Physica B 163 (1990) 606-608 North-Holland

NEUTRON S C A T T E R I N G STUDY OF M A G N E T I C F L U C T U A T I O N S IN C e I ~La~Ru2Si2(x = 0, x = 0.2)

L.P. R E G N A U L T ", J .L. J A C O U D ~, J .M. M I G N O T h'~, J. R O S S A T - M I G N O D ~, C. V E T T I E R d, P. L E J A Y and J. F L O U Q U E T ~ ~Centre d'Etudes NuclOaires, DRF/SPh-MDN, 85X. 38041 Grenoble Cedex, France bLaboratoire L~on Brillouin, CEN-S, 91191 Gif sur Yvette, France ~CRTBT, CNRS, 166X, 38042 Grenoble Cedex, France dlnstitut Laue-Langevin, 156X, 38042 Grenoble Cedex, France

We report neutron scattering experiments on single crystals of Ce~ xLaxRu2Si2 with x = 0 and x = 0.2. In CeRu~Si 2 the magnetic scattering is the superposition of two contributions: (i) a single site (q-independent) quasi-elastic contribution, and (ii) a strongly peaked inelastic contribution ascribed to magnetic correlations. The correlation lengths and the fluctuation rates of both contributions have been studied as a function of temperature. In Ce0sLa 02Ru2Si~, the quasi-elastic neutron scattering measurements as a function of temperature show the coexistence of strong magnetic fluctuations at low temperature together with the incommensurate long range order.

1. Introduction

In cerium intermetall ic compounds, the hybridiza- tion of f-electrons with electrons in the conduction band gives rise to various kinds of interesting phenomena . In particular a magnetic (M) or a non- magnetic (NM) ground state can be achieved at low temperatures , depending on the strength of the hy- bridization character ized by the so-called Kondo tem- perature T K. When increasing the hybridization, the ordered magnetic moment decreases gradually and a ground state without long range magnetic ordering ( L R O ) is finally reached. General ly compounds lo- cated at the borderl ine of the M - N M transition exhibit the so-called heavy fermion (HF) behaviour , characterized by a very large value of y, the linear term in the specific heat. This is usually attr ibuted to the formation of quasi-particles, having a very large mass compared with the bare electron mass. CeRu2Si 2 is certainly one of the most suitable representat ive of non-magnet ic H F compounds, with 7 = 385 mJ /KZ/mol [1,2] and T K = 2 5 K [3, 4]. The substitu- tion of a small amount of Ce by La in Ce~ LaxRu2S i 2 drives the system from a short-range correlated ground state to a long-range ordered ground state above x ~> 0.08 [5]. This cross-over has been extensive- ly studied by various techniques [2, 6]. In this paper we have focused our at tention on the well-representa- tive compounds CeRu2Si 2 and Ce0sLa02Ru2Si 2, which are located on both sides of the NM-M bor- derline.

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2. Experimental

The ternary (Ce, La)Ru2Si 2 crystallizes in the well- known tetragonal structure with space group I 4 / m m m and lattice parameters a = b = 4 . 1 9 7 , ~ and c = 9.797 A. Large single crystals of about 0.5 cm ~ have been grown in a three-arc furnace using the Czoch- ralski method. Neutron scattering experiments have been carried out on various spectrometers at ILL reactor (IN3, D10), L L B / O r p h e e reactor (4F1) and C E N - G / S i l o e reactor (DN3) . The experiments were performed in the constant k~-mode, with k. = 2.662 A 1.

3. CeRu2Si 2

Previous inelastic neutron scattering (INS) experi- ments at low temperatures ( T / T K = O . 0 5 ) have re- vealed the existence of incommensurate magnetic cor- relations in the H F regime ( T < T*), peaked at two different wave vectors k 1 = ( 0 . 3 , 0 , 0 ) and k 2 = (0.3,0.3, 0) [7]. We have shown that the magnetic response at low temperatures can be described by the superposit ion of two different contributions [4, 8]: i) a localized one, q- independent , arising from the single site (SS) Kondo-type fluctuations which is well de- scribed by a quasi-elastic Lorentzian function in ener- gy, with a fluctuation rate Fss = 2 meV at T = 1.5 K (T~ ~-- I s s / k ~ ) . ii) An inelastic contribution, peaked at the wave vectors k~ and k 2 and at an energy, weakly

L.P. Regnault et al. / Magnetic fluctuations in Ce~_ ~La~Ru2Si 2 (x = O, x = 0.2) 607

dispersed, h w o = 1.2 meV. This last contribution is as- sociated with short range magnetic correlations arising from intersite (IS) magnetic interactions. The charac- teristic damping parameter is F~s =0.9meV. More- over, the relation I]s(q)- Xis(q)= constant is roughly verified as in C e C u 6 14 ,8 l . Both contributions are associated with longitudinal magnetic fluctuations along the c-axis. The temperature dependences of the correlations lengths ~,, and ~:c along the a and c directions have been investigated in detail and results are summarized in fig. 1. The in-plane and inter-plane correlation lengths expressed in a number of corre- lated moments are anisotropic and reaches the values sea = 3 and ~c = 1 at low temperatures. Their behaviour versus temperature is also quite different: ~:c is slightly T-dependent whereas ~ is found to increase first slowly, with decreasing temperatures ( ~ : , - 1.5 at T = 2 5 K = T K ) but then more rapidly below T~<8K ( = T * = F~s/k~). Finally, ~:, saturates at low tempera- tures, which means that quantum (Kondo) fluctuations inhibit the thermal divergence of the in-plane correl- tion lengths and that LRO does not develop. The temperature dependences of the parameters Fss and F~s are given in fig. 2. For temperatures T ~> TK, Fis becomes approximately equal to Fss and the inelastic character disappears. When temperature decreases Fss exhibits a weak temperature dependence. Fis is found to decrease more rapidly below a characteristic cross- over temperature T o= 15K=hw0/k B and then to saturate at low temperature at a value Fis = 0.9 meV. All these results are in fact very similar to those obtained in CeCu 6 [4], (even the ratio Fss/F~s = 2) and

