. Babi6, E. Girt, R. Krsnik, and B. Leonti6, J. Phys. E: ScL Instr. 3, 1015 (1970). E. Babi6, P. J. Ford, C. Rizzuto, and E. Salamoni, Solid State Comm., 11,519 (1972). E. Babi6, P. J. Ford, C. Rizzuto, and E. Salamoni, J. Low Temp. Phys. 8, 217 (1972). E. Babi6, C. Rizzuto, and E. Salamoni, J. Phys. F. Metal Phys. 4, L20 (1971). G. Boato, M. Bugo, and C. Rizzuto,/~ao.vo Cim. X45, 226 (1966). C. Rizzuto, E. Salamoni, and P. Zani, Cryogenics 11, 306 (1971). E. Babi6, R. Krsnik, B. Leonti6, Z. Vu~i6, J. Zori6, and C. Rizzuto, Phys. Rev. Letters 27, 805 (1971). 19. W. M. Star, Thesis, University of Leiden (1971). 20. S. Ledda, Thesis, Univ. of Genoa, unpublished (1971).
The Impurity Resistivity of ZnFe Alloys
21. 22. 23. 24. 25. 26. 27.
255
M. R. Cimberle, G. Bobel, and C. Rizzuto, Advan. Phys. 23, 639 (1974). P. Salvadori, E. Babi6, R. Krsnik, and C. Rizzuto, J. Phys. F: MetaIPhys. 3, L195 (1973). M. O~ko, unpublished. J. R. Cooper, to be published (1974). R. L. Singh and G. T. Meaden, Phys. Rev. B6, 2660 (t972). J. S. Schilling and W. B. Holzapfel, Phys. Rev. B8, 1216 (1973). L. A. Hall and F. E. E. Gerrnann, NBS Technical Note 365-1 (1970), p. 71.