A comparative study of suppression of the energy gap with La substitution in the Kondo insulators: CeNiSn and CeRhSb

~ ,~ ELSEVIER

Journalof magnetism and magnetic meterlals

Journal of Magnetism and Magnetic Materials 161 (1996) 157-168

A comparative study of suppression of the energy gap with La substitution in the Kondo insulators: CeNiSn and CeRhSb D.T. Adroja a, B.D. Rainford a, A.J. Neville a, p.

Mandal

b,

A.G.M. Jansen b

~ Department of Physics, Southampton Unicersio', Southampton S017 1BJ, UK b High Magnetic Field Laboratory, Max-Planck-lnstitutfur Festkgrperforschung, CNRS, Grenoble Cedex 9, France

Received 6 November 1995; revised 7 January 1996

Abstract We report structural, transport and magnetic measurements on the solid solutions of Ce t _xLaxNiSn and Ce~ _,La~RhSb (x = 0 to 1). The results have been used to compare and contrast the effect of La substitution on the ground state properties of the Kondo insulators CeNiSn and CeRhSb. The resistivity measurements reveal that the energy gap in CeNiSn and CeRhSb decreases with increasing La concentration; no gap type behaviour was observed for La concentration >_ 0.2. At low temperature, Ce~_xLaxNiSn alloys show a cross-over from a Kondo insulator (x = 0) to a single ion Kondo ground state (x > 0.2) with increasing La concentration, while Ce l_xLa~RhSb alloys show a cross-over from a Kondo insulator (x = 0) to a coherent Kondo lattice (x = 0.2) and eventually to a single ion Kondo ground state at x = 0.5, Magnetic susceptibility measurements of Ce~_xLaxNiSn alloys exhibit a dramatic change in behaviour with La concentration; Curie-Weiss behaviour for x = 0, valence fluctuation behaviour for x = 0.2 and again C - W behaviour for x >_>_0.4. On the other hand, susceptibility of Ce~_xLaxRhSb alloys continue to show a valence fluctuation behaviour up to x = 0.7, and C - W behaviour for higher La concentrations. CeNiSn and CeRhSb exhibit a large negative magnetoresistance at 20 T field and at 1.5 K.

1. Introduction Recent reports on the resistivity measurements on Ce3Pt3Bi4, CeNiSn and CeRhSb compounds show the rapid rise in the resistivity in the low temperature limit [1-3]. The rapid rise in the resistivity, which follows a thermal activation laws, has been attributed to the opening of the energy gap in the electronic density of states at Fermi energy in the coherent regime. The value of the energy gap reported from the transport measurements is 70 K for Ce3Pt3Bi z, 2 - 8 K for CeNiSn and 4 - 6 K for CeRhSb. For

Ce3Pt3Bi 4, the gap energy (70 K) is the same order of magnitude as that observed for SmB6, gold SInS and YbB~2 [4,5]. It is generally believed that the hybridization between 4f band and the conduction electrons is responsible for the gap formation. However, in the case of StuB 6, the hybridization gap model has been called into question from two recent experimental reports [6,7]; neutron scattering studies suggest the formation of a local band state, whereas high pressure resistivity and Hall effect measurements show that the activation gap vanishes discontinuously between 45 and 53 kbar pressure. These

0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S 0 3 0 4 - 8 8 5 3 ( 9 6 ) 0 0 0 3 4 - 0

158

D.T. Adroja et al. /Journal of Magnetism and Magnetic Materials 161 (1996) 157 168

results are inconsistent with the hybridization gap model, but suggest a striking parallel to Mott-Hubbard insulators [7]. The previous alloying studies show that the energy gap in CeNiSn and CeRhSb are very sensitive to the partial substitution of either La on the Ce sublattice or the transition metal on the Ni(Rh) sublattice [8-12]. Recently, we have shown that the substitution of 38% Co for Ni in CeNiSn, induced a first order valence phase transition like that observed in YbInCu 4 [12,13]. With the hope of obtaining more detailed information about the low temperature insulating ground state of CeNiSn and CeRhSb, we have synthesized the alloy series Cej xLaxNiSn and Ce~_xLa~RhSb with x = 0 to 1 and studied their physical properties. The purpose of the present paper is to report our results on crystal structure, resistivity and magnetic susceptibility of Ce~ xLaxNiSn and Cel_xLaxRhSb (x = 0 to 1) alloys, as well as high field magnetoresistance measurements on CeNiSn and CeRhSb, with emphasis on the stability of the energy gap at E F and change of Ce valence state in these alloys. The results have been used to compare and contrast the effect of La substitution for Ce on structural, transport and magnetic properties of the Kondo insulators CeNiSn and CeRhSb.

2. Experimental Polycrystalline samples of Ce~_xLaxNiSn and Ce~_xLaxRhSb (x = 0 to 1) were synthesized by arc melting of the stoichiometric amounts of the con-

stituent elements of purity 99.9% for Ce, La and 99.99% for Rh, Ni, Sb and Sn on the water cooled Cu-hearth under a high purity argon atmosphere. A Siemens powder X-ray diffractometer was used to check the phase purity. The resistivity measurements were carried out using a four probe dc method between 4.2 K and 300 K. The magnetic susceptibility measurements were carried out using a vibrating sample magnetometer (VSM) between 4.2 K and 300 K in applied fields between 0.5 and 1 T. The high field magnetoresistance measurements were carried out using a four probe ac technique and dc magnetic field (up to 20 T) at the High Magnetic Field Laboratory Grenoble, France. The current was passed parallel to an applied field.

