Magnetic properties of CeAl2 at low temperature

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Magnetic properties of CeAl2 at low temperature

B. Barbara, M. Cyrot, C. Lacroix-Lyon-Caen, M. Rossignol

To cite this version:

B. Barbara, M. Cyrot, C. Lacroix-Lyon-Caen, M. Rossignol. Magnetic properties of CeAl2 at low temperature. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-340-C5-341.

�10.1051/jphyscol:19795117�. �jpa-00218901�

JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-340

Magnetic properties of CeAl ² at low temperature

B. Barbara, M. Cyrot, C. Lacroix-Lyon-Caen and M. F. Rossignol

Laboratoire Louis-Neel, C.N.R.S., 166X, 38042 Grenoble Cedex, France

Résumé. — Un simple modèle s-f permet d'obtenir les principales caractéristiques d'un réseau Kondo. En parti- culier la diminution de la température d'ordre, due à l'effet Kondo, a été évaluée en fonction de la pression et comparée à des mesures de susceptibilités effectuées jusqu'à 6 kbar.

Abstract. — A simple s-f model allows one to obtain the main characteristics of a Kondo lattice. In particular the lowering of the ordering temperature, due to the Kondo effect, has been evaluated as a function of pressure and compared with the susceptibility measured up to 6 kbar.

1. Introduction. — There have been many studies T

K

is not a free parameter but results of the calculation of CeAl

2

(for a review, see ref. [10]). Recently, various itself.

experiments have been carried out in Grenoble [1-4,81 In the case of CeAl

2

, we use the expression (1) at in order to clarify the magnetic behaviour of CeAl

2

each site i, replacing the applied field by an internal in its low temperature phase. A magnetic ordering was field H., which is related to the others spins S

^;

through found which corresponds to a sinusoidally modulated the R.K.K.Y. interaction :

antiferromagnetic structure [3]. The incommensurate

modulation remains stable down to 0.4 K, which H, = — $<*,- = J Z Xy Sj

implies a non magnetic level as ground state [4].

J

However the crystal field ground state is a T

7

doublet.

w i t h % i s t h e s u s c e p t i b

i i i

t y o f

the conduction band.

This contradiction can be removed by a consideration

A s t h e a n i s o t r o p y i s

relatively large [1, 3] we assume of the Kondo effect [4]. Therefore, m this paper, we

t h a t a l l s p i n s g a r e p a r a l l e l I f

^

t h e F o u r i e r

apply to CeAl

²

a standard calculation describing the

t r a n s f o r m o f Zy> i s m a x

i

^{m U}

m for q = q

⁰

# 0 and Kondo properties.

^{% ( 3}

^ ^

^q

^

e t c a r e m u c h s m a

n

^e

r than

^z

(

^{? 0}

) , then

only the q

0

component of M

t

is large and the magne- 2. Calculation method and results. — The s-f tization obtained is modulated, with the incommen- coupling is responsible for the Kondo effect and for

the ordering through R.K.K.Y. (Ruderman-Kittel- I

Kasuya-Yosida) interactions. At each site of the

% 10

— ^ _ _ ^ ^ / lattice, cerium ions interact with the conduction ^ d(LnT)/dP ^ ^ ~ ^ ^ ' electrons through the s-f coupling, which can be ^ ^ v /

written — JS; <s

ⁱ

(7f is the negative coupling cons- \ 0.75 ^ \ /

tant [4, 5], S

^;

and <T

^;

are respectively the spins of the if / \

ion and of the conduction electron on the site i). ** 0.01 - ^ ^ / \ The density of states at the Fermi level, p, characte- \ i i ' \

rizes the conduction band. ' 0 ^ — ^ \ t

²

— I P ^ I / \

We start from the method of Schlottmann [6], \ / \ which describes the single impurity Kondo properties. "

0-01

' \ / \ The interest of this method is that the magnetization

0 2 5

_

002

\ / \

M is obtained as a function of the applied field H, / \ at any temperature : y \

Fig. 1. — Variations of the normalized Kondo and ordering tem- Q, function of H and T, is denned in ref. [61. At low pe«ture

S

(7-

K

/r

No

- - -) and (T

N

/T

NO

), with the product of . . , , c 1 j ii_- ,.- j x ^i the density of states at the Fermi energy and the s-f exchange temperature and low field this equation reduces to the

c o n s t a n t

^ ,

I n s e r t : r d a t i v e pressu

^

y i n d u c e d modificatio8n

well known result M = H/kT

K

where T

K

is propor-

o f t h e orde

ring temperature (in kbar"

1

) as a function of | p^ |.

tional to |p3'|

1 / | p 3

'- It may be remarked that, here, The arrow indicates the measured value of d(Ln 7"

N

)/d/>.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19795117

MAGNETIC PROPERTIES OF CeAI, AT LOW TEMPERATURE C5-341

surate period I/q,, in agreement with the experimental neutron result.

Equation (1) can be expanded in powers of Hi.

