Phonons and Specific Heat of electron High Tc Nd1.85Ce0.15CuO4 Superconductor

Applied

Superconductivity

Printed

tn Great

Nos 3-6,

Vol.1,

Britam

All rtghts

Phonons

and

pp. 405 - 409.

Copyright

Specific

NdingCeo Bal

K. mawal,

heat

&h04

5.

of Physics, Allahabad

of electron

a%6;h Tc

Superconducfoc

.

J.S. Negi,

Departmernt

0964-1807/93 $6.00 + 0.00 @ 1993 Pergamon Press Ltd

1993

reserved

-rawal

and of

Utiverslty

PS.

Y&v

AUahabad.

- 211 002, India, ABSTRACT

A expiain neutron

simple Born reasonably data

model has been seen to well the optical and available for the high Tc OXi&

superconductor. The high frequency phonon bands reveal highiy two-dimensionai behaviour. PIanar dispersions are significant for the different Iayers. The Lattice specific heat in the low temperature region shows a non-Debye behaviour i.e., a variation different from a

T3 - one. The Nd a_xC"xCu04 CI4Anmm unit

> crystal cell

structure.

oca,;

lattice parameters are

The

a-3.95 A

formula

<2/2,1/2,1/2> with respect In the

present

have

carried

over

OUT

earlier

the

and

units

cakulation values

of

of

calculations

thus,

we

to

have

interactions with

the

interaction

reproduce assumed

and

have

The

c-12.07 A. In one

unit

; one

unit

displaced

by

Cu-0 bonds 1) TI-systems and

experamentai

only two

for

values

Table I. 405

for

a reasonably

data. The the

for

we

from have

determining their values in has been chosen for

the

achieved

Nd2_xO”xCu04,

the



the

avnllrrhle measured parameters

<0,1/2,0>;

tvz,o,y/4>.

for

employed a l/d3 vazdation for present system. A set of bonds

in the

to other.

the

Nd-0

positions

Ocl>:,

co,in,y/4,,

are

two

T'phase has a bet

atomic

cu:<0,0,0>;

are

NdE<1/2,1/2,~06>;

cell there

allays possessing

various

data.

In

for

all, Nd-0

well agreement

used

values

bonds

are

of the

skwn

in

World Congress on Superconductivity

406

1 1;,, ]

t\ lg K,,

Ntl: Ntl,,

Ntl; ( &.,,, Nh,r

1 1

tfjl (157) 230

I ]

I 35

139 150

I

I ( 139) 228

1 t 230

12!) 228

World

The

calculated

compared II, we

with have

of Heyen

the

frequencies

et

The

The

t

data

the

phonon

reWts

systems

along

some

3. The

symmetry

O>, X

Cl 2 0)

paizkts are and

axrves

symmetry Z
0

0

of

phonon

d2spersion

m

in Table

freqmncAes 3-m with the experiment.

agreement

at "

for

sxperime~

inclrrcksld a&o

407

ore Superconductivity

Congress

been

II. In T&ale caicuiat~on

the

me

in reasonable

Nd,~Ceo_~CM14

for

d%rectians

have

am3

shown

desftraated as EC0

in Pig.

0 O>, D

1). It is observmd

that

C* 0

ail the

optic& phonons involving: oxygen motions appear above -2 cm and exhibft. a two- dimensSoz~& C2 - D> behavkmr.

The

B_

The

mode

reved

calculated phonon

smaii

dispersion

density of s+a+es

neutron

d&P

observed

in the neutron

tn

2.

Fig.

AU

a.Lory the

c-axis.

are compared

the

300

with the

cdcul&aM

pedcs

data and their locations are

are

aiso

500

‘; E s *

400

300

100

i s e)

300

500

Density

of States.

200

Fig.2.

G

Phonon

100

f

Fig.1.

in

Good

Location 120

am+

D

Phonon

dispersion

of

peaks: which

aro&

2

curve.

There

agreement.

sxpewimentcaf obtained

r

X

the is

are

lowest abou+

counterpart. 400 cm -1

two

calculated 20

cm-l

other

The nhure

discrepancies

the

cal-

peak h3.@aer

in

appears than

at the

dlscreparkcy d peaks

the

is

appear

World Congress on Supercondactlvity

408

at

30-40

about

Keep*

in

agreement

view

the

between

is not far from

The

In

our

we

have

of

in

the

linear region

of

thu

up

to

acoustiemode

certain

calculated and

Born

the

model,

measured

the

results

has

been

calcuiated

wave Temperature

specific

Co

for

600

(K)

the Fig.3.

COmpOU2-M-i

Ndl.8S%MSc*4 been depicted

400

200

The

vector. calcuLated

Specific

heat

vs Temperature,

has in Fir;

3. The specific heat i~SJWF%S

with In

temperature. order

to

law

in

V43PSUS

the

the

T3 low

the

frequency have

test of

validity

regicxk

plotted T

for

we

O-%%I K in

Fit;. 4.

Fig.4.

C,/T3

is quite different

100

50 Temperature

the r-e

behaviour

0

QU/T3

temperature

The

one. the

mtnimum

of

heat

the

Vebye

the

approximation

value

simplicity

experlmental

the

range

caIculation,

a

than

specific heat

phonon

K.

involved

the

loner

satisfaction

temperatt.uW O-600

cm-*

(K)

vs Temperature.

from

the T3 law.

for a

409

World Congress on Superconductivity RE-

1)

Bal

2)

E.T