PHYSICAL REVIEW B VOLUME 22, NUMBER 7 1 OCTOBER 1980

Electrical resistivity and antiferromagnetism of chromium-palladium alloysbetween 77 and 700 K

C. A. Moyer, Sigurds Arajs, and Asian Eroglu*Departs)le]tt of'Physi(. 's, ClaI ksoit College nf' Teehitolopv, Potsdai)l. New Yoik I3676(Received 23 February 1979; revised manuscript received 25 February 1980)

Electrical resistivity p has been measured as a function of temperature for binary chromium

alloys containing 0.99, 1.48, and 1.99 at. % palladium. The Neel temperature, determined from

the &l p/dT method, oscillates with palladium concentration, first decreasing to a minimum at—0.6 at. % palladium and then rising again to a peak at —1.5 at. % palladium. Similar behavior

is observed for the temperature coefficient of resistivity in the paramagnetic regime. We attri-

bute the initial decrease in both cases to competition between Fermi-surface nesting lnd

resonant scattering of band electrons from palladium impurities. The observed oscillations may

result from a small moment on palladium impurities coupling to the spin-density wave of the

host.

I. INTRODUCTION

It is well known that the itinerant electron antifer-romagnetism in pure chromium can be strongly influ-enced by dissolved solutes. One experimental tech-nique which is particularly useful for exploring thegeneral features of the above antiferromagnetism isthe electrical resistivity. For this reason, we havebeen investigating this property on all binary chromi-um alloys containing elements soluble (I at. % ormore) in chromium. In this paper we report suchmeasurements on the chromium-palladium system.In general, very little has been done on these alloys.The only known previous study is by Noor andBooth' who investigated the electrical resistivity andmagnetic susceptibility of dilute chromium-palladiumalloys and found that the Neel temperature exhibits aminimum below 1 at. % palladium.

and 700 K. The insert in Fig. 1 presents the residualelectrical resistivity po determined at 4.2 K, as a func-tion of palladium concentration. The straight line,whose slope is about 5.8 p, Ocm/at. % palladium, con-firms the good quality of the prepared alloys.

The p,„„,(T) curves in Fig. 1 are typical plots foritinerant electron antiferromagnets with incommensu-rate magnetic structure. The anomalies are caused bythe antiferromagnetic paramagnetic transitions. TheNeel temperatures can be conveniently determinedfrom the d p,„„,(T)/dT curves as temperatures where

II. EXPERIMENTAL CONSIDERATIONS

The chromium-palladium alloys containing 0.99,1.48, and 1.99 at. "/0 palladium were prepared by anarc melting method using procedures described be-fore. ' Details on the purity of chromium used formaking these alloys are also given in Ref. 2. Palladi-um of purity 99.99% was purchased from EngelhardIndustries, Inc.

The experimental facilities for determining theelectrical resistivity have been described elsewhere. "

E~~ 20-

CLXCb

12,—.

III. RESULTS AND DISCUSSION

tt4-

Figure 1 shows the measured electrical resistivity,

p,„„,(T), uncorrected for thermal expansion, as a

function of the absolute temperature T between 77

T (K)FIG. l. Electrical resistivity of chromium-palladium al-

loys.

22 3277

3278 C, A. MOYER, SIGURDS ARAJS, AND ASLAN EROGLU 22

this derivative has its minimum value. The resultsare summarized in Table I and Fig. 2. Figure 2 alsosho~s the values of T~ obtained by Noor and Booth. '

Two observations can be made at once. First, the T~determinations by the dp, „„(T)/dT method by us arein good agreement with the susceptibility values. .

Second, the T& versus palladium content curve notonly shows a minimum but exhibits an oscillatorybehavior, i.e., the minimum is followed by a max-imum at about 1.5 at, %. The only other binarychromium system which shows such characteristicsare the chromium-cobalt alloys. 4

According to Fedders and Martin, ' the Neel tem-perature of dilute chromium rich alloys is given by

3/0

T~ 2eo-

250

~ Noor and Booth~ This study

1 2

Pd content (at.%)

T =Oexp( —I/X)

TABLE I. The Reel temperature Tz and electrical resis-tivity coefficient A for dilute chromium-palladium alloys.

c (at. % Pd) A (10—6]K2)

0.000.991.481.99

312306310302

—0.128—0.237—0.207—0.296

0.999 940.999 870.999 270.999 75

where 0 and A. are parameters which depend uponthe host band structure. The quantity A. for anitinerant two-band antiferromagnet is a function ofseveral factors, but is most sensitive and proportionalto the interaction area for the two nesting Fermi sur-faces. Presumably palladium, which lies four placesto the right of chromium in the Periodic Table, wouldact as a strong electron donor when substituted in thechromium matrix, thus improving the nesting ofelectron jack and hole octahedron and increasing T~.