3. Results and discussion

3.1. X-ray diffraction Our powder X-ray diffraction studies reveal that the Ce~_,LaxNiSn and Ce~_ ~LaxRhSb (x = 0 to 1) alloys are single phase materials and crystallise in the orthorhombic TiNiSi-type structure, space group Pnma. In TiNiSi-type structure, there exist three different crystallographic sites, Ce, Ni(Rh) and Sn(Sb) atoms preferentially occupy these sites. The lattice parameters obtained taking into account of the position of observed X-ray diffraction peaks for angles 20 between 20 ° and 60 ° and using CELL program are given in Table 1 and 2. The lattice parameters for x = 0 and x = I alloys agree well

Table 1 Structure type, lattice parameters, effective paramagnetic moment (/~eff) and paramagnetic Curie temperature (0 v) (obtained from the high temperature C u r i e - W e i s s behaviour of susceptibility) of Ce I .~LaxNiSn ( x = 0 to 1) alloys

Compound

Structure type

a (~,)

b (~,)

C (,~)

/Zeff (]ZB)

Op (K)

CeNiSn Ce0.95 La0.osNiSn Ceo.9 Lao i NiSn Ceo 8Lao.2 NiSn Ceo. 6 Lao.4NiSn Ceo.sLao.5 NiSn Ceo. z Lao 8NiSn Ceo osLa095NiSn LaNiSn

TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi

7.545 7.550 7.566 7.577 7.595 7.610 7.646 7.662 7.671

4.605 4.606 4.607 4.61 l 4.621 4.627 4.639 4.648 4.652

7.627 7.622 7.622 7.617 7.609 7.610 7.599 7.596 7.592

2.92 2.93 2.75 3.09 3.02 2.96 2.92 * -

- 196 - 199 - 181 -211 - 177 - 152 - 165 * -

* Unphysical value, see text.

159

D.T. Adroja et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 157-168

with those reported in the literature [14,15]. The plots of the unit cell volume versus rare earths' atomic number (not shown here) for RNiSn and RRhSb (R = La to Yb) reveal that the unit cell volume of CeNiSn follows usual lanthanide contraction, while that of CeRhSb shows a deviation from it. This suggests that the valence of Ce ion in CeNiSn is close to trivalent, while in CeRhSb it is intermediate valence. This is in agreement with the magnetic susceptibility measurements [3,8]. Fig. l shows the lattice parameters (a, b and c) as a function of La concentration x for Ce=_xLa~NiSn and Cel_xLaxRhSb ( x = 0 to 1) alloys. For Ce ~_ xLa, NiSn alloys, lattice parameters a and b increase almost linearly with La concentration x, while the parameter c decreases with increasing x. The values of a and c are almost equal for the alloy with La concentration x = 0.5, while for alloys with higher La concentration (x > 0.5), value of a is greater than c. This suggest that the alloys having La concentration close to 50% may have tetragonal symmetry. A neutron diffraction study is required to further confirm the tetragonal symmetry and space group for these alloys. On the other hand, all three lattice parameters (a, b and c) of Ce~_xLa,RhSb alloys increase almost linearly with

7.68-

4.66

Ce l,J.,a.,NiSn J . i ..~/ " 7.64"

¢

.t..../..= ........

~---..,,,--~,.~_ 7.60 .

.

.

7.56

~""

.

'

""

4.64

"-'---",~ 4.62

"" ....

7.52~

¢1

0:2

0:4

0:6

1.60

0:8

8.00"

7.85, ~ ¢"1

4.70

e Ce~ ~La~RhSb ~-~----"--"~'~--"=~",,---

7.70-

b

, . ........... - . . . . .

~..~w-:.~--D=.-

7.55,

7400

0.2

0.4

0.6

275

Cel.,~Sb

~

/~lr j

j j/

,.----'¢"~"~

27°I . ..i. mtl /

/.I-~"

265 |Ce~.j.a~NiSn 2 6 0 /

0

r

,

,

0.2 0.4 0.6 018 X

Fig. 2. Unit cell v o l u m e versus L a c o n c e n t r a t i o n for Ce L_ ~La~NiSn and Ce I _ ~La~RhSb alloys. The dotted lines are guide to the eyes.

increasing La concentration, which agree well with reported behaviour [14]. The variation of the lattice parameters, when La is substituted for Ce are: Aa/a = 1.67%, Ab/b = 1.02% and Ac/c = - 0 . 4 6 % for CeNiSn and A a / a = 1.89%, A b / b = 1.06% and Ac/c = 0.93% for CeRhSb. The different behaviour of the lattice parameter c in Ce]_xLa~NiSn and Cel_xLaxRhSb alloys could arise from the difference in the atomic radius of Ni(Sn) and Rh(Sb) atoms. The unit cell volume for both alloy series increase almost linearly with increasing La concentration (Fig. 2). The rate of increase of volume V, according to the derivative dV/dx = 5.89 ~3 for Cel_xLaxNiSn and 10.43 43 for Ce~_xLaxRhSb. This may result in a negatiL'e pressure effect on the Ce ion. The La substitution for Ce, increases the unit cell volume AV/V = 2.24% for CeNiSn and 3.97% for CeRhSb. The volume expansion for CeNiSn is 1.77 times smaller than that observed for CeRhSb, which is primarily caused by a small contraction along the c-axis; Ac/c = - 0.46%.

..

3.2. Electrical resistivity

4.67 .,/'

3.2.1.

4.64

~. . . . .

