Field-induced renormalization observed by magnetoresistance in CeRu2Si2

Solid State Communications,Vol. 95, No. 7, pp. 449-453, 1995 Elsevier Science Ltd

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FIELD-INDUCED RENORMALIZATION OBSERVED BY MAGNETORESISTANCE IN CeRupSip S. Kambe*l, H. Suderowl, J. Flouquetl, P. Haen*, and P. Lejay* lD&partement de Recherche Fondamentale sur la Mat&e Condens&, SPSMS/LCP, CEA/CENG, 38054 Grenoble-Cbdex 9, France *Centre de Recherches sur les Tr+s Basses Tern &atures**, C.N.R.S., BP 166, :38042 Grenoble-C&dex 9, ! rance (Received 8 November 1994; revised version received 28 March 1995 by P. Burlet)

Keywords : Electronic transport, Heavy fermions.

1. Introduction The ph sical properties of the heavy fermion compoun dyCeRu$& which possess the tetraBonal ThCr2Si2 structure have been widely studied m the past few years. Specific heat measurements revealed that fairly lar e effective masses exist in this compound (r = 35 8 mJ/mol.K2)‘~*, caused by strong correlation effects between f-electrons. Neutron scattering studie@ have shown that incommensurate antiferromagnetic correlations develop at low temperature, suggesting this compound is close to a ma may instabihty. Actually, a recent muon study 5gnebc show the existence of small static magnetic moments below 1.5 K. On t+ other hand the static susce tibility is largely amsotro pit (Xc/& = 15-20pt7 anZof Isine character at low temperature. The above proe&es indicate that a strong competition between R ondo effect, RKKY interactions and crystal field effects occurs in this compound. The most striking feature seen in the properties of CeRu2Si2 is the occurrence of a metamagnetic-like transition (MT) at low temperature6 when the field is applied parallel to the c-axis. The value* of the MT transition field B* is close to 7.7 T for T + 0. The effective mass of the renormalized quasi-particles derived from specific heat* and magnetization8 measurements increases with increasmg field below B*,

then decreases above B*. Although no satisfying mo-

del has been proposed so far for the MT, it is obvious that this behavior cannot be explained by a single site Kondo picture and that intersite magnetic correlations must be considered. Since de Haas-van Alphen effect measurements9-1* confirmed the presence of a strongiy rertormalized Fermi surface below and above B*, a Fermiliquid model can be applied to the ground state of CeRu2Si2. In such a heavy fermion system, the resistivit usually exhibits a quadratic behavior (p = po+x p) in the coherent repon, where the maP?de of the A term is considered to be correlate with enormalized electron mass. In fact, the relation A = Y is oredicte83 on the basis of the Fermi-liauid ‘ictur& oflthe periodic Anderson model for strofigl ocalized f-electrons. In the present study we wl*H confirm that the resistivity of CeRu& exhibits a uadratic behavior whatever is the magnetic field LB4. \- .- ,-

r;p”

P

*Permanent address : Institute for Solid State Physics, Univ. of Tokyo, Roppon *, Tokyo 106, Japan. **Laboratoire asso& a P Universite Joseph Fourier, Grenoble.

crystal of CeRu2Si2 was grown by i technique in a three-arc furnace 449

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FIELD-INDUCEDRENORMALIZATION here with Ce, Ru and Si N, 5 N and 5 N, respec-

