Critical Fields of the "Heavy-Fermion" Superconductor CeCu2Si2

Vor.UMz 49,NvMszR 19

PHYSICAL

REVIEW LETTERS

8 NovzMszR 1/82 'OH. _{Stanley, in proceedings ofthe fnternational}

Con-ference on _{Disordered Systems} and

I.

ocalization, ed-ited by C.Di Castro (Springer-Verlag, Berlin, 1981),

and references therein.

'Y.Gefen, A.Aharony,

B.

B.

Mandelbrot, and S.Kirkpatrick, Phys. Rev. Lett. 47, 1771(1981).

B.

B.

Leibovitz,

E.

I.

Alessandrini, and G.

Deutsch-er,

Phys. Rev. B25, 2965 (1982).

Critical Fields of

the

"Heavy-Fermion"

Superconductor CeCu2Si2

U. Rauchschwalbe, W. Lieke,

C.

D. Bredl, and

F.

Steglieh

Institut fur FesthorPerPhysih, Technische Hochschule Darmstadt, D 6100D-armstadt, West Germany

J.

Aarts,

'"

K. M. Martini, and A.

C.

Mota' '

II.Physikalisches Institut, Unix exsitat zu Koln, D-5000Koln 41, West Germany (Received 12 April 1982)

Measurements are reported ofthe lower and upper critical fields, g &(T)and

~

2(T}, of CeCu&Si~. The observed, extremely high values ofthe slope

(-dB,

~/dT)z, lend strong

CP

support tothe formation ofCooper pairs bythe heavy fermions which exist in the normal state of CeCu&Si2. Characteristic parameters ofthe system ofheavy fermions are de-rived.

PACS numbers: 74.60.-w, 72.15.Qm, 74.70.Rv

Unusual superconducting materials,

e.

g.,

Chev-rel

phases,

'

oxides,

'

or organic conductors,

'

have recently become of great interest in view of potential technical applications and the possibility

of nonconventional mechanisms in

superconductiv-ity.

The (nearly) trivalent ternary compound CeCu,

-Si,

shows well-defined, localized magnetic

mo-ments above T

—

=

10K (Ref. 4), but approaches a.

nonmagnetic state below T

=10

K displaying the

properties of a heavy Fermi liquid';

e.

g., the

specific heat was found tobe C=—

'yT,

_{where y}

=1

J

mole

'

K

'

is

about a thousand times larger

than for simple metals. CeCu,

Si,

becomes

super-conducting below

T,

=0.

6 K (Ref. 5). The height of the specific-heat jump at

T„comparable

to

the giant normal-state specific heat, y

T„has

led to the conclusion' that the superconducting

state of CeCu,

Si,

must be of

a

hitherto unknown kind, in that its Cooper pairs are formed by

quasiparticles of very large effective mass (heavy

fermions). In

fact,

the reference system LaCu,—

Si„showing

usual metallic behavior, does not

become superconducting.

'

To further support CeCu,Si,being the

first

heavy-fermion superconductor, we present in this

Letter

results ofthe lower and upper

critical

fields,

B,

,

(T) and

B„(T).

Special emphasis has been put on the slope of

B~(T)

at

T„which

should

reflect'

the high y coefficient. Analysis

ofthese data will be used to estimate the key

parameters of the normal Fermi-liquid

state.

A wide

scatter

of

_T,

's

has been reported

for

polycrystalline samples of CeCu,

_Si„ranging

from &0.06 K(Ref. 6)to

0.

65 K(Ref. 7). As was

recently shown,

'

however,

T,

= 0.

55 +

0.

15K can always be achieved _{by powdering} and subsequent

proper heat treatment. On the other hand, no superconductivity has so

far

been observed for

CeCu,Si,single

crystals.

"

This might be due to a considerable

(=

—

20%) deficiency in Cu

occupa-tion, as established

for

one of those single

crys-tals.

'

For

the present investigations, two

poly-crystalline bulk samples were used. One of them (No. 7) was annealed at 1100 C and found to be very clean,

'

while the other one (No. 4), annealed at only

900'C,

was

less

clean.

"

Figure 1 shows the field dependence at constant

temperatures of the magnetization Mfor sample No. 7, which exhibits a

static

Meissner effect

corresponding to 60% of the volume, when mea,

s-ured in powder form.

'

Mwas measured by using

a

superconducting flux transformer between the sample and a flux-gate magnetometer

(Hewlett-Packard Model 428B). In the inset, the initial

slopes of these M(B) curves are plotted as a

func-tion oftemperature. The magnetization curves

show broad maxima, probably caused by abroad distribution of demagnetizing fields within

thepoly-crystalline sample. In such a situation, a lower

VOLUME 49,NUMBER 19

PHYSICAL

REVIEW LETTERS

8NovEMBER 1982 M (o.u.) I I I I I I

B„(T)----OO 2.