The chromium-palladium system is anomalous in

that T& initially decreases even though electrons areadded. Two competing mechanisms are indicatedhere: in addition to the nesting effect there appearsto be unusually strong impurity scattering which, byitself, is known to decrease T~. Similar anomaliesobserved in chromium alloys containing smallamounts of iron, cobalt, and nickel have been attri-buted by some to resonant scattering of the bandelectrons by the dissolved solute. ' We believe thesame interpretation applies to our chromium-palladium alloys. In particular, a scattering resonancein the electronic spectrum of the alloy somewhatbelow the Fermi energy of pure chromium wouldcapture (into virtual bound states) some of the hostband electrons as well as any additional electronsdonated by palladium impurities. The result wouldbe a net reduction in the number of itinerant elec-trons, a smaller degree of nesting, and a lower Neel

FIG. 2. The Heel temperature of chromium-palladium al-

loys.

temperature. This process would continue only solong as the Fermi energy of the alloy EF exceeds theresonance level E, of the impurity scatterers; ulti-mately EF becomes pinned somewhere near E„and,in the absence of other mechanisms, T~ should leveloff. However, the increased Coulomb repulsion ofthe electrons "piled up" in virtual bound states atthe impurity sites further serves to decrease T&, evenbeyond the concentration needed for pinning the Fer-mi energy.

This resonance model accounts qualitatively for allbut the observed rise in T~ again at —1.5 at. %.Such behavior is strikingly similar to that observed inchromium-. cobalt alloys, and the same explanationshould apply, i.e., we attribute this rise to impuritymoments coupling to the host spin-density wave.These moments likely accompany the formation ofvirtual bound states. Based on his susceptibility in-vestigations, Booth has dismissed the idea of localmoments on palladium impurities in chromium. Wenote, however, that even a small moment could ac-count for the slight rise of T+ from a minimum 306K at —1.0 at. % to a maximum 310 K at —1.5at. %—a swing of only 4 K. By comparison the T~ ofchromium-cobalt alloys swings some 55 K from aminimum 270 K at —1.5 at. % to a maximum 325 Kat —3.1 at. %. According to Shibatani the impuritymoment enhancement of T~ for itinerant antifer-romagnets goes roughly as (JS)' where S is the im-purity spin and J its coupling strength to the spin-density wave (SDW). From the known cobalt mo-ment in chromium —2.8p, a, and assuming equalcoupling strengths, we would predict a palladium mo-ment —0.7 p, ~ based on the swings in T&. Our esti-mate is very crude; unequal coupling strengths couldeasily reduce this value by a factor of 2. Moreover,if, as we believe, the palladium moments result fromthe population of virtual bound states, T& could beaffected indirectly via exchange splitting of theresonant level. This would shift the Fermi energy ofthe alloy, with T~ changing accordingly. If anything,

ELECTRICAL RESISTIVITY AND ANTIFERROMAGNETISM OF. . . 3279

then, our analysis probably overestimates the mo-ment size. Given the difficulty in analyzing thehigh-temperature susceptibility of chromium alloys, itdoes not seem impossible that impurity moments upto at least several tenths of a Bohr magneton mightgo unnoticed.

Further information concerning the electronicstructure of our. alloys can be had from the resistivitydata in the paramagnetic regime above T~. Atelevated temperatures, i.e. , for T )& T&, it is reason-able to assume that p(T) —po= p, ~ results primarilyfrom the s —.d type electron-phonon scattering, i,e.,

d'Ng

Ng dE21 2 2 1 dNdA= —eke 3

Ng dEE FF

where kq is Boltzmann's constant, Nq the density ofd-electron states, and EI: the Fermi energy. In ouranalysis we also have employed an alternate form for

eQ 1 dN 6 eQ e dQ2T N dE ~k )2T 2T dE

p, ,/T = const(1+ 6yn T ) (1 —AT)'