'4.61

0.8

¢.58

X Fig. 1. Lattice parameters versus La C e j - ,LaxNiSn and C e j - ,La ~RhSb alloys.

280]

concentration

for

Ce I -

x LaxNiSn alloys

Fig. 3 shows the resistivity of Cel_xLaxNiSn (x = 0 to 1) alloys as a function of temperature. The resistivity of the parent compound CeNiSn shows the characteristic feature observed earlier [9, I 1], namely - I n T) behaviour at high temperatures, a shallow maximum around 48 K followed by a sharp increase with decreasing temperature below 10 K. The latter

D.T. Adroja et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 157-168

160 400-

X=O

Cel.xLarNiSn

300200 100 =

~

o 4 - ~

..~ ¢L

x=-,L

-0 350.

__

100

300.

X=0.05 | ~

250.

x=o.1

200

•

_

300

.

200 X=0.5

150

100

- 200

300

TEMPERATURE (K) Fig. 3. Resistivity versus temperature for Ce I_XLaxNiSn alloys. The inset shows In Tmh~ versus In x.

behaviour has been attributed to the opening of the energy gap in the electronic density of states at Fermi level, E F. In order to estimate the energy gap from the low temperature activation behaviour, p = Po exp(A/kT), we have plotted magnetic scattering resistivity (Pro) of CeNiSn, obtained by subtracting the resistivity of LaNiSn from CeNiSn, as In Pm versus 1 / T ( K ) in Fig. 4. From this plot it is clear that Pm of CeNiSn exhibits an activation type behaviour below 7 K with the energy gap of 2.9 K, which agrees well with the value of the gap 2 - 8 K reported previously [9-11]. The resistivity of La substituted alloys show an interesting change as a function of La concentration in the low temperature regime. The resistivity of x = 0.05 and 0.1 alloys at low temperature exhibits an activation behaviour similar to CeNiSn with the energy gap of 0.8 K and 0.6 K, respectively. Although, the gap energy for x = 0.05 alloy is smaller than for CeNiSn, the magnitude of resistivity at low temperature is quite high (see Fig. 3), which is not understood at present. A similar behaviour in the resistivity was observed for Ce09GdoANiSn alloy [16]. Furthermore, the resistivity of x > 0.2 alloys shows the substantial suppression of low temperature rise, indicating that the energy gap is almost closed. The resistivity of x = 0.4, 0.5, 0.8 and 0.95 alloys exhibits a minimum at Tmi. = 200 K, 84 K, 35 K and

18.1 K, respectively and negative temperature coefficient below this. The plot of in Tmi. versus In x shows a linear variation with a slope of - 2.57 (inset Fig. 3). The negative temperature coefficient in the resistivity might arise either from the development of an energy gap in the electronic density of states at E F as observed for parent compound CeNiSn or from the presence of the single ion Kondo type interactions. In order to distinguish these possibilities, we have plotted Pm of C c l _ x L a x N i S n alloys as Pm versus in T in Fig. 5. It is clear from this plot that the alloy with x = 0.2 exhibits - I n T dependence in two different temperature regimes: high temperature and low temperature regimes. This behaviour could be explained on the basis of Kondo effect in the presence of crystalline electric field, as treated by Cornut and Coqblin [17]. According to this theory, the ratio of the slopes of low temperature and high temperature - In T behaviour is determined by the ratio of the spin degeneracies at low and high temperature. The observed ratio of the slopes of low temperature and high temperature - I n T behaviour is 0.083, which is very close to 3 / 3 5 = 0.086, as predicted for a doublet ground state for Ce 3+ ion by Counut and Coqblin. This is also consistent with our inelastic neutron scattering studies on CeNiSn, which

6.01

"

x

I

, 4v-t

,

.

a

.......

5 e.0e

6.O-r

,.5'.o"

"

~

"X=0 05

-'x'-'-gS""

o.08

o.16

to o.'2 5

o,16 ...

17.5

_,_

T 5.o

o.; l.o

Fig. 4. ln Pm versus I / T for Cel_~La~NiSn alloys. The solid lines represent the fit to activation behaviour.

161

D. T. Adroja et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 157-168 350

I

X=0.4

250

X=0.2 150 ~

×=0.8

50

"~

2

4

6

lOO

350 X=O.05

E 250

X=0.1 X=0.5

15O

50

X=0.95

50 o

2

In

,$

625

[T(K)]

Fig. 5. Pm versus InT for Ce L xLa~NiSn alloys. Top figure: the solid lines represent - In T behaviour in two different temperature regimes. show two broad crystal field excitations centred at 30 meV [18]. Further, Prn of CeNiSn also exhibits a -lnT dependence in two different temperature regimes (Fig. 5). However, due to the presence of an activation behaviour below 7 K, we could not estimate accurately the slope of - In T behaviour at low temperature. On the other hand, p~ of x = 0.4, 0.5 and 0.8 alloys exhibit - I n T behaviour only in the high temperature regimes and reach a constant residual resistivity at low temperatures, the so-called unitarity limit as observed for single ion Kondo systems [19]. Pm of dilute Ce alloy ( x = 0 . 9 5 ) does not saturate down to 4.2 K. These suggest that the observed negative temperature coefficient in the resistivity at low temperatures for 0.2 < x < 0.95 alloys is due to the single ion Kondo behaviour.