5—

L.

I-BL.

,

=16.8 K 2.

0—

0 10 15 20 B(mT)

FIG.

1.

dc magnetization, M, ofCeCu2Si2 (No. 7)as a function ofthe external magnetic field, &, at different temperatures. Inset shows low-field slopes of M(B) curves vstemperature.

bound of the lower

critical

field

is

provided by

B„—

=

_B„/(1

—

D) where

B„,

plotted in the inset

of

Fig.

2,

is

the field at which the

first

deviation

from the low-field linear M(B) dependence

occurs.

The demagnetization

factor,

D=-0.20, of sample No. 7was experimentally determined with a Cd sample of the same geometry (4.1x 2.1x 2.0

mm'). Figure 2 shows the temperature depen-dence of Bc2as determined from the midpoints of

either inductive or

calorimetric

transitions for

both samples.

We shall discuss the results on the clean CeCu,

-Si,

sample No. 7

first.

When the data in

Fig.

2

are extrapolated to T=_{0, we find}

_B„(0}=1.

_{8 mT,}

resulting in

B„(0)

=2.

3mT and

B„(0)

=1.

7

T.

This clearly indicates type-II behavior with a large Ginzburg-Landau (GL) parameter K. For

example, in proportion to the relatively low

T„

B„(0)

is

comparable to that of Chevrel-phase superconductors.

'

An upward curvature

is

ob-served at low fields for both

B„(T)

and

B„(T},

presumably caused by inhomogeneities in the

samples.

For

B„(T),

we obtain from the linear

region

(-dB„/dT)

r,

—₌

B„'

=_{5.8 T/K, which}

_is

comparable to the highest values found for

Chev-rel

-phase super conductors.

'

In the following, we shall attempt to analyze this initial slope by using an expression which has been successfully applied to

815

supercon-ductors.

"

Ignoring possible anisotropy effects

in the polycrystalline CeCu,Si, samples, we shall

assume a spherical Fermi surface determined

B()--S.8— L ₀ -1.5 -1.0

j

0.2 0.4 T(K) p~& 1.0 _{Bp) (mT}} 0 I I I

T/

Tc 0.5

FIG.2. Upper critical field,

_B,

2, of CeCu2Si~ as a function of the reduced temperature, T/T,

.

While

_T,

isthe transition temperature at & =_{0as measured,} T,ois defined by ext~aPolation of linear

&„(T)

depen-dence to &

=0.

Data were obtained from ac susceptibil-ity (triangles: No. 7, T 0=

0.

64K; squares: No.4,

T 0=

0.

66K) or specific heat (circles: No.4, T

0-

—

_0.

56

K). Inset shows

_B,

&vs T (No. 7) as explained inthe

text.

by a mean Fermi wave number k_F, yielding"

I

~

7 95X 1032

™

K 7 c C2 ~

J

2 _P 4 F + 4780 _ypo.

Inserting into

Eq.

(1) measured' data for

_T,

(=0.

64 K), the residual resistivity _p,

(=3.

5&10

'

0

m), and the giant (heavy-fermion derived)

co-efficient y

(=2.

0x10~

J

K

'

m

',

with

V,

_q,

=5.

03

&10

'

m'), we obtain 5F

=

1.

7

X10"

m

'.

Prob-ably because of anisotropy

effects,

this

is

slight-ly larger than k_F

=1.

6&10"

m

'

of the ordinary

conduction-electron gas as previously estimated from the maximum high-temperature

resistivity.

"

The latter kFvalue corresponds to areasonable

valence-electron concentration of about 2/atom.

We conclude that both the ox'dinary

conduction-electron gas at high temperature and the l.

ow-temperature Fermi-liquid phase can be described

by similar mean values of the

Fermi

wave

num-ber.

This strongly suggests a description of the

Fermi-liquid phase in CeCu,

Si,

in the

spirit

of Landau' s phenomenological theory,

"

i.e.

_{, by} assuming some strong interaction between

VOLUME 49,NUMBER 19 PH

YSI

CAL

RE

VIEW

LETTERS

8NOVEMBER 1982 duction electrons which leaves the

Fermi

wave

number unchanged but dramatically ~enormalizes

the properties

of

the conduction ele-ctron

states

near

hF.

For

example, the Fermi velocity of the

quasiparticles, vF

=(6.

02x10

"

JK

's

')h F'y

'

~8.

7&10'

m

s

',

and their effective mass, m*

=5k

F

v„'

=220mo, differ by two orders of

magni-tude from the corresponding

free-electron

values.

We wish to

stress

that, because ofthe measured

B„'

value, this Fermi-liquid phase cannot be

attributed to anarrow

4f

band originating from

one tightly bound electron per Ce ion,

"

since

this would imply

a

much too small kF,

i.

e.

,

=0.

