Point contact spectroscopy of heavy fermions

Journal of Magnetism

and Magnetic

Materials

54-57

POINT CONTACT SPECTROSCOPY M. MOSER,

P. WACHTER,

(1986)

373

373-374

OF HEAVY FERMIONS

J.J.M. FRANSE

*, G.P. MEISNER

** and E. WALKER

+

Pomt contact spectroscopy (PCS) has been performed on the heavy fermion systems CeAI ,_ CeCu,. UPt,. l&Co and U,PtC2. The dynamical resistance dU/dl is a function of the electromc density of states (EDS) at E, The width of the EDS inferred from the PC measurements can he compared with the y-value of the specific heat.

Point contact spectroscopy (PCS) has been used more and more for exotic materials like intermediate valence or heavy fermion compounds [l]. Usually a sharply etched MO wire is contacted with the material to be investigated at temperatures T around 4.2 K. The dynamical resistivity dU/d I and its derivative d’U/d I* are then measured with a conventional modulation technique as a function of an applied dc voltage in the meV range. The theory of PCS is well developed in the case where the electronic density of states (EDS) is constant near the Fermi energy E,. In that case d*I/dU’ is proportional to a*F, the quasiparticle density of states times the square of the matrix element of the electron-quasiparticle interaction [2]. But when the EDS is a strongly varying function of energy, as expected for a heavy fermion system, no general theory exists. As already mentioned in ref. [3] the first derivative dU/df is related to the electronic density of states: A maximum (minimum) in the symmetric part of (dU/dI) (U) corresponds to a minimum (maximum) in the EDS. where a minimum in the EDS means a gap or a pseudogap. A simple model [l] illustrates this result which was gained by comparing PC data with results obtained by other methods (e.g. far infrared spectroscopy). On the other hand, the antisymmetric part (ap) of dU/dI is not coupled in an obvious way to physical properties like mixed valency or heavy fermion features. There are mixed valence and heavy fermion compounds with symmetric dynamical resistivities (e.g. Sm$ and UPt,, respectively) as well as such with asymmetric ones (e.g. YbCu2Siz and CeAI,, respectively). The compounds showing asymmetric dU/dl functions all contain either Ce or Yb. The ap of dU/dI of these Ce-compounds (Yb-compounds) increases (decreases) with increasing voltage. (The sign of the voltage refers to the sample.) Thus the ap of dU/dl seems to be related to the nature of the charge carriers, i.e. electrons or holes [4]. Here we shall concentrate on the symmetric part of dU/d I. Experiments have shown that the contributions of the inelastic processes to the PC signals are at least one order of magnitude smaller than the observed structure in dU/dl around zero bias, as no phonon traces are 0304~8853/86/$03.50

visible in d’U/dl’. One observes two extrema in d’U/dl’ which are due to the points of inflexion of dU/dZ. We have taken the energy separation between the two extrema in d’I/dU’ as a measure of the width of the peaks or (pseudo) gaps in the EDS at Et. (The model mentioned above [l] implies that, for T= 0, dI/dU is proportional to the EDS. Therefore we consider d//dU and its width determined by the distance of the two extrema in d’I/dU’ instead of the measured derivatives of U.) Intermediate valence or heavy fermion compounds are precisely the materials in which one expects narrow EDS structures near E,. For these compounds the standard experiment is the measurement of the specific heat, which delivers unusually large y-values and, therefore. demands narrow (a few meV) EDS structures. However, conventional methods like XPS or UPS never revealed these structures, because, in principle these methods measure the bare electron EDS some eV below E,. The physical properties of these materials, however, are determined by the electron quasiparticles at E,, i.e. the manybody interactions. PCS is one of the few low energy spectroscopic methods which can investigate quasiparticles in the meV range. It is thus capable of revealing these narrow structures. We have measured 5 heavy fermion systems with PCS. CeCu,, CeAI, [I]. UPt,. U,Co and QPtC,. The U-compounds also become superconductors. In the case of a CeCu, single crystal dU/dI is extremely asymmetric (fig. 1). similar only to the intermediate valence compound CePd, [3]. Fig. 1 shows the differential resistance dU/dI and its symmetric part. The two insets contain the antisymmetric part of dU/dI and the derivative of the symmetric part of d f/dU. respectively. In fig. 2 we display dU/d I of UPt, single crystals. where instead of a Mo tip we used another single crystal of UPt, (homojunction). Homojunctions guarantee that all contributions to the PC spectra have their origin in the physical properties of the material one would like to investigate (surface contaminations excluded). A second advantage is that they are usually more stable than heterojunctions. In fig. 3 we finally exhibit PC spectra of a U,PtC, homojunction. (It should be noted that all

G Elsevier Science Publishers B.V.