fall-off below the maximum is due to the freezing out of the inelastic scattering process for the conduction electrons as the temperature is lowered [20]. The resistivity of La substituted alloys changes dramatically with La concentration at low temperatures, while gradual change at high temperature behaviour is observed. The low temperature rise in the resistivity of CeRhSb is suppressed strongly for x = 0.05 and x = 0.1 alloys. The value of the energy gap obtained from the linear part of In p~ versus 1 / T ( K ) plot (Fig. 7) is 6.4 K for CeRhSb, 0.8 K for x = 0.05 and 0.3 K for x = 0.1. The observed gap value for x = 0.1 alloy agrees well with the value 0.28 K of the previous report [14]. Further, the resistivity of x = 0.2 alloy exhibits a normal valence fluctuating type behaviour without any sign of low temperature rise down to 1.8 K, which indicates that the energy gap is suppressed completely. Between 1.8 and 39 K, Pm of x = 0.2 alloy exhibits a A T 2 dependence with the coefficient A = 0.03 (/zg2 c m / K 2) (Fig. 8). The overall temperature dependent resistivity of

800'

Cel-xLaxRhSb

x=o

ooo

400 200

'~

=

0 X=0.3 ~dl~

='~

-~----,-,-~z~ =~:~

.......

,~ 400 ¢~,

300

X=0.2

300! X=O.5

3.2.2. Ce I x L a x R h S b alloys

Fig. 6 shows the resistivity of Cel_xLaxRhSb (x = 0 to 1) alloys as a function of temperature. The resistivity of CeRhSb exhibits a - l n T dependence at high temperature, a broad maximum at 125 K and sharp rise below 15 K. This is in agreement with the previous reports [3,14]. The high temperature - I n T behaviour arises from the incoherent scattering of the conduction electrons by the 4f localized spin, and the

l o o ~

3,, \ o

0

..v

~,~L' ''''''< J

x=o.,s

160

20

200

to

300

TEMPERATURE (K) Fig. 6. Resistivity versus temperature for Ce~_~La,Rhgb alloys. The inset shows resistivity versus temperature for x = 0.5 alloy.

162

D.T. Adroja et al. /Journal of Magnetism and Magnetic Materials 161 (1996) 157-168

700 "

=

500

6.0" 5

5'40

0.1

0.2

!0 ! '

5.0

0.3

6.0

~

~

5.7'

~ ~ ~ ' ~

5.4

'

. . . . . . . .

~_

X=0.3

. . . . . = ~ ........... ~

~-,-,,,,,~-0.1

X=0.5

-

x=o.gs 0.2

~'

350 00

,~

3oo

~

2~c

X=O.3

4

6

2

-100

~ 1 7°

x 095 .....,.,_.,,.~. 2

4

2

4

~

640

300

=== x=o.e X=~.2 = 4.8 -~"

I

~-130 2

5.8

x=o.7

...........................

100

O

=.

~

Cel'rLa~JaSb

300'

,~, 4.9

J(=o~k

x

O

240 X=O.7 180 X = 0 . 8

-~.8

120

I/T (K "I) Fig. 7. In Pm versus 1 / T for Ce i ,LaxRhSb alloys. The solid lines represent the fit to activation behaviour.

6

in rr (K)] Fig. 9. p,, versus In T for Ce~ ,LaxRhSb alloys.

x = 0.2 alloy is qualitatively similar to the resistivity of a Kondo Lattice calculated by Cox and Grew [20]. The observed high temperature maximum in the resistivity of CeRhSb shifts towards a low temperature with increasing La concentration x (Tmax = 80 K for x = 0.3 alloy) and eventually disappears for x > 0.5. The resistivity exhibits a minimum at Tmin = 19

400

375 ~ ~" 350

~

S

b

=

325 3000

K for x = 0.5, 17 K for x = 0.7, 15.5 K for x = 0.8 and 12 K for x = 0.95 (inset Fig. 6 for x = 0.5). It should be noticed that the appearance of the minimum in resistivity coincides with the disappearance of the coherence maximum at high temperature• In order to further check the presence of the single ion Kondo effect in the resistivity of Ce I xLaxRhSb alloys for dilute Ce concentration at low temperatures, we have plotted resistivity as Pm versus In T in Fig. 9. From this plot, it is clear that the alloys with x = 0.5 to 0.95 exhibit a single ion Kondo type behaviour as observed for Ce z_xLa,NiSn (x > 0.2) alloys.

3.3. Magnetoresistance 1000 2000 3000 4000

1a (K2) Fig. 8. Prn versus T z for Ce0.sLa0.eRhSb alloy. The solid line represents fit to T 2 behaviour.

As the gap energy for CeNiSn and CeRhSb is 2.9 K and 6.4 K respectively, which is smaller than 70 K that observed for Ce3Pt3Bi4, one expects a measurable effect of high magnetic field on the stability of

D.T. Adroja et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 157-168 5'

0

.....

-5- ~

~

'

.

- ~ ~ -,,~-..~ 30.1K

~

-10'

~'~

~

~

-15"

~20

-25 -30

11.8K ~

~ 8,2K

\

CeRhSb

~ . 4.SK 1.51(

5

20 10 CeNISn

10

15

20

25

.28.7K 13.6K

j//19.8K

~

0 -10

-2oJ -30-.^,

2.4K

~

-'+u- ~ -500

1.7K 5

10

15

20

25

40 30

LaNiSn

j

20 10 0 -100

~ 5

14.9K 10

15

20

25

lift) Fig. 10. The normalised magnetoresistance as a function of applied magnetic field at various temperatures for CeRhSb, CeNiSn and LaNiSn.