7

x

10"

m

'

(associated with v

„=1.

5

x10'

m s

and m*

=

530m,

).

The estimation of some important parameters,

which characterize the novel superconducting

state of CeCu,

Si„

is

also straightforward. Using

relations given in Ref. 11and the above values

for T pp and y, we find the BCS coherence length $0

=1.

9x10

'

m. This

is

comparable to the mean

free

path ofthe quasiparticles, l

= 1.

2

x10

'

m. The London penetration depth

(as

T

-0)

assumes an unusually high value,

i.e.

_, A.

=2&10

'

m. The GL parameter

is

estimated to be

~=22

for

sample No. 7 and

=10

in the "pure limit" (l

»

$0).

With use of this ~value, the above analysis of the initial slope of

B„(T)

can now be supported by the calculation of certain quantities for sample No. 7 and comparing them with the

correspond-ing quantities

as

either directly measured or

cal-culated from the results of other experiments.

For

this purpose, we

first

estimate' the

"orbital

critical field"

(as

T-O),

i.e.

,

B„*(0)

=0.

69B„'

x

T,

~2.

6

T.

This

is

about 50'fo higher than

B„(0)

as measured, pointing to the presence of other

pair-breaking mechanisms like Pauli paramag-netic limiting

or

exchange scattering from

para-magnetic impurities. Now we can estimate the thermodynamic

critical

field (as

T-0)

from

(i)

B„*(0)

and (ii) the

specific-heat

coefficient y

[assuming a parabolic

B„z(T)

dependence]. We find almost the same values, namely (i)

B„h(0)

=B„"(0)/v

2 v,(0)

=66

mT [with v,(0)

=

1.

26m _(Ref. 15)] and (ii)

B,

&(0)

=[7.

65x10

4(m'/J)"']y'"T,

=69

mT (Ref.

16).

This is much higher than

B„h(0) =3

mT of the conventional superconductor Cd with comparable

T,

.

Since

_B„t,

(0) determines the "condensation energy" of asuperconductor,

we find the superconducting state of CeCu,

Si,

to be of much higher thermodynamic stability than

its conventional counterpart. This

is

caused by the extremely high density of Cooper-pair

states,

which tracks the giant _y coefficient, in the

form-er

material.

With

B„q(0)

and ~we can also estimate the

low-er critical

field through B„-(0)=

_B„h(0)

_inK,(0)/

v2_x,(0)

=6

mT, where z, (0)=

_1.

_{15mwas used.}

"

B„(0)

agrees within an order of magnitude with the measured value

(~2.

3 mT), which may be

considered to be satisfying enough, especially

if one keeps in mind the difficulties in measuring

B„(O).

Finally, we

are

able to estimate the

size

ofthe

specific-heat jump at

T„namely

LC

=(6.

86x

10'

JT

'm

_')(22-1)

'T,

B„"

~1.

53x10'

J

K

'

m

'

which

is

very

close

to the experimental value, bC

=1.

59x10'

J

K

'

m

'

(Ref.

7).

These

thermo-dynamic relations give strong evidence that the

Fermi-liquid phase of CeCu,

Si, is

formed by

re-normalized conduction-electron states in the vicinity of hF

=(1.

6-1.

7)

x10"

m

',

and they

dis-prove, again, the picture of one

4f

-derived heavy

f

ermion per Ce

ion";

for

in this

case

k&

=

0.

7

x10"

m

'

results _{in g,}

=

3

x10

'

m, X

=

3

x10

'

m, and ~

=100,

which

is

much too large avalue.

Having found consistency in the various results

for

the pure sample No. 7, we now turn to the

B„data

ofsample No.

4.

As

is

shown.in

Fig.

2, the initial slope of

B„(T)

is 16.

8 T/K for this

sample, the highest value observed for any

super-conductor. From the residual resistivity, _p,

-4

x10

'

0

m (Ref. 17), the mean

free

path of sample No. 4

is

estimated to be much smaller

than the coherence length,

i.

e.

, sample No. 4

clearly represents the "dirty limit.

"

Using the

expression for

B,

2' in the "dirty limit,

""

B„'

=

_(4.

₄₈x 10'

T

K m'

J

'

|7, ')_y

p„with

_{y =}

1.

4

x

10'

J

K

'

m

'

(Ref. 10), we estimate

B„'

~25

T/K.

Again, there

is

satisfactory agreement with the experimental

result.

"

To conclude, we have found that (i) the purer

CeCu,

Si,

sample shows an initial slope of the upper

critical

field

_B„(T)

of the same size

(=6

T/K) as

B„'

of the best high-field

superconduc-tors

(with much higher transition temperatures)

known so

far;

this is caused by the very small

Fermi velocity of the heavy fermions forming the Cooper pairs in CeCu,

Si,

[in the "pure

limit"

B„'-T,

/v~',

first

term in Eq.