374 5. I

r

E

6

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CeCu,

H

-0

?I

I

7l

\

I

Ll,PtC,

-25

0

25

Energy 4.4

_E

-25

0

Energy Fig.

I.

dti/d/

of

a

i 4.65 50

25

Mo/CeC‘u,

PC

T=

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3.

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eta

(JLQ’dl),. Insert.\: antisymmetric part of d(l/dl of the symmetric part and derivative (d,‘dU(dI,‘dL:),).

Fig.

[meVl

tracer

of

uncertainty.

dl/d(,

most

K.

like that of a normal

The

and

metal

with

For

U,Co

dLi/dl

which

certainly

widths

of

separations 15 meV

respectively.

the of

EDS

no significant

for CeCu,, The

structures

the second

structures

CeAl,

narrower

taken

derivatives [I].

UPt,

the structure.

and

4.2

d’//dL’

(full

Ilnc)

of

‘1

K.

from are

and

the

2. 2, 4 U,PtC,.

the larger

measure

of

roughly

scale

to he

the

of only

the

width

corresponds

&

standard

above

innovative

420.

compound\

the

that

From

the

can

also

fermionx.

1 eV

In the sequence

we obtain

U,C‘o

the EDS

heavv a

75

men-

for

we

that

a

is found

by PCS.

of

is

should

1600,

mol f-atom)

value

L’,

If PCS

This

1600.

structures

masse5 textbook

mentioned and 66~1.

EDS

one clec-

peaks

no surprise

to W* = m.

hand

of com-

HI* = 50On1.

5OOrt7.

respectively.

Summarizing. 0

the

the

the four

I<, EDS

around

y-value. of

21 mJ/(K’

effective

the

pounds

the

to be detected

of

using

250/>1

with

the

[I].

of

y-values

meV.

only

structure

width

I of

not he SO large.

fractional

It is therefore

width

estimate

only

[5] for

is too weak

could

repulsion, EDS

the

using

f-atom)

above.

mcasurcd

E

EDS

to

maximum

y-values

total

inversely

a y-value

structure

1.5

the

the

mol

tioned

the

is thus

case.

amounts

at the

to Coulomb

occupy

mJ/(K’

the

due

occupation

with

2.5

otherwise

can

The

probably

lies right

addition.

tron

looks

T<.

above

peak

plots.)

line) 7‘=

symmetric part ((dC’/dl),,,)

In are direct

(dashed

homojunction:

structures,

figures

se

ImeVl

PCS

has proved

method

providing

on

narrow

to be a powerful

a wealth

of

and

information

l-i

m

especially

> -u

Wongly

[II

upt,

’

M.

Moser.

Solid

Ill

P.

State

A.G.M.

0

-15

Energy 2. d(i/dl

homojunction:

(dashed T = 4.2

line) K.

15

d’//db”

the

EDS

01

Wachter.

F.

A.P.

Hulliger

54 (19X5) van

Gelder

and

J.R.

Etourneau,

241. and

P. Wader.

J. Phy.

C‘

and

P.

Wachter.

I. 141 0. Busslan, Let. 49 (19X2)

FrankowL

and

151 G.R.

Rev.

J.

Appl.

Phyh.

Si

(IYXZ)

7xx7.

CmeVl and

in

6073.

131 I. Frankowskl

0

_’

structures

electrons.

Commun.

Jansen.

13 (1980)

Fig.

the

interacting

(full

Ilne)

of a UPt

1

ence

Stewart. cited

D.

Wohllrben.

Phys.

Kc\.

and

refer-

1026.

therein.

Mod.

Phys.

56

(lYX4)

755