the energy gap at E F. In order to investigate this effect, we have carried out magnetoresistance measurements on CeNiSn and CeRhSb up to a field as high as 20 T. The magnetoresistance of the non-magnetic isostructural reference compound LaNiSn was also measured for comparison. Fig. 10 shows the normalized magnetoresistance, ( p ( H ) - p(O))/ p(O), as a function of an applied magnetic field for CeNiSn, CeRhSb and LaNiSn. CeNiSn and CeRhSb both exhibit a large negative magnetoresistance, - 4 0 . 8 % and - 2 8 % , respectively at 1.7 K (1.5 K) and 20 T (19 T) field. As estimated value (from the Hall coefficient) of o~c~-< 1, where wc is the cyclotron frequency and ~- is the relaxation time, for CeNiSn and CeRhSb, one does not expect a large magnetoresistance on the basis of the classical model. Therefore, the observed negative magnetoresistance of

163

CeNiSn and CeRhSb at 1.7 K (1.5 K) is attributed to the suppression of the energy gap by the applied field H. In order to check whether the Zeeman effect is responsible for the reduction in gap energy ( A ( H ) A( H = 0 ) - gJ/zB H, where the symbols have their usual meaning), we plotted low temperature magnetoresistance of CeRhSb and CeNiSn as In p(H) versus H (figure not shown here)• The absence of the linear region in this plot indicates that the Zeeman gap reduction mechanism is not important in the present case. A similar interpretation was given for the magnetoresistance of Ce3Pt3Bi 4 [21]. Other possible mechanism responsible for the gap suppression with field is that the applied field may reduce the gap by suppressing the physical interactions which are responsible for the stability of the insulating ground state at low temperatures. The observed small magnetoresistance for CeRhSb compared to CeNiSn also suggests that the gap energy in CeRhSb is bigger than that in CeNiSn. An analysis of magnetoresistance data at 1.5 K reveals a H 2 dependent magnetoresistance up to 12 T field for CeRhSb, while no power law behaviour was observed for CeNiSn. The magnetoresistance of CeRhSb changes sign from negative to positive above 20 K. This behaviour is inconsistent with the reported large positive magnetoresistance at 4.2 K up to 15 T field [22]. In the high temperature regime (T > 20 K), CeRhSb exhibits a small positive magnetoresistance, which is a linear function of applied field. The negative magnetoresistance of CeNiSn decreases with increasing temperature. At 9.4 K, magnetoresistance of CeNiSn exhibits a minimum at 15 T field and above this field magnetoresistance increases (in the positive direction) with field up to 20 T. The field at which magnetoresistance exhibits a minimum decreases with increasing temperature. LaNiSn exhibits a small negative magnetoresistance at low fields and at low temperatures. A crossover from negative to positive magnetoresistance has been observed in this compound with an increase in either temperature or field. Above 13.6 K, the overall magnetoresistance behaviour, except the magnitude, of LaNiSn is almost similar to that observed for CeNiSn. This suggests that CeNiSn and LaNiSn share a similar electronic structure at the high temperature.

D. T. Adroja et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 157-168

164

lOl/x=o

3.4. Magnetic susceptibility 3.4.1. Cej ~LaxNiSn alloys

°~o x=" to,

~

~-

~oo

=o8

-]

8 X .

0

100

200

300

6

T E M P E R A T U R E (K)

Fig. 11. Magnetic susceptibility versus temperature for Ce I_~LaxNiSn alloys.

Fig. 11 shows the magnetic susceptibility as a function of temperature for Ce~_~La ~NiSn (x = 0 to 1) alloys. The values of paramagnetic Curie temperature, 0v and effective paramagnetic moment, i/Leff obtained from the high temperature Curie-Weiss behaviour are given in Table 1. The susceptibility of CeNiSn exhibits Curie-Weiss behaviour down to 100 K with /Zet.f= 2.92 /ZB and a large value of 0p = - 1 9 6 K, while deviates considerably from it below 100 K. The later one could arise due to the presence of crystal field effects on the ground state J = 5 / 2 of C e 3+ ion. The high temperature susceptibility of x = 0.05 and x = 0.1 alloys is almost similar to that of CeNiSn, while low temperature susceptibility is smaller than that of CeNiSn. Further, x = 0.2 alloy exhibits a shallow maximum in the susceptibility at 100 K and small rise at low temperatures.

.8

6¸

Ce.xLa,,RhSb

.6

4 ¸

4 2

X=0.2

i 0

X=I 10o

20o

300 0

1O0

200 8

6

6

4'

4

2' 2

:=0.5 X=0.1

100

2(~)0

300 0

1O0

200

31

TEMPERATURE (K) Fig. 12. Magnetic susceptibility versus temperature for Ce t , LaxRhSb alloys. The solid line represents fit to the Coqblin-Schrieffer model.

D.T. Adroja et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 157-168

This behaviour is similar to that observed for valence fluctuating Ce system, suggesting an increase in hybridization between localised 4f electron and conduction electron, which makes the Ce ion less magnetic than trivalent Ce. These results are consistent with muon spin relaxation measurements on CeNiSn and Ce0.85Lao.tsNiSn [23]. The transverse field muon spin relaxation rate at 0.25K in Ce0.85La0.~sNiSn is 7 times less than that in CeNiSn. This indicates that Ce0.85La0.15NiSn is less magnetic than CeNiSn. The increased in hybridisation on substituting La for Ce in CeNiSn is somewhat unexpected. With the larger ionic size of La, and the corresponding increase in cell volume (negative chemical pressure), one normally finds evidence of decreased hybridization. This is the case in Cel_xLaxRu~Si2 for example, where La substitution leads to an antiferromagnetic ground state [24]. Further, the susceptibility of higher La concentration ( x = 0 . 4 , 0.5, 0.8) alloys again exhibits a normal Curie-Weiss behaviour, suggesting the decrease in hybridization with further increasing La concentration. The value of 0p varies between - 2 1 1 and - 152 K. The observed large values of 0p even in dilute Ce alloys could arise from a large axial crystal field term; there may also be a contribution from the Kondo effect. The susceptibility of LaNiSn is almost independent of temperature between 300 and 30 K, which suggests that the Ni atoms are nonmagnetic in LaNiSn. A small rise in the susceptibility is observed below 30 K, which has been attributed to a small amount of paramagnetic