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7.5T

200 H

3. Results and Discussions The room tern erature (RT) resistivity observed here (- 120 and 5B u&m for p // a and p // c, respectively)‘are in ood agreement with those revibusly renorted@J@ within some error bar resu Ptine from thk measurements of the sample dimentions;es eciall the distance between the voltage contacts. #he rest*Bual resistivity (po) is - 0.4 @cm and - 0.3 p&m for j // a and j NC, respectively ; for j // a, this leads to a RRR (ratio between RT value and pe) larger than 300, comparable to those reported [12] for the best CeRuzSiz samples. Figures la and lb show the field de ndence of the resistivitv at different temperatures F. or I// a and j // c, respectivily. The soldering material used in the oresent studv becomes suoerconductine below 7.2 K. due to some’ free Pb and has a small”critica1 field: (e uivalent to a variation in However, no anomal detected at low field in the contacts distances Pbe can the magnetoresistance curves of Figs. la and lb. The MT manifests itself bv a maximum at 7.7 T f= B*) for both directions, as pr&iously reported@ (except ‘that the values of B* reported in ref. 6 for a sample of higher p. seemed- to stay around 8 T do&n to 70 mK). However. our results show some features not observed in the previous studies. For j//a (Fi . la), at 1 K p increases rather suddenlv around P.5 T: then it is almost linear with B bedeen 2.5 and 55T and finally increases very fast between 7 T and B’. These features disappear at lower temperatures and the variation of p vs. B becomes quite smooth below 0.2 K. Thus, contrary to what the authors of ref. 9 deduced from a 0.5 K curve, p does not follow a B1.7 variation up to 6.5 T below 1 K. In all cases, p varies like 82 below about 1 T. Figure la also shows that for i // a the resistivitv at B+ IS auite much larger than in’&ro field : by a factor of 3.8,3.5 and 2.9 at 1 K, 0.7 K and 20 mK, respective1 p(B*)/p(B=O) values reported in ref. 6 for a with p. = 1.5 @cm were only 2.5, 1.8 and 1.13 K, 0.7 K and 70 mK, res ctively. At 0.5 K we find p = 0.55 @cm and p( Er )/p(B=O) = 3.3, while from ref. 9, for a sam le with ~(0.5 K) = 1.6 &Ian, p(B*)/p(B=O) is only oY the order of 1.8. This shows that the enhancement at 8’ is strongly reduced on increasing pc$. The behavior for j // c (Fig. lb) sensibly differs from that ford // a :g increases quite slowly with B up to about T, an seems less peaked at B*. The ratios p(B*)/p(B=O) are close to 1.6 at 1 K and 0.5 K

2T

180

and c-axis, respectively were spark cut frc?m this crystal for resisuvity measurements. rformed using a The latter measurements were conventional four leads method. E ads were soldered to the sam les in order to get low contact resistance (c 0.05 K at 300 K). The samples were placed onto a co per sam le holder insulated by a 5 pm kapton fo g and the Peads thermally anchored to this sample holder. The latter was then scrued to the n&&g chamber of a dilution refri erator equiped with a suoerconductine maenet of 9 %. A low-temnerature tra‘mformer a&a lorkk-in am lifier were uied to improve the signal to noise leveP ( 0.05 pR could be detected with a current of 10-SA).

r

n

OT

170

140 : 1

j

1. Field de a-axis and b : j

c-axis in single

trsudi~,the temperature range (AT) in which a quadratic behavior is observed mcreases on increasin the characteristic spin fluctuation energy (k$P).16#9 7 Thus, AT is supposed to be the shortest at the MT where an enhancement of the spin fluctuations is ex cted. In the rsent study, howy AT, thus .T* I;fas no clear eld dependence (FI . 3). Indeed, u&astrc neutron scatterin studies4 dr not probe any enhancement of the spin % uctuations at the MT. However, the latter measurements were performed only down to 1.4 K. In contrast to those, magnetostrictron studiesaJ8J9 suggest the existence of a auantum fluctuation reg&for the MT below 358 mK. The quasi-invariance of AT with B emnhasizes the kev role of the volume effect at 8”. Thebr e difference in the temperature variation of the drf*Berential susceptibility measured at different fields is governed by the large variation

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FIELD-INDUCED RENORMALIZATION

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4

6

8

10

0.01

0.1

10

100

&,

H(T)

19.75 K -

Fig. 4.

12)c. 9K

1

a” -0.15 -0.2

Fig. 2. Tern rature dependence of the resistivit in constant fie $d for a) : j // a-axis and b) : j // c-axis. 1;he residual resistivity has been subtracted.

of the magnetostriction at B* while the specific heat and the resistivity show a smooth temperature variation with the applied magnetic field. Fi ure 4 shows the field dependences of & and Ac,B e A term for j // a and ’ // c, respectively. These two variations are quite drf*/ erent. At this point, one must notice that the uncertainty in the absolute values of the resistivi , due to the error made in measuring the size of ttZe samples as mentioned above, induces a similar relative uncertainty on the values of Aa and Ac. However, except erha s for the zero field values, the differences in la ang Ac are much

for heavy fermion compoun & > & implies that in zero field the renormalized mass is lar er along the a-axis. Strictly speaking, the averaged e t9ective mass shows this amsotropy because every sheet of the Fermi surface can contribute to the resistivit Recent band calculations21 and de Haas-van Aphen effect measurementsl**** have confirmed the presence of four hole and one multi ly-co~ected electron sheets at the Fermi surdominant face. Irn ong them, the thermodynamically sheet is considered to be the largest hole sheet which has a larger effective mass along the a-axis, while the other sheets have the opposite anisotropy. Therefore, the transport properties may also be governed donu-