(1)];

(ii) a.

de-crease

of the quasiparticle mean

free

path

re-sults in a further increase of

8„'

tothe

record

value of

=17

T/K, which

is

due to an additional contribution [second term in Eq.

(1), -(tvF)

'];

(iii) surprisingly enough, possible anisotropy

effects,

"

which might originate from the quasi two-dimensional structure of CeCu,

Si„do

not 1450

voLUME 49,NUMBER 19

PHYSICAL

REVIEW LETTERS

8NovEMBER 1982 dominate

B„(T)

in the Polycrystalline samples

studied, for the reduced specif

ic-heat-

_jump height

is

of the order of the BCSvalue in either

case'"

and, in addition, the

dirtier,

" i.

e.

, more

iso-tropic, sample shows the higher

8„'

value

[pro-viding an a Posteriotiju'stification of the

assump-tion of a spherical Fermi surface made when using Eq.

(1)];

(iv) the low-temperature

Fermi-liquid phase of CeCu,

Si, is

described by a Fermi

wave number

close

to that of the ordinary con-duction-electron

gas.

The physical origin of both the formation of the

extremely heavy fermions and the attractive

inter-action between the fermions, which constitutes

the novel superconducting state of CeCu,

Si„re-mains unknown.

One ofus

(F.

S.

) should like to acknowledge

stimulating discussions with D. Rainer,

R.

A. Klemm,

@. Fischer,

E.

Muller-Hartmann and

P.

Entel, and one of us (A.C.M.) with K. Kwas-nitza and D. Wohlleben. This work was supported by Sonderforschungsbereiche 65and 125 of the Deutsche Forschungsgemeinschaft.

~ )Present address: _Natuurkundig Laboratorium,

Universiteit van Amsterdam, NL-1018XE Amsterdam, The Netherlands.

i~iPresent address: Laboratorinrn fiir Festkorperphys-ik, Eidgeno'ssiche Technische Hochschule, CH-8098 Ziirich, Switzerlan. d.

For a review, see

g.

Fischer, Appl. Phys. 16, 1 (1978)

.

2See,

e.

g., A. W. Sleight,

J.

L.Gillson, and

P. E.

Bierstedt, Solid State Commun. 17, 27 (1975).

~D.Jerome, A.Mazaud, M. Ribault, and K.

Bech-gaard,

J.

Phys. (Paris), Lett. 41, L95 (1980).

4S. Horn, M. Loewenhaupt,

E.

Holland-Moritz,

F.

Steglich, H. Scheuer, A. Benoit, and

J.

Flouquet, Phys. Rev. B 28, 3171(1981).

F.

Steglich,

J.

Aarts, C.D.Bredl, W. Lieke, D.Meschede, W.Franz, and H. Schafer, Phys. Rev. Lett. 48, 1892(1979).

6G.W.Hull,

J.

H, Wernick,

T.

H.Geballe,

J.

V. Waszczak, and

J.

E.

Bernardini, Phys. Rev. B 24, 6715(1981).

VW. _{Lieke, U. Rauchschwalbe,} C. D. Bredl,

F.

Steg-lich,

J.

Aarts, and

F.

R.de Boer,

J.

Appl. Phys. 53, 2111 (1982).

C.D. Bredl, H.Spille, U.Rauchschwalbe, W.Lieke,

F.

Steglich, G.Cordier, W. Assmus, M. Herrmann,

and

J.

Aarts, in Proceedings of the International Con-ference on Magnetism, Kyoto, 1982(to be published).

F.

G.Aliev, N.

B.

Brandt, 8,

. B.

Wociev, V. V.

Moshtaukov, and S.M. Chubinov, Pis'ma Zh. Eksp.

Teor. Fiz.35, 435 (1982).

F.

Steglich,

J.

Aarts, C.D. Bredl, W. Lieke, D. Meschede, W.Franz, and H. Schafer,

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Magn. Magn. Mater. 15-18,889 (1980).

T.

P.

Orlando,

E.

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McNiff,

Jr.

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~4K._Andres,

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_E.

Graebner, and H. R.Ott, Phys. Rev. Lett. 85, 1779(1975).

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Serin, in Superconductivity, edited by R.D.

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9.

"R.

R.Hake, Phys. Rev. 158, 856 (1966). Whereas &,2(T) of sample No. 4 was determined after annealing at 900'C, the resistivity was measured

in the unannealed state only and, therefore, can be taken only as an upper bound ofpo for the annealed sam-ple.

From &,2'——_{16.8T/K we would expect the residual} resistivity ofthe (900'C) annealed sample No.4 to be po

=2.

7x.10

0

m, quite a reasonable value.

See,

e.

g., M. Ikebe, K.Katagiri, N. Noto, and

Y.Muto, Physica (Utrecht) 99B,209 (1980);

P.

Entel

and M.Peter,

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