Heavy fermions in kondo lattices

Journal of the Less-Common Metals, 127(1987) 321-327

HEAVY

FERMIONS

V. V. MOSHCHALKOV”,

321

IN KONDO LATTICES*

F. G. ALIEV”, N. E. SLUCHANKOq

0. V. PETRENKO”

and I. CIRICb

a Low Temperature Physics Laboratory, Department of Physics, Moscow State University, Mo.scou~ 1~?23~~U.~.~.R.) b institute of Physics, 11&31Beograd ~Yugo~~au~~~ (Received June 12,1986)

Summary Electric, magnetic and thermoelectric properties of cerium solid solutions realizing the transition from Kondo impurity to Kondo lattice ((Ce,La)Al~) and from low TK Kondo lattice to high TK Kondo lattice (Ce(Cu,Ni)~) were studied. The anomalous low temperature properties of these compounds are related to the formation of the giant Abrikosov-Suhl resonance in the vicinity of the Fermi level. The effect of the crystal field splitting of the f level on Kondo anomalies is discussed. Resistivity and a.c. susceptibility of ferromagnetic Kondo lattice CeSi, is studied under pressures up to 15 kbar. A threedimensional picture of the upper critical field in superconducting KL CeCu,Si, is obtained. The dH,,/dT value is constant within 5”/, when His rotated in the basal plane whereas dH,,/dTis decreased by a factor of two when His rotated by 5”-8” from that plane. These data are analysed within the framework of symmetry classification of possible superconducting classes in heavy fermion superconductors. The Hall coefficient R,(T) in CeAl,, CeCu,Si, and UBe,, is measured. It has been shown that the drastic decrease in the R,(T) value at T-K TK is caused by the transition from non-coherent Kondo singlets to coherent Kondo spin ~uctuations in Kondo lattices.

1. Introduction There are several useful types of experiment which help us to know more about heavy fermions in Kondo lattices: (i) using systems where the substitution of one element by another induces the transitions: normal-metal-Kondoimpurity-Kondo-lattice ((Ce,La)Al,, (Ce,La)Cu,Si,, (Ce,La)Cu, etc.); (ii) studies of concentrated Kondo systems with the Kondo temperature TK *Paper presented at the 17th Rare Earth Hamilton, Ontario, Canada, June 9%12,198f.X

Research

Conference,

McMaster

‘> Etsevier Sequoia~Printed

University,

in The Netherlands

322

increasing from Tk very much less than the crystal field energy splitting E,, to ‘l’k >>EC, due to the controlled variation of alloy composition (Ce(In,Sn),, Ce(Cu,Ni), etc.); (iii) high pressure studies of concentrated Kondo systems. In this paper we report the latest results obtained by our Moscow group on (Ce,La)Al,, Ce(Cu,Ni),, CeSi, as well as on Kondo lattices CeCu,Si,, UBe,, at ambient pressures and on CeSi, at high pressures.

2. The variation

in the Tx/Ecf ratio in Ce(Cu,Ni),

alloys

Using the controlled variation in composition we can traverse the classification scheme of Kondo lattices [l-3] from magnetic to non-magnetic Kondo lattices. For that purpose we have chosen Ce(Cu,Ni), isostruct~al solid solutions. Measurements of resistivity [4], lattice parameters, thermoelectric power, a.c. andd.c. susceptibility were performed at temperatures between 2 and 300 K (Fig. 1). In CeCu, the susceptibility us. temperature curve shows a peak at T = TM = 7.1 K and a bump at T = TN = 3 K, whereas the heat capacity [7] displays a small bump at TM and a high peak at TN.In a magnetic field the H-T phase diagram of CeCu, resembles that of CeB, [8]. The increase in the nickel content in Ce(Cu,Ni), alloys leads to the suppression of TMand TN(Fig. 1). The characteristic Kondo anomalies in resistivity and thermoelectric power depend strongly on the nickel concentration. Analysing this dependence we have estimated the variation in TK in Ce(Cu,Ni), alloys: if the nickel-to-copper content ratio x: is less than 0.5 then these compounds are low TK Kondo lattices with two TK (T, = 10K and TK,, = lO&llOK); for r > 0.5 there is one TK increasing from 1lOK to 650K for x = 1.0. The sharp growth in TK at x > 0.5 looks similar to the y-a transition in cerium. In the concentration range corresponding to the T, enhancement, anomalous temperature dependences of lattice constants were observed [9]. Therefore the variation in the T&Y,, ratio in Ce(Cu,Ni), alloys induces Kondo lattice-non-magnetic, Kondo lattice.

