PHYSICAL REVIE% B VOLUME 15, 5 UMBER 6 15 MARCH 1977

Anomalous resistivity behavior in singlet-ground-state systems

C. Y. Huang~

Los A/amos Scientific Laboratory, Los Alamos, New Mexico 87545

K. Sugawarat

Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106

Bernard R. CooperDepartment of Physics, West Virginia University, Morgantown, West Virginia 26506

(Received 5 February 1976; revised manuscript received 21 July 1976)

%'e present data showing that an anomalous maximum in the electrical-resistivity-versus-temperature [p(T)]curve, similar to that in Pr, La, ,Sn, , is present for all c in Tb,Y, ,As, but is absent for all c in Tb,Y, ,P and

Tb,Y, ,Sb. An interesting question is why there is no maximum in p(T) for both Tb,Y, ,P and Tb,Y, ,Sb for

any c, while there is a maximum for all c in Tb,Y, ,As. This question is particularly striking since the crystal-

field splitting and Neel temperature of TbP and TbSb bracket that of TbAs.

In recent years, the crystal-field related elec-trical resistivity of rare-earth compounds has at-tracted the attention of many authors. ' ' HesselAndersen etaL' have found that the resistivity p ofthe singlet-ground-state paramagnetic systemTb,Y, Sb (c= 0.05, 0.20, 0.4), increases monotoni-cally with temperature T. These authors haveattributed this temperature dependence to the elas-tic and inelastic scatterings of the conduction elec-trons by the crystal-field split 4f states of Tb"within the first Born approximation. %'e have alsomeasured' pin Tb,Y, ,Sb with the same values of c at9.2 GHz, and our results agree with those of Hes-selAndersen etal, .' Qur microwave data for c= 0.6,O.V, and 1.0 have similar temperature variation tothose at lower terbium concentrations except forthe appearance of the inflection points associatedwith the magnetic-ordering effects on spin scatter-ing at the respective Noel temperatures. (Veryrecent data of Hessel Andersen eta/. ' for these in-termediate concentrations agree with our own datain this regard. } Thus the resistivity behavior forthe system Tb,Y, ,Sb shows no indication of anyanomalous behavior. Qn the other hand, Abou Alyetal. ' and Lethuillier and Haen are in close agree-ment with each other in observing an anomalousmaximum in the resistivity-versus-temperaturecurves of another singlet-ground-state systemPr, La, ,Sn„where this anomalous maximum ap-pears at an approximately constant temperaturefor all c (0& c ~l). In this paper, we report ourmicrowave data showing that an anomalous maxi-mum similar to those exhibited" in Pr, La, ,Sn, ispresent for all c in Tb,Y, Qs, but is absent forall c in Tb,Y, P, i.e. , Tb,Y, ,P is similar toTb,Y, ,Sb in the absence of anomalous behavior.

Powder samples prepared according to a method

similar to that used previously' have been used.The microwave resistivities of the cubic Tb,Y, ,As(c=0.2, 0.2, 0.4, 0.5, 0.75, 1.0) and Tb,Y, P (c=0.2, 0.2, 0.5, 1.0) intermetallic compounds have

been measured from 5 to 80 K by monitoring thefrequency shift of the microwave cavity of a con-ventional EPR spectrometer operated at 9.2 GHz,the technique developed for the study" of super-conducting microbridges. The reasons for thechoice of these systems are threefold: (a} to study

the effects of elastic and inelastic conduction-elec-tron scattering processes on p; (b) to investigatethese effects both in materials that order anti-ferromagnetically and that are paramagnetic at alltemperatures; and (c} to systematically search forthe presence of any anomalous temperature behav-ior.

lgl-0)5

TbY PCW

Tb La P (C=0.&)C l-C

0.5

8 10 12 14 16T (K)

FIG. 1. Resistivity data (solid line, in arbitrary units)and theoretical curves (dashed line) for Tb~ Y&, P(c=0.2, 0.3, 0.5, 1.0) and Tbp iLap 9P.

15 3003

C. Y. HUANG, K. SUGAWARA, AND BERNARD R. COOPER

V}

C

1

U

I //

I

.575

20 40 60 80T (K)

r12-

„1Q-5

Q(0.2 Q4 G6 0.8

C

(b)I

1.0

FIG. 2. (a) Resistivity data (in arbitrary units) forTb~Y& ~As (=0. 2, 0.3, 0.4, 0.5, 0.75, 1.0). (b) Tem-perature at the resistivity maximum vs Tb concentration.

Our microwave resistivity data (in arbitraryunits) for Tb,Y, ,P and Tbo, La,P (relative to thatat T= 6 K} are shown by the solid curves in Fig. 1.(Note that the unit of the relative resistivity of agiven value of c is not related to those for differentvalues of c.} These curves are similar to those ofTb,Y, ,Sb given in Refs. 1 and 2. For pure TbP,the Noel temperature T„ is" 8 K, and hence T~ forthe diluted samples are below the temperaturerange studied. The curve for pure TbP exhibits aslight inflection near T~.