165

impurities. It is to be noted, that the susceptibility of Ceo.05Lao.95NiSn alloy exhibits Curie-Weiss behaviour down to 50 K with /zeff = 5.46 /~B- A similar behaviour was also observed for a second batch of Ce0.osLa0.95NiSn alloy and Ce0.05La0.95RhSb alloy. At present we do not understand the origin of such a high value of /Zeff for low Ce concentration alloys. Therefore, these results are not included here.

3.4.2. C e / _ ~La x R h S b alloys

Figs. 12 and 13 show the magnetic susceptibility of Ce l_xLaxRhSb (x = 0 to 1) alloys as a function of temperature. The susceptibility of CeRhSb and La substituted alloys with x = 0.05 to 0.7 exhibits a weak temperature dependent behaviour between 300 and 30 K and a broad maximum at intermediate temperature: Tmax = 117 K for CeRhSb and 80 K for x = 0.7 alloy. These indicate that the Ce ions in CeRhSb and La substituted alloys with x = 0.05 to 0.7 are in the valence fluctuating (or intermediate valence) state. At low temperature, below 20 K, all alloys exhibit a Curie-Weiss tail. The origins of this low temperature upturn are discussed below and compared with the low temperature susceptibility of Ce~_xLaxNiSn alloys. The susceptibilities of Ce t .,.LaxRhSb (x = 0 to 0.7) alloys exhibit CurieWeiss behaviour in a small temperature range (200300 K). The values of /~eff and 0p obtained from the high temperature Curie-Weiss behaviour are given in Table 2. The observed values of /Xeff are higher

Table 2 Structure type, lattice parameters, effective p a r a m a g n e t i c m o m e n t (P-elf) and p a r a m a g n e t i c Curie temperature (0p) (obtained from the high temperature C u r i e - W e i s s b e h a v i o u r o f susceptibility) o f Ce I - ~ L a ~ R h S b ( x = 0 to 1) alloys

Compound

Structure type

a (~,)

b (A)

c (A)

lU,eff ( ].£B)

0p (K)

CeRhSb Ceo 95 L a 005 R h S b Ceo.9 Lao I R h S b Ceo.sLao 2 R h S b Ceo 7Lao.3RhSb Ceo s L a o 5RhSb Ceo 4 Lao.6 R h S b Ce o ~L a o 7 R h S b Ceo 2 L a 0 . s R h S b Ceo 05La0.95RhSb LaRhSb

TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi

7.416 7.417 7.432 7.439 7.442 7.486 7.500 7.515 7.535 7.542 7.556

4.609 4.616 4.619 4.619 4.627 4.635 4.637 4.640 4.650 4.653 4.660

7.846 7.847 7.855 7.857 7.863 7.876 7.885 7.894 7.898 7.917 7.919

3.37 3.22 3.03 2.95 2.99 3.06 3.20 3.10 2.87 * -

* -

* Unphysical value, see text.

324 309 299 299 267 254 250 215 195

D.T. Adroja et al./Journal of Magnet&m and Magnetic Materials 161 (1996) 157-168

166

8

5 °

E~6.

°

4

-~

.-.=

= 4

-3

D

oo

1oo 200 TEMPERATURE (K)

Fig. 13. Magnetic susceptibility versus temperature for Ce0.2 Lao.sRbSb alloy. The solid line represents fit to Curie-Weiss behaviour.

than 2.54 /~B, the value for free Ce 3+ ion. We believe that the observed high value of /zet.~, is an artifact arising due to the small temperature range where susceptibility exhibits Curie-Weiss behaviour. The negative and large value of 0p for CeRhSb suggests a strong hybridization. Sometime 0p used as a crude approximation of the Kondo temperature, decreases from - 3 2 4 K for CeRhSb to - 2 1 5 K for x = 0 . 7 alloy. On the other hand, susceptibility of x = 0.8 alloy exhibits an entirely different temperature dependence from that of x = 0 to 0.7 alloys (Fig. 13): no maximum was observed in the susceptibility down to 5 K. The susceptibility follows Curie-Weiss behaviour between 300 and 150 K with #err = 2.87 /% and 0p = - 1 9 5 K, but deviate considerably from it below 50 K. The observed susceptibility behaviour suggests that the valence of Ce ion in x = 0.8 alloy is close to trivalent. The observed susceptibility of Ce~ _., La xRhSb (x = 0 to 0.7) alloys have been analysed on the basis of Coqblin-Schrieffer ( C - S ) model [25]. This model is derived from the degenerate Anderson model by means of a canonical transformation, known as Schrieffer-Wolff transformation [26]. The C - S model takes into account impurity mediated hopping of the conduction electrons between various eigenstates of J, where J is the total angular momentum of the impurity: for Ce 3+ J = 5 / 2 . Based on the Bethe ansatz solution of the C - S Hamiltonian, Rajan has calculated the temperature dependent impurity susceptibility for J = 1 / 2 to 7 / 2 [27]. The model is