3. High pressure

studies

the following successive transitions: low TK Kondo lattice-non-magnetic,

of magnetic

Kondo

magnetic high TK

lattices

The alternative way to vary the TdE,, ratio in Kondo lattices is to use high pressures, In this section we report our preliminary results on ferromagnetic Kondo lattice CeSi,. Temperature dependences of resistivity, magnetic susceptibility and Hall coefficient were studied under pressure p up to 15 kbar for T = 1.5-300K. The R,(T) and x (!Z’) curves for z < 1.85 show anomalies corresponding to a paramagnet-antiferromagnet transition at T = TM.The TM value is decreased under pressure with the rate dTddp = - 0.1 K kbar - ’ (Fig. 2). A flat plateau in the I”(2’) curves at T = 50430 K is transformed into a maximum (Fig. 2) which is shifted to low temperatures at a rate of 3-4K kbar-‘. This transformation of the r(T) curves is analogous to that in systems with TK

323

(b)

2

IO

20

loo

T,K

(d)

T, U

I I

.J

T,IK

01

02

03

0.4

05

xNi

Fig. 1. (a) Temperature dependences of resistivity in Ce(Cu, _,Ni,), alloys with nickel content: curve I. x = 0; curve 2, x = 0.1; curve 3, x = 0.38; curve 4, x = 0.4; curve 5, x = 0.45; curve6 x = 0.5; curve 7, r = 0.55. The inset shows the variation of resistivity with x at 4.2 K for Ce(Cu,Ni), (a) and La(Cu,Ni), (0) alloys. (b) The Seebeck coefficient S( T,,, x) us. nickel content z in Ce(Cu.Ni), alloys: l, T, = 50K; A, T,, = lOOK; +, T, = 300K: 0, T, = 500K. The insert shows the concentration dependence of the Kondo temperature and the temperature corresponding to the S(T) maximum: x, ref. 5; A, ref. 6. (c) Temperature dependences of a.c. susceptibility in CeCu,,,,Ni,~,, in different magnetic fields: curve 1, no field; curve 2.50 Oe; curve 3,&l Oe; curve 4,120 Oe; curve 5,250 Oe; curve 6,500 Oe; curve 7,900 Oe. (d) The magnetic H- Tand T-X phase diagrams of Ce(Cu,Ni), alloys: I, II and III are antiferromagnetic, ferromagnetic and paramagnetic phases respectively.

324

T,K 100 I

I

200 I

I

----*-

p= 9.2 kbar p= 14.3 kbor p = 14.9 kbar

t

5 8 Q

b_ .

9t

0

Ei

p, kbar t

L

I

I

I

I

9

10

Ii

12 T,K

Fig. 2. Temperaturedep~nd~nc~~sofresistivityfor CeSi 1.8underpressurep.ThedMjdHvs. Tcurves illustrate the paramagnetic-ferromagnetic transition in different magnetic fields. The inset shows the magnetic transition temperature us.pressure.

decreasing with pressure, whereas usually in cerium Kondo lattices a growth of the Kondo temperature under pressure is observed. Pressures higher than 15 khar are necessary to bring about magnetic-non-magnetic Kondo tattice transition.

325

4. The anisotropy of the upper critical field in CeCu,Si, In single CeCu,Si, crystals grown from the stoichiometric composition pressures p > 2 kbar are needed to induce heavy fermion superconductivity. Using these “stoichiometric” samples we have carried out the detailed studies of the upper critical field anisotropy to obtain information about the nature of the superconducting state in CeCu,Si,. It has been found ttiat the Hcz derivative at T = T, (0) is isotropic in the basal plane within the limits of about 5”/,-8% and at the same time the dH,,/dTvalue is sharply decreased by a factor of 1.8-2.0 when His rotated by 5” to 8” from basal plane towards the c axis (Fig. 3). The threedimensional picture of the dH,,/dT angular dependencies looks like “UFOs, unidentified flying objects” (Fig. 3). The Hc2 us. T curves near T, in CeCu,Si, (HII c) (Fig. 3) show curvature analogous to that found in UPt, (H/l a) by Chen et al. [lo]. It is interesting to note that there is an empirical law which is valid for CeCu,Si,, UPt, and URu,Si, [ll]: the dH,,/dT values are higher for those directions which correspond to lower magnetic susceptibility. Comparing our Hc2 data with the symmetry analysis of possible superconducting classes [12,13] leads to the suggestion that the superconducting gap is zero along the equatorial line. This suggestion is in agreement with the NMR [14] and heat capacity [15] data. Taking into account the absence of any noticeable H,, anisotropy in copper-rich CeCu,Si, single crystals [16, 171 we have to assume that the anisotropy of both Hc2 and the susceptibility is strongly dependent on

(b)

,380

.4OO .420

Tc,K (a) Fig. 3. (a) The upper critical field H,, vs. temperature Tfor different orientations of H: A; H 11c2, 0, H rotated away from c2 by lo’ or by 80’ ; 0, H 11c4. c2 and c4 are twofold and fourfold axes respectively. (b) The three-dimensional picture of the dH,,/dT anisotropy in CeCu,Si,. (c) The angular dependence of dH,,/dTin the plane P which is rotated away from the basal plane by 5”.

326

the copper content in CeCu,Si,. The absence of the dHc21dT anisotropy in the basal plane might be interpreted as an evidence for anisotropic s pairing in CeCu,Si,. Taking into account the calculation of dH,,/dT in the basal plane for p pairing [lS] we can state that if this theoretical prediction is valid for CeCu, Si,, then the electron effective mass along c axis must be at least three times higher than those along a axis and b axis. In this case the fourfold anisotropy of dH,,/dT is small even for p pairing and we could not notice it within the error bars.