nantly by this sheet, which seems to be confirmed by the resent results. I% e renormalization effects in CeRupSip strongly depend on the field. The A term increases with mcreasing field below the MT and decreases above the MT, in good agreement with s cific heat*, magnetizations and magnetostrictionJ% results. A remarkable fact in the resent study is that the enhancement of A is fairly Parge for j // a as compared with j // c (Fig. 4), indicating that the field-induced renormalization at the Fermi surface is anisotropic. This anisotropy can be attributed to the existence of several Fermi surfaces with different topology. However, such a topolo ical effect of the Fermi surface on the temperature Bependence of the ma not straightforward to understand. sence case we will regard the field-de A term as a consequence of a field-in lization effect. Since the MT occurs only when the field is applied along the c-axis, one can consider that the observed anisotropic renormalization is correlated with the anisotropic magnetic behavior in the In order to clarify this behavior theoretiorbital degeneracy of the f-electrons and stal field effect have to be included in the vans** succeeded

to ex

results with ma

A=&,

(1)

where Ak is the imaginary art of the f-electron self energy (the dumping rate o P f-electrons). If the valence fluctuation of the f-electrons is small and if Ak has no kdependence, we can obtain the following relation : +=Y.

(2)

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-_AA~d

g “O

0.1

I T(K)

CeNiSn 1

IO

100

Fig. 5. Field dependence of Aav as determined from eq. 3. The dashed line shows the value of dH)/y(O) estimated from magnetization measurements8 via a Maxwell relation.

0.1

1

T(K)

IO

100

Fig. 4. Field dependence of A for j // a-axis and j // c-axis. The value of A is estimated by a fitting procedure of the quadratic region in Fig. 3. The dashed lines are guides to the eye.

In the present case, Ak is considered to be anisotropic and y robes the average value of the renormalization e Rect over the Fermi surface. In tetragonal symmetry, the y term can be expressed approximately by the following equation : Aav=(2+G+GQ/3=~.

(3)

Figure 5 represents the field dependence of Aa”. This figure also shows for corn arison the relative variation of y (dotted line) de Buced from magnetization measurements8 below 1 K a pl ing a Maxwell relation. Although the peak at #e R[IT is rather broader ‘tude of the mass enin the present case, the ma hancements (Aav(B*)/Aa,(&u and y(B*)/T(O)) are about the same. The agreement could even be better if one could leave apart the zero field Aav value. A similar variation of has been observed by specific heat measurements. I However, a quantitative comparison with the present stud is rather difficult because the measurements of re Y.2 were not performed below 1 K. The origin of difference between the )/$O) terms above the MT A&B)/Aav(0) and the is not clear so far. We %a ve to perform resistivity measurements in higher field in order to clarify tlus , equation 3 roughly holds below and lxxv; pewa M’ry thus we can consistently explain the relation betw&n A and y on the basis of a Fermi-

liquid model for the case of strong correlations if the observed field dependence of A is due to a renormalization effect. The itinerant f-electron model looks quite suitable in the present case, at least below the .lOtl* On the other hand, the observed relation A = y is based on a localized f-electron model. This is not surprising because CeRu& ma show both Kondo and valence fluctuation regime &r acters. On the basis of the de Haas-van Alphen effect results, Aoki et al. 10 have proposed that the contribution of the f-electrons at the Fermi surface drastically vanishes at the MT. However, the present results suggest that the renormalization effect due to felectrons decreases gradually above the MT. 4. Conclusion The temperature dependence of the resistivity in i2 is quadratic below - 0.3 K and the relation Ce of A 0~y roughly holds below and above the metamagnetic-like transition. The observed Fermi-liquid behavior at low temperature is consistent with the dia ram recently proposed.*3 The seudo-phase Held dependence oB the quadratic term coefficient A has been estimated for both j // a and j // c. On applying a magnetic field, the A term for j //a increases stron y as corn ared to that for j//c. This means that g field-lnc&ed renormalizatron shows an anisotropy, which seems to be coupled with the strong anisotropic magnetism in this compound. Neither any drastic change in the renormalization effect nor any indication for an enhancement in spin fluctuations can be observed at the metamagneuc-like transition in the present study. We now consider as very im ortant to clarify the dynamical properties of Ce i u*Si* around the MT at very low temperatures.

Acknowledgements - The was grown by A. Verniere. Sam by F. Mallmann. He and Dr. their room temperature and wish to warml thank them. We are also very grateful to J.-M. Myartinod for help with the measurements.

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