based on a single parameter, a characteristic temperature To, which is related to the Kondo temperature (T K) through Wilson number, T K = WT0. For J )" l, susceptibility exhibits a peak below T0, which grows with increasing J. In the zero temperature limit, susceptibility exhibits a temperature independent behaviour and scales with degeneracy. The details of this model and analysis are given in Refs. [27] and [8]. In order to account for the low temperature rise in the susceptibility, an impurity term nC/T (where n is impurity percentage and C is Curie constant of free Ce 3+ ion) was included in the analysis of the susceptibility data. The temperature independent susceptibility, Xp was also included in the analysis. The value of parameters, characteristic temperature To , impurity percentage, n and temperature independent susceptibility, Xv obtained from a least squares fit to the susceptibility data of Ce ~_ .,.Lax RhSb alloys with x = 0 to 0.7 is given in Table 3. The quality of the fit may be seen from the calculated susceptibility as shown by solid line in Fig. 12. TO remains almost constant with initial increase of La concentration up to x = 0.3 and then decreases gradually with further increasing x: T0 = 2 7 0 K for x = 0.7 alloy. The decrease in T0 with increasing x is expected, as the negative pressure on Ce ion arising from the expansion of lattice, reduce the hybridization between 4f and conduction electrons. Fig. 14 shows the susceptibility of Ce ~_.,.Lax RhSb and Cel _ xLa ,.NiSn alloys at 5 K as a function of La concentration x. An interesting feature notice is a peak in the susceptibility of Ce~_ ~La,.RhSb alloys about x = 0.1. In our analysis of the susceptibility

Table 3 The characteristic temperature (To), impurity percentage (n) and the temperature independent susceptibility (Xv) obtained from the analysis of susceptibility of Ce I _ ,LaxRhSb (x = 0 to 0.7) alloys on the basis of the Coqblin-Schrieffer model Compound

Tu (K)

n

Xp (emu/mol)

CeRhSb Ceo.9sLao.osRhSb Ceo.9Lao.l RhSb Ceo.sLao.2 RhSb Ce07Lao.3RhSb Ce0.sLao.sRhSb Ceo.4L%.rRhSb Ce03Lao.TRhSb

441 439 446 448 418 372 321 270

0.012 0.025 0.024 0.010 0.010 0.004 0.006 0.016

8.843 x 10 -4 7.104X 10 4 4.656× 10 -'~ 5.500 X 10 -4 5.597× 10 -4 5.697 X 10 -4 7.482 X 10 -4 5.463 × 10 -4

D,T. Adroja et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 157-168

""\\ T=SK

/

/R \

\

J ~'~

\ \

2"

Ce~La~RhSb

o~

o12

014

016

-

018

12 ,? 0

91

[\..

T=SK

. ...,-----'----'-~,\

-,w..~

\\

3

Ce~.Ja,~rtsn 0,

012

0]4

016

\

167

pretation. The rise in the susceptibility of x > 0.5 alloys with increasing x is attributed to the decrease in the hybridization between 4f and conduction electrons, which shifts Ce valence close to trivalent. On the other hand, the susceptibility of Ce]_xLaxNiSn alloys (at 5 K) decreases with initial increasing x and exhibits a minimum at x = 0.2. This is due to the increase in the hybridization as evident from the weak temperature dependent susceptibility of x = 0.2 alloy and /xSR measurements on Ce0.ssLao.~sNiSn alloy. These results suggest that a partial replacement of Ce by La in CeNiSn does not show the effect of the Kondo hole.

0:8

X Fig. 14, Magnetic susceptibility at 5 K versus La concentration, x for Cel_~LaxRhSb and Ce I _ ~La,NiSn alloys. The dotted lines are guide to the eyes.

data, a low temperature tail was attributed to the free Ce 3+ ion impurity stabilized on the lattice defect. It is seen from Table 3 that the impurity percentage n also exhibits a maximum about x -- 0.5-0.1. A similar rise in the low temperature susceptibility with La substitution for Ce in CeRhSb has also been reported [14]. It is interesting to note that for La substituted in Kondo insulator CeRhSb, apart from the free Ce 3+ ion stabilised at lattice defect contributing to low temperature susceptibility, there is another contribution coming from the so called Kondo-holes, as predicted in the theoretical work of Schlottmann on the effect of impurities on the ground state of Kondo insulator [28]. According to Schlottmann theory, nonmagnetic impurity (like La and Y, called Kondo holes) on the Ce sublattice are predicted to produce bound states in the energy gap at Fermi energy. The spectral response associated with these bound states resides on the Ce atoms which are nearest-neighbours to the impurities. These are actually more magnetic than a Ce atom in the undisturbed lattice. Schlottmann has shown that for low Kondo hole concentrations the extra susceptibility is Curie-like and ground state is insulating, while at high concentrations, when impurity-impurity interactions set in, it displays Curie-Weiss behaviour with metallic ground state. Further work on the high purity single crystal of Ce~_xLa,RhSb alloys is needed to check this inter-