5. Hall effect in Kondo lattices in the coherent regime Earlier we have reported [l, 41 that the existence of the giant AbrikosovSuhl resonance in non-magnetic Kondo lattice is accompanied by the anomalous low temperature increase of the Hall coefficient R,(T) at T = 2-200 K. It was of interest to know how Ru( 2’) would behave in the case of coherent Kondo spin fluctuations at temperatures much below TK, To obtain the answer we have measured R, us. Tin CeAl,; CeCu,Si, and UBe, 3 at temperatures down to 0.2 K (Fig. 4). It has been found that the decrease in T below 2-3 K leads to a severe

3-

AAAa

AA *AA

!

!?A

.

CeCu,Si,

.O

.

.

la

. =o .O a0

0.

.

.

.

n0

80

0’

m ‘-0-Q

0.8 L”0.2AL3

0

50

0. .

0

.

0

.

0 .

0

.

0

.

0

.

0 0

3-

0 0

-UBe,,

CeAL,

. . ,’

l:

I I

I

2

I

3

T. K

Fig. 4. Temperature dependences CeCu,Si, and UBe,,.

of the Hall coefficient

R, for heavy fermion

systems CeAl,,

327

of RH( T) curves : the RH( T) values

transformation

even a sign inversion CeCu,

[19,20].

of Kondo

of RH( T) is observed.

To check

centres

indicates

that

coherent magnetic

Kondo Kondo

the noticeable

the R,(T)

the cerium

suppression

anomaly

fluctuations lattices.

are decreased behaviour

of the RH( 57) decrease

the connection

we have substituted

and have observed

Similar

in CeAl,

array

and

by lanthanum

(Fig. 4)

This result

by the transition

of Kondo

in

to the periodicity

of the RH( 7’) decrease.

at T < TK is caused

in a periodic

strongly

was also found

centres

to

in non-

Acknowledgments The authors

would

sions with A. A. Abrikosov,

like t,o acknowledge N. B. Brandt,

helpful

L. P. Gor’kov

and stimulating

discus-

and N. E. Alekseevskii.

References

: 7 8 9 10 11 12 13 14 15 16 17 18 19 20

N. B. Brandt and V. V. Moshchalkov, Adu. Pkys., 33 (1984) 373. G. R. Stewart, Rev. Mod. Phys., 56(1984) 755. V. V. Moshchalkov, J. Magn. Magn. Mater., 47-48(1985) 7. N. B. Brandt, V. V. Moshchalkov, N. E. Sluchanko, E. M. Savitskii and T. M. Shkatova,, Solid State Commun., 53(1985) 645. R. V. Lutsiv et al., Sov. Phys ~~Solid State, 26(1984) 716. F. Steglich etal., Solid State Commun., 51(1984) 909. P. A. Alekseev, V. N. Lasukov, I. P. Sadikov, I. A. Sergeeva, M. N. Khlopkin and 0. D. Christyakov, Pis’ma Zh. Eksp. Tekh. Fiz., 41(1985) 492. A. Takase, K. Kojima, T. Komatsubara and T. Kasuya, Solid State Commun., 36 (1980) 461. A. S. Ilyushin, V. V. Moshchalkov,A. A. Nikolaev, A. P. Perov, N. E. Sluchanko, G. S. Burkhanov and T. M. Shkatova, Fiz. Tuerd. Tela, 28 (1986) 3423. J. W. Chen, S. E. Lambert, M. B. Maple, Z. Fisk, J. L. Smith, G. R. Stewart and J. 0. Willis, Phys. Rev. B, 30 (1984) 1583. T. T. M. Palstra, A. A. Menovsky, J. van den Berg, A. J. Dirkmaat, P. H. Kes, G. J. Nieuwenhuys and J. A. Mydosh, Phys. Rev. Lett., 55 (1985) 2727. G. E. Volovik and L. P. Gor’kov, Zh. Exp. Teor. Fiz., 88 (1985) 1412. P. W. Anderson, Phys. Rev. B, 30 (1984) 4000. Y. Kitaoka, K. Ueda, T. Kohata, K. Asayama, Y. Onuki and T. Komatsubara, J. Magn. Magn. Mater., 52(1985) 341. F. Steglich, C. Bredl, W. Lieke, U. Rauchschwalbe and G. Sparn, Physica B, 126 (1984) 82. W. Assmus, M. Herrmann, U. Rauchschwalbe, S. Riegel, W. Lieke, H. Spille, S. Horn, G. Weber, F. Steglich and G. Cordier, Phys. Reu. Lett., 52(1984) 469. Y. Onuki, T. Hirai, T. Komatsubara, S. Takayanagi, A. Suminyama, A. Furukawa, Y. Oda and H. Nagano, J. Magn. Magn. Mater., 52(1985) 338. I,. I. Burlackhov, Zh. Exp. Teor. Fiz., 89(1985) 1382. T. Penney, J. Stankiewicz, S. von Molnar, Z. Fisk, J. L. Smith and H. R. Ott, J. Appl. Pkys., 54-57 (1986) 370. K. Winzer, Preprint 1986.