1 . ~ o<

¢-

g

c_

0 L~

r

C e R u 2 S i 2

0 1~0 ' :20 ' 310 ' 4 0

Temperature (K )

Fig. 1. Correlation lengths ~a and ~c as a function of tem- perature of CeRu2Si 2.

3.0

2.0

E L

1.0

i i i i

Q = (0.7,0.7,0)

' ' t 0 ' g0 ' ;0 ' 00

Temperature ( K )

Fig. 2. Single site (Fss) and intersite (F~s) fluctuation rates as a function of temperature of CeRu2Si 2.

correspond to general features of HF systems. They show the existence of two energy scales: Fss and F~s, which are related to T K and J (The intersite interac- tion constant), respectively.

4. Ceo.sLao.zRu2Si 2

The main effect of a small substitution of Ce by La is to induce a LRO above x ~> 0.08 [2, 5]. This mag- netic ordering is characterized by an incommensurate wave vector k = (0.309, 0, 0) weakly dependent on x, which corresponds precisely to the wavevector k 1 ob- served for magnetic correlations in the pure system [5, 7]. No Bragg peak is observed around k 2 in zero field. Nevertheless k 2 c a n be favoured by an applied magnetic field [9, 10]. Thus the Ce substitution seems to have little influence on the relative strength of magnetic interactions which determine k, but modifies strongly the hybridization of 4f and conduction elec- trons. The existence of quantum fluctuations compet- ing with thermal fluctuations is believed to modify quantitatively the "critical" behaviour near T N. Re- cently we have undertaken elastic and quasi-elastic neutron scattering experiments on the compound Ce0.sLao 2Ru2Si2 to clarify this point. Our main con- clusions are the following: i) Intensities of magnetic Bragg peaks are found to increase more or less linear- ly in the temperature range T / T N = ( 0 . 7 - 1 ) below T N =5.4-+ 0.1 K, characteristic of a pseudo critical exponent/3 = 0.5 (see fig. 3). This value, close to the MF value, reflects in fact the difficulty for the order to be established because of quantum fluctuations. This result is quite different from that expected for a 3d

608 L.P. Regnault et al. / Magnetic fluctuations in Ce~ ~La RueSi 2 (x = O, x = 0.2)

I I i i i

250 CeosLac~2Ru2~5 i i~ • 2 ~ . 6 9 5 , 1 , O) d ffl

~ 50._~

&1~O 0 0~

o ' X

o c ~ a t u r ' e (K)

O U

5c

J I ~ I i t I i I ~ 0 2 4 6 8 lO Temper-aMr-e ( K )

Fig. 3. Correlation lengths ~: as a function of temperature of Ce o 8Lao 2Ru:Si2. In inset the temperature dependence of the magnetic Bragg peak peak Q - (0.695, 1,0) as a function of temperature for Ce 0 ,La o 2Ru2Si~.

lsing system (/3 =0 .31 ) . ii) Magnet ic fluctuations are found to be maximum at T N but they do no t exhibit the strong divergence typical of a convent ional 3d- Ising phase transition. This is clearly shown in fig. 4 which represents the tempera ture dependence of the neutron intensity measured at the scattering vector Q = (0.715, 0.98, 0) located near the magnet ic Bragg peak (0.695, 1 ,0) . This magnetic scattering persists at low temperatures indicating that strong magnet ic fluc- tuations persist and reduce the ordered moment . Q- scans recorded at different temperatures , confirm un- ambiguously the existence of strong magnet ic fluctua- tions coexisting with the L R O below T N. The T- dependence of the correlat ion length along the a- direction (~, , ) , repor ted in fig. 3, exhibits no diver- gence near T N, contrary to a convent ional phase transition. In contrast, ~:~ increases continuously as the tempera ture decreases and becomes large only below T < 2 - 3 K, i.e., in the tempera ture range where the squaring up of the moment modulat ion develops. However , there is no indication of a possible satura-

c

g ~ 4 0 C

o - - 3 5

c 2 ~

8 ? Z

i

Ceo.8Lao.2Ru2Si2 :/o.~s,o.98,o/

{ + ~ ; + °

B.G.

Temper-ai'ure ( K ) Fig. 4. Neutron intensity at Q : (0.715, 0.98, 0) as a function of temperature for Ce0 sLa02RuzSie.

tion of sc as T----~0. Finally we want to ment ion that studies of the dynamics of Ce0sLa02Ru2Si 2 are in progress and will be published elsewhere. They give evidence for fluctuation rates much smaller than in the pure system, characteristic of a slowing down of mag- netic fluctuations.

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