4. Conclusions The present studies show a detailed investigation on the effect of La substitution for Ce on the Kondo insulating ground state of CeNiSn and CeRhSb. The powder X-ray diffraction study reveals that though all the alloys crystallize in the orthorhombic TiNiSitype structure, the lattice parameter ' c ' shows opposite behaviour in Cel_ xLaxNiSn and Cel_~LaxRhSb alloys. The transport measurements show that the energy gap in CeRhSb and CeNiSn decreases with increasing La concentration and eventually the gap disappears for 20% La concentration for both systems. This suggests that the well ordered Ce lattice is playing an important role in the stability of the energy gap. This is further supported through our studies of Pr and Gd substitution on Ce site in CeNiSn, which also reveal that the gap disappears at 20% of Pr and Gd substitution [16]. At low temperature, Ce~_ xLa~NiSn alloys exhibit a cross-over from a Kondo insulator (x = 0) to a single ion Kondo behaviour (x > 0.2) with increasing La concentration, while Ce l xLa,RhSb alloys show a cross-over from a Kondo insulator (x = 0) to a coherent Kondo Lattice (x = 0.2) and eventually to a single ion effect for x > 0.5. The magnetic scattering resistivity of Ce0.sLa0.zNiSn shows the presence of Kondo and crystal field effects. The magnetic susceptibilities of Ce ~_, Lax NiSn and Ce ~_ xLa ~RhSb exhibit an opposite behaviour with initial increase in La concentration: the former shows a increasing hybridization with La concentration, while the latter reveals that the hybridization decreases gradually with increasing

168

D.T. A droja et al. / Journal o[ Magnetism and Magnetic Materials 161 (1996) 157-168

La concentration. For the dilute Ce concentration, both alloy systems exhibit Cure-Weiss susceptibility. The low temperature susceptibility of Ce~_xLaxRhSb may suggest the presence of Kondo hole contribution, which was absent in the susceptibility of Ce l_~LaxNiSn alloys. The high field magnetoresistance measurements show that the energy gap decreases with increasing magnetic field for both systems.

[10]

[l 1] [12] [13] [14] [15]

References [l] M.F. Hundley, P.C. Canfield, J.D. Thompson, Z. Fisk arid J.M. Lawrence, Phys. Rev. 13 42 (1990) 6842. [2] T. Takabatake, F. Teshima, H. Fujii, S. Nishigori, T. Suzuki, T. Fujita, Y. Yamaguchi, J. Sakurai and D. Jaccard, Phys. Rev. B 41 (1990) 9607. [3] S.K. Malik and D.T. Adroja, Phys. Rev. B 43 (1991) 6277. [4] See, e.g., T. Kasuya, Jpn. J. Appl. Phys., Ser. 8, 3 (1993). [5] M. Kasaya, F. Iga, K. Negish, S. Nakai and T. Kasuya, J. Magn. Magn. Mater. 31-34 (1983) 437. [6] P.A. Alekseev, J.M. Mignont, J. Rossat-Mignod, V.N. Lazukov, I.P. Sadikov, E.S. Konovalova and Yu.B. Paderon, J. Phys.: Condens. Matter 6 (1994) 1. [7] J.C. Cooly, M.C. Aronson, Z. Fisk and P.C. Canfield, Phys. Rev, Lett. 74 (1995) 1629. [8] D.T. Adroja and B,D. Rainford, J. Magn. Magn. Mater. 135 (1994) 333. [9] F.G. Alive, V.V. Moshchalkov, M.K. Zalyutdinov, G.I. Pak,

[16] [17] [18] [19] [20] [21] [22]

[23]

[24] [25] [26] [27] [28]

R.V. Scolozdra, P.A. Alekseev, V.N. Lazukov and I.P. Sadikov, Physica B 163 (1990) 358. F.G. Alive, R. Viltar, S. Vieira, M.A. Lopez de la Torte, R.V. Scolozdra and M.B. Maple, Phys. Rev. B 47 (1993) 769. T. Takabatake, Y. Nakazawa and M.I. Shikawa, Jpn. J. Appl. Phys. 26 (1987) 547. D.T. Adroja and B.D. Rainford, Pbysica B 199-200 (1994) 498. L Felner and I. Nowick, Phys. Rev. B 33 (1986) 617. S.K. Malik, L. Menon, K. Ghosh and S. Ramakrishana, Phys. Rev. B 51 (1995) 399. Powder Diffraction File-2, Hanawalt Search Manual, Inorganic Phases, JCPDS-ICDD, file no. 38-897 (1993). D.T. Adroja and B.D. Rainford, to be published. B. Cornut and B. Coqblin, Phys. Rev. B 5 (1972) 4541. D.T. Adroja, B.D. Rainford, AJ. Neville and A.G.M. Jansen, Physica B 223/224 (1996) 275. G. Griiner, Adv. Phys. 23 (1974) 941. D.L. Cox and N. Grewe, Z. Phys. B 71 (1988) 321. M.F. Hundley, A. Lacerda, P.C. Canfield, J.D. Thompson and Z. Fisk, Physica B 186-188 (1993) 425. T. Takabatake, G. Nakamoto, H. Tanaka, Y. Bando, H. Fujii, S. Nishigori, H. Goshima, T. Suzuki, T. Fujita, I. Oguro, T. Hiraoka and S.K. Malik, Physica B 199-200 (1994) 457. G.M. Kalvius, A. Kratzer, R. Wappling, T. Takabatake, G. Nakamoto, H. Fujii, R.F. Kiefl and S.R. Kreitzmann, Physica B 206-207 (1995) 807. M.J. Bensus, P. Lehmann and A. Meyer, J. Magn. Magn. Mater, 63-64 (1987) 323. B. Coqblin and J. Schrieffer, Phys. Rev. 185 (1969) 847. LR. Schrieffer and P.A. Wolff, Phys. Rev. 149 (1966) 491. V.T. Rajan, Phys. Rev. Lett. 51 (1983) 308. P. Schlottmann, Phys. Rev. B 46 (1989) 998.