We have fitted our data for Tb,Y, ,P to the ex-pression first derived by Hirst"

where c is the concentration of the magnetic ions,A is a constant dependent on parameters describingthe conduction electron system and the s fexchange-constant, P(l} is the Boltzmann factor giving occu-pation of the crystal-field states lI), E», is theenergy difference between crystal-field states,J is the total angular momentum of the rare-earthion, and s is the conduction-electron spin. Equa-tion (1) has taken into account both elastic- and in-elastic-scattering effects in the first Born approxi-mation. These theoretical curves are shown by thedashed curves in Fig. 1. In order to obtain thesetheoretical curves, we have assumed the crystal-

field parameter x = -1.0 and have used the energylevel scheme as shown in the inset of Fig. 1. Thefittings yield the splitting between the I', groundstate and the I'4 first excited state b, to be 20 +2 Kfor c. = 1.0 and 18 ~ 2 K for c = 0.2, 0.3, 0.5 forTb,Y,+. These splittings are consistent with thevalue L = 18 K obtained from" the temperature var-riation of the EPR linewidth of Gd" doped in TbP.However, 6 for Tbp gLag 9P has been found to be14 + 2 K, somewhat lower than that for those sam-ples diluted by Y. This result is not surprising,since the lattice constant for" LaP (6.025 A} isgreater than those for TbP (5.686 A) and YP (5.662A). Hence, our data for the phosphides, like theantimonides, "' can also be interpreted in termsof the scattering processes in the first Born ap-proximation.

The most striking result of our experiments is,as shown in Fig. 2(a), the presence of an anomalousmaximum in the temperature dependence of p forTb,Y,~s for all c. Since T„=10.5 K for" TbAsand T„=5.5 K for" Tb, „Y,„As, magnetic order-ing does not occur in the temperature range studiedfor all the samples except for pure TbAs. The po-sitions of the anomalous maxima for various con-centrations shown in Fig. 2(a) are plotted in Fig.2(b). For c s 0.75, the maxima occur at - 8.5 K,which is about half of 6 expected for Tb" in TbAs.In the case of pure TbAs, the anomaly takes placeat T = 12.5 K, which is somewhat higher than thosefor the dilute samples. This may have to do withthe proximity to the Noel temperature (T„=10.5 K).

These anomalies in Tb,Y, Qs are similar tothose" in Pr,Y, ,Sn,. For Tb" and Pr", bothwith singlet ground states, the elastic channelsgiving the ordinary Kondo effect are ineffective.Such effects can only arise from excited tripletstates, and these have populations only at temper-atures well above where the elastic scatteringeffects would give ordinary Kondo anomalies inp(T) On the othe. r hand, the second-order inelas-tic scattering involving transitions for Tb" fromF, to F4 can be effective. This second-order effectgives rise to the Kondo sideband effect, which asdemonstrated by Maranzana and co-workers, " "often gives rise to maxima in p(T). Thus the ex-planation for the anomalous maxima may lie in theKondo sideband mechanism. However, if that isthe case, it is puzzling why the anomaly is absentin Tb,Y, ,P and Tb,Y, ,Sb. We do not believe thatthe complications in the sideband mechanism dis-cussed by Mott" for the case of CeAl, are apt toapply here since Tb" is a well localized 4f systemwith no reason for expecting valence fluctuationbehavior.

15 ANOMALOUS RESISTIVITY BEHA VIOR IN. . . 3005

*Work performed under the auspices of the U.S. ERDA.~Research supported by NSF Grant No. DMR-74-08033.~N. Hessel Andersen, P. E. Gregers-Hansen, E. Holm,F. Berg Ramusen, and D. Vogt, Proceedings of theInternational Magnetism Conference ICM-73, Moscow,USSR, Aug. ~973, (Nauka, Moscow, 1974)VI 234(1974); N. Hessel Andersen, P. E.Gregers-Hansen,E.Holm, H. Smith, and O. Vogt, Phys. Rev. Lett. 32, 132{1974).

2N. Hessel Andersen, P. E. Lindelhof, H. Smith,O. Splittorff, and O. Vogt, Phys. Rev. Lett. 37, 46(1976).

3A. I. Abou Aly, S. Bakanowski, N. F. Berk, J. E. Crow,and T. Mihalisin, Phys. Rev. Lett. 35, 1387 (1975).

4P. Lethuillier and P. Haen, Phys. Rev. Lett. 35, 1391(1975).

5S. Bakanowski, J. E. Crow, ¹ F. Berk, and T. Mihali-sin, Solid State Commun. 17, 1111(1975).

6K. Andres, J. E. Graebner, and H. R. Ott, Phys. Rev.Lett. 35, 1779 (1975).

7K. Sugawara, C. Y. Huang, and B. R. Cooper, SolidState Commun. (to be published).

8K, Sugawara and C. Y. Huang (unpublished).

9K. Sugawara, C. Y. Huang, and B. R. Cooper, Phys.Rev. B 11, 4455 (1975).F. J. Rachford and C. Y. Huang (unpublished). AlsoF. J. Rachford, Ph. D. thesis (Case Western ReserveUniversity, Cleveland, 1975} (unpublished}.G. Busch, P. Schwob, O. Vogt, and F. Hulliger, Phys.Lett 11 100 (1964)

~2L. L. Hirst, Solid State Commun. 5, 751 (1967). Theformula used in Ref. 1 is identical to Eq. (1).

~3K. Sugawara, C. Y. Huang, and B. R. Cooper (unpub-lished).

4A. Iandell. i, Rare Earth Research, edited by E. V.Kleber (Macmillan, New York, 1961), p. 135.G. Busch, O. Vogt, and E. Hulliger, Phys. Lett. 15,301 (1965).This value was computed using the procedure used byB. R. Cooper and O. Vogt, Phys. Rev. B 1, 1218(1970).' F. E. Mananzana, Phys. Rev. Lett. 25, 239 (1970).K. H. J. Buschow, H. J. van Daal, F. E. Mananzana,and P. B. van Aken, Phys. Rev. B 3, 1662 (1971).

9F. E. Mananzana and P. Bianchessi, Phys. StatusSolidi B 43, 601 (1971).N. F. Mott, Philos. Mag. 30, 403 (1974).