The quantity p( T) is the total electrical resistivitycorrected for thermal expansion, o. the coefficient oflinear thermal expansion, and y the Gruneisen con-stant, Aside from thermal expansion effects, thedeparture of p(T) from linearity at high temperaturesis determined by A, a quantity whose value is fixedby the electronic band structure of the alloy, andwhich may be positive or negative, Jones' gives forA

I

This implies that plots of B/T' vs 1/T' should bestraight lines, from which one could determine thequantity A. In our previous work on the chromium-gold alloys, we found that the straight-line behaviorwas observed not only in these alloys but also in purechromium for T & 450 K. The chromium-palladiumalloys behave in a similar fashion for T & 500 K.Figure 3 shows this behavior for all our alloys. Thequantities o. and y needed for the calculations of 8were obtained from Refs. 11 and 12, respectively. Atlower temperatures deviations from the straight lineare observed (not shown in Fig. 3) which result froma precursor effect" associated with the onset of anti-ferromagnetism. A least-squares fit to the data ofFig. 3 gives the values for A listed in Table I. Alsotabulated there are the linear correlation coefficientsR, from which it is apparent that the data folio~closely the straight-line behavior predicted by Eq. (7).

From Table I we see that values-of A, as for thechromium-gold system, are negative. The quantity A

as a function of palladium concentration is shown inFig. 4. For the chromium-gold alloys, A decreaseslinearly with the gold content; in contrast, the plot ofA versus palladium content is oscillatory, with A

reaching a local maximum at —1.5 at. %. The gen-eral behavior of A is consistent with that of T~ notedearlier, suggesting that both anomalies are due to thesame underlying mechanism, viz. , the formation ofvirtual bound states accompanied by local momentson the impurity atoms. To our knowledge, the effecton A of impurity moments has never been investigat-ed; the solid line in Fig. 4 is the prediction of Eq. (3)when only resonance scattering is operative. Specifi-cally, we used

(4) Ng ( E ) = N~~ ( E) + 8N ( E ) (9)

which follows from the well-known theoretical rela-tion between conductivity cr and thermoelectricpower Q:

n kaT3e dE

E EF

Equation (4) is interesting in that it relates A toanother measurable property Q, but its usefulness islimited since thermopower data on alloys are oftenunavailable,

In Ref. 2, we have shown that, using the first-order approximation for the thermal expansion ef-fects, i.e.,

where Nq is the host density of states and 5N thechange due to alloying. %'e approximated Nq with

p(T) = p, „p,( T) (1+n T)

the following equation is valid:

B/T'=const(1/T' —A )

where

(7) 2

1/$ {~P6 K j

p, „p,(T)(1+nT) —po

1+6o.y T(g)

FIG. 3. The quantity B/T as a function of 1/T ofchromium-palladium alloys.

3280 C. A, MOYER, SIGURDS ARAJS, AND ASLAN EROGLU 22

the first three terms in a Taylor expansion aroundEF, the Fermi energy of unalloyed chromium; for SNwe took the form expected near a scattering reso-nance'

SN (E) =(E —E,)'+ (V/2)'

(10)

which is consistent with the assumed form Eq. (9)for the alloy density of states. Here Sn (=4) is thenumber of electrons donated to the host per palladi-um atom. The solid curve of Fig. 4 was generatedusing the values E, —EF = —0.21 eV, I =0.22 eV,and Sn, = 6 (as befits a d resonance split by the cubiccrystalline field of the chromium lattice). The differ-ence between this and the experimental points, then,is the contribution to A from the presumed palladiummoments and, again, may reflect some exchangesplitting of the resonant level.

The resonance parameters obtained from the datafit in Fig. 4 may not be reliable, since Eq. (3) as-sumes the energy dependence of o.(E) enters solelythrough the state density N&. This is not exact andprobably exaggerates the variation of A, especiallynear resonance. In turn, the use of Eq. (3) leads toI values which may be too large. To remedy thiswould require an adequate theory for A in transition-

E„and I are the position and width of the resonance,respectively, 5n, its degeneracy, and c the solute con-centration. The Fermi energy in the a11oy EF wasfound from

N (EF)(Eq —EF)=Snc+ arctan0 0 Sn, c r7r 2(E, -E, )

metal alloys, but any such theory must overcomemany difficulties, both conceptual and computational.The complexity of the problem is evident from ourexpression for 3 in terms of thermopower Q [Eq.(4)]. We need only remark that the thermoeiectricpower of transition metals and their alloys is, at best,only qualitatively understood at the present time.Nonetheless, Eq. (4) affords an alternative computa-tional method for 3 if thermopo~er data for-thechromium-palladium alloys were available. Alas,this, too, is not the case. However, such data havebeen reported for chromium and some chromium-ruthenium alloys, thus enabling us to calculate A

from Eq. (4) at least for pure chromium. " We esti-mate from the data of Ref. 16, Q/T = 0.026 p, V/K'and dQ/dc = —0.877 pV/Kat. % at T =727 K. As-suming the addition of ruthenium donates two elec-trons per impurity atom to the Fermi sea, and takingfor the chromium density of states No(EFO) =1.28/eVatom, "we find

= -0.0771 dT O'EF o

F

expressed in pV/K'. Even for pure chromium, theslope of the density of states at the Fermi leveldN/dE is not known accurately. Substituting the

EF0

above values and the measured value for A fromTable I into Eq. (4) gives

—7.81 dN

N dE EO

in eV '. This can be compared with rough estimatesmade from the band-structure calculations of Yasuier aI, ".

—1.21 dN

NdE 0F

again in eV '. In view of the many approximationsinvolved, the agreement should be considered en-couraging.

2

io

Pd content (at.%)

FIG. 4, The quantity A of chromium-palladium alloys.The solid curve is the theoretical prediction of Eq. (3) as-

suming resonance scattering; experimental values are denot-ed by ~ .

IV. SUMMARY

In summary, we conclude that the high-temperature-resistivity data of our chromium-palladium alloys follow the form expected on thebasis of the s-d scattering mechanism. Moreover,the initial-decrease with palladium content of theresistivity temperature coefficient 3 and the Neeltemperature T& is consistent with the existence of ascattering resonance in the electronic spectrum ofthese alloys somewhat below the Fermi energy ofpure chromium. It is suggested further that theanomalous oscillations of 3 and T~ with palladiumconcentration are signatures of the existence of asmall magnetic moment on the palladium impurities.

22 ELECTRICAL RESISTIVITY AND ANTIFERROMAGNETISM OF. . .

ACKNOWLEDGMENTS

3281

The authors are grateful to the National Science Foundation and the Research Corporation for the support ofthis work.

*Present address: Ege University, Bornova-lzmir, Turkey.'S. S. Abdul Noor and J. G. Booth, Phys. Lett. A 43, 381

(1973).A. Eroglu, S. Arajs, C. A. Moyer, and K. V. Rao, Phys.

Status Solidi B 87, 287 (1978).3S. Arajs, K. V. Rao, Y. D. Yao, and W. Teoh, Phys. Rev. B

15, 2429 (1977).4S, Arajs, G. R. Dunmyre, and S. J. Dechter, Phys. Rev.

154, 448 (1967).5P. A. Fedders and P. C. Martin, Phys. Rev. 143, 245

(1966).J. Zittartz, Phys. Rev. 164, 575 (1967).S. N. Behera and K. S. Viswanathan, Can. J. Phys. 47, 477

(1969}.8A. Shibatani, J. Phys. Soc. Jpn. 31, 1642 (1971).J. G. Booth, J. Phys. Chem. Solids 27, 1639 (1966).

' H. Jones, in Encyclopedia o/'Physics, edited by S. Fluge

(Springer-Verlag, Berlin, 1956), Vol. 19, p. 227.''Atnerican Institute of'Physics handbook, 3rd ed. (McGraw-

Hill, New York, 1972).' K. A. Gschneidner, Jr. , in Solid S(ate Physics, edited by F.

Seitz and D. Turnbull (Academic, New York, 1965), Vol.16, p. 412.

' C. H. Chin, M. H. Jericho, and R. H. March, Can, J. Phys.49, 3010 (1971).

'4J. Callaway, J. Math. Phys. 5, 783 (1964).'5We assume that the main alloy contribution to 0 in dilute

Cr-Ru alloys results from Fermi-level shifts.'6T. F. DeYoung, S. Arajs, and E. E. Anderson, J. Less-

Common Met. 29, 93 (1972).'~F. Heiniger, E. Bucher, and J. Muller, Phys. Kondens.

Mater. 5, 243 (1966).'8M. Yasui, E. Hayashi, and M. Shirnizu, J. Phys. Soc. Jpn.

29, 1446 (1970).