Assuming that only ~ ( q , ) has a non zero value, this expansion gives M(q,) as a solution of a self consistent equation, but there is a critical value of I p% ( above which M(qo) is always equal to zero. Below this value, the self consistent equation has a non zero solution M(qo) at 0 K, but it can be easily solved only when M(q,) is small, i.e. near TN. Figure 1 shows the varia- tion of the ordering temperature TN and of the Kondo temperature TK for ~(q,) = 1.2 ~ ( 0 ) . Three regions can be distinguished : (i) I p % ( < 0.2, TK is small and the ordering temperature is not much reduced by the Kondo effect; (ii) 0.2 < I p.2 I < 0.37, the Kondo temperature becomes similar in magnitude to the ordering temperature : there is a strong reduc- tion of the ordering temperature; (iii) for larger values of I ^p% I there is no ordering at all and the Kondo compensation occurs.

3. Effect of pressure.

^-

The variation of TN with pressure can be easily deduced if we use the results of ref. [7] to evaluate the variation of p and 8 with pres- sure. The results are plotted on figure 1. d(Ln TN)/dp can be positive or negative depending on the value of

1 ^p% I. Resistivity [7] and specific heat [S] measure- ments under pressure have been performed at low temperature in CeAl,. However the observed ano- malies under pressure do not seem associated with the ordering temperature only. We have determined the pressure variation of the ordering temperature by measuring its initial susceptibility X as a function of temperature at several pressures. Such experiments have been performed at the S.N.C.I. in Grenoble in the range of temperature 1.7 K-5 K and for hydro- static pressures up to 6 kbar. The magnetic field, applied parallel to a [l l l] direction, was equal to 10 kOe. Though this field is relatively large it corres- ponds to a quasi-linear part of the magnetization curve under pressure [2]. The ordering temperature TN is defined by the inflexion point of x(T). We deduce for d(Ln TN)/dp the value - 4.4

X

10- kbar

^-

'

which corresponds (insert of Fig. 1) to I ^p;i I z 0.28.

For such a value the reduction of the ordering tempe- rature TN/TN, is found equal to 0.65 (Fig. 1) and as TN = 3.9 K, TK is about 7 K. This value, much higher than that of Ce diluted in LaAl, [9], is of the order of that given by Bred1 et al. [IO]. This result can be explained by a decrease of the volume available for conduction electrons of d character (which are loca- lized in the cerium ion sphere) when La ion are replac- ed by Ce ions ; as the density of states is in the expo- nential a small change of volume can produce a large change in TK.

1 2

3 I

5 6

7

8

Temperature (K)

Fig. 2.

-

Thermal variation of the initial susceptibility measured on a single crystal of CeAI, parallel to a [l 1 l] direction for different hydrostatic pressures (in bar).

4. Conclusion.

-

Several others models [10-121 have already described the phenomenon of competi- tion between the Kondo effect and antiferromagnetic ordering. However, the above calculation, based on the simple idea that the S-f coupling is responsible of both Kondo effect and magnetic ordering through R.K.K.Y. interactions, has allowed to obtain some low temperature properties of CeAl,.

Acknowledgments. - We wish to thank Dr.

K. D. Schotte for his interest and useful remarks.

References

[I] BARBARA, B., ROSSIGNOL, M. F., PURWINS, H. G., WALKER, E., [8] BERTON, A., CHAUSSY, J., CHOUTEAU, G., CORNUT, B., PEY- Solid State Commun. 17 (1975) 1525. RARD, J., TOURMER, R., Proc. of the Valence instabilities [2] BARBARA, B., BARTHOLIN, H., FLORENCE, D., ROSSIGNOL, M. F., and related narrow band phenomena, Conf. Ed. by

WALKER, E., Physica 86-88B (1977) 177. R. D. Parks (Plenum Press, New Yqrk) 1977,471.

[3] BARBARA, B., BOUCHERLE, J. X., BUEVOZ, J. L., ROS- [g] BADER, S. D., PHILLIPS, N. E., MAPLE, M. B., LUENGO, C. A., SIGNOL, M. F., SCHWEIZER, J., Solid State Commun. 25 Solid State Commun. 16 (1975) 1263, and references

(1977) 481. therein.

[4] BARBARA, B., BOUCHERLE, J. X., BUEVOZ, J. L., ROS- [l01 BREDL, C. D., STEGLICH, F., SCHOTTE, K. D., 2. Phys. B 29 SIGNOL, M. F., SCHWEIZER, J., This conference, J. Physique (1978) 327.

Colloq. 40 (1979) C5. [l11 JULLIEN, R., FIELDS, J., DONIACH, S., Phys. Rev. Lett. 38 [5] COQBLIN, B., RATTO, C. F., Phys. Rev. Left. 21 (1968) 1065. (1977) 1500.

[6] SCHLOTTMANN, P., J. Mag. Mag. Mat. 7 (1978) 72. [l21 BENOR, A., FLOUQUET, J., RIBAULT, M,, FLOUQUET, F., [7] NICOLAS-FRANCILLON, M., PERCHERON, A., ACHARD, J. C., CHOUTEAU, G., TOURNIER, R., J. Physique Lett. 39 (1978)

GOROCHOV, O., CORNUT, B., J~ROME, P., COQBLIN, B., L-94.

Solid State Commun. 11 (1972) 845.

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