TEMPERATURE DEPENDENCE OF THE ELECTRICAL RESISTIVITY OF (V1-xCrx)3Si SINGLE CRYSTALS

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TEMPERATURE DEPENDENCE OF THE

ELECTRICAL RESISTIVITY OF (V1-xCrx)3Si

SINGLE CRYSTALS

K. Berthel, B. Pietrass

To cite this version:

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JOURNAL DE PHYSIQUE _{Colloque C6, suppldment au no 8, Tome 39, aofit 1978, page}

_C6-383

K.H. Berthel and B. Pietrass

Zentralinstitut ftlr FestkBrperphysik und Werkstofforschung der A& der DDR, 8027 Dresden,DDR

Rlsum6.- Nous avons mesur6 la rbsistivitg de la phase (VI-XCrX)3Si monocristalline (x = O...l) entre 4,2 K et 400 K. Lorsque la concentration de Cr augmente, la resistance P basse temperature Bvolue continuement de p ~ ~ ( x = O ) 1 @T5 (x=l). Les rlsultats sont discutBs dans le cadre d'un modile P 2 ban- des (s-d) avec un pic logarithmique pour la densitl d'ltat de la bande d. Le modile dlcrit la discon- tinuitd observle dans la pente de la rlsistivitd 1 la transition de la phase cubique 1 la phase t6tra- gonale dans V,Si, ainsi que les dlviations 1 la linBarit6 observBes 1 hautes tempgratures.

Abstract.- Theelectrical resistivity of single phase (VI-xCr,)gSi single crystals (x = 0...1) has been measured between 4.2 K and 400 K. With increasing Cr-content the resistance at low temperature changes continuously from p~~ (x=O) to p T 5 (x=l). The experimental results are discussed on the basis of a two-band (s-d) model with a logarithmic peak in the d-band density of states. The model describes the observed discontinuity in the slope of the resistivity at the cubic-tetragonal phase transition in V3Si as well as the deviation from linearity at higher temperatures.

EXPERIMENTAL RESULTS.- The investigation of the electrical resistivity of A15 intermetallic com- pounds can contribute to a better understanding of the electronic structure of these materials which have attracted much interest because of their unu- sual properties/l,2/. The V3Si and (Vl-xCrx)3Si single crystals used in our measurements were 0.5 cm in diameter and of 5 cm length/3/. The electrical resistivity was determined by dc current potentio- meter methods. In order to measure the resistance of superconducting samples below Tc a longitudinal magnetic field up to 190 kG was applied. The residual resistance ratio of the best V3Si single crystals reached values R(300K)/R(17,5K) 2 80.

In figure 1 experimental results are given of the temperature dependent par pi = p-p of the resistivity of (V Cr ) Si single crystals between

I-x x 3

4.2 K and 400 K, where pr is the residual resistance. With increasing Cr concentration the superconducting transition temperature Tc decreases and the resistivity curves are changing substantially. The magnitude of the temperature dependent part and the bending of the resistivity curves at room temperature decrease. In particular, the T2 and T~ dependent parts of the resistivity become smaller. For

creased oxygen content (sample 4). Increasing deviation from the stoichiometric composition increa- ses the residual resistivity p and decreases the lattice transformation temperature T as well as

m

the magnitude of the kink in the resistivity curves at Tm. Oxygen impurities also increase the residual resistance, and the kink at T but they do not chan-

m ge T essentially.

m

DISCUSSION.- The experimental results are discussed within a simple two-band model. For this purpose the

traditional s-d-model/4/ has been modified to inclu- de the sharp peak in the d-band density of states near the Fermi-energy. Assuming a logarithmic peak

151,

D~(E)%~~(E~/

1

E

1

)

,

with the cut-of f energy Ec, the resulting expressions allow to fit the observed temperature dependence of the resistivity, in particular the deviation from the linear behaviour above % 200 K and the anomalous behaviour at the cubic-

tetragonal lattice transformation.

Under the influence of a tetragonal deformation the peak in the density of states splits up in two peaks,

CrgSi a T' law the resistivity has been found

where the splitting energy 3A is proportional to the at low temperatures.

magnitude of the tetragonal deformation. For the In figure 2 the temperature dependence of the

residual resistivity we find the expression resistivity near the cubic-tetragonal lattice

2 p+A 1 p-2A

+

7 s(T)9s(T)}

transformation is shown for V3Si-samples of diffe- Pr = pO+pl"n T (2)

rent stoichiometry (salnples 1, 2 and 3) and with in- where is the chemical potential and and are

(3)

constants. The monotonic function S(x) introduced by Gorkov/5/ is proportional to -x2 for x?O and has the asymptotic behaviour S(x)bln(l. 13

1 XI

) for

1x1 j r n

Fig. 1 : Temperature dependent part of the electrical resistivity pi = p(T)-pr of (Vl-xCrx) Si single crystals. : (I) x = 0, Tc = 16.7 K, or<] pdcm ; (2)

x = 0.05, Tc = 14.7 K,pr = 37 pncm ; (3) x = 0.2, Tc =8.4 K,p, =

41

W c m ; (4) x = 1, Tc<O.l K, pr=2 pacrn.

It is noted that due to the narrow peak in the density of states the residual resistivity depends on temperature, directly as well as indirectly over the chemical potential and the spontaneous tetragonal deformation.

Necr T where A/T is small, the residual m

'

resistivity (2) can be expanded in powers of A/T. To second order we find

p, = pr(A=O)+pI ($)2~'7

($1

+.

. .

(3)

Fig. 2 : Reduced resistivity ratio Ar(T) = {R(T)- R(17,5 ~)}/{~(293 K)

-

R(17,5 K)} as function df T~

of V3+ySil-y single crystals, both without and with 02 impurities : (1) yLO.001, r" : 0.015, Tm=22.3 K; (2) y=0.003, rX=0.032, T,=21.2

K,

(3) y=0.010, rx0.078, no lattice transformation

;.

(4) g=0.04, rX=0.14 (oxygen impurities), Tm=20.7 K. (r = R(17.5 K)/(R(293 K)

-

R(17.5 K)).

the tetragonal deformation. Moreover, it is negative if the Fermi energy is near the center of the peak in the density of states (

I

EF

I

/Tm 6 1 )

.

Hence, we conclude that (3) describes well the experimental facts expressed in figure 2.

The authors wish to thank Dr. M. Jurisch and G. Behr for the preparation of the siqgle crystals.

References

/I/ Weger,M. and Goldberg,I.B., Solid State Phys. 28 (1973) 1

-

/2/ Milewits,M., Williamson,S.J. and Taub,H., Phys. Rev.

B13

(1976) 5199

/3/ Jurisch,M., Berthe1,K.H. and Ullrich,H.J., Phys. Status Solidi (a)

66

(1977) 277

/4/ Wilson,A.H., The Theory of Metals (Cambridge) 1954

/5/ Gorkov,L.P.and Dorokhov,O.N., J. low Temp. Phys. 22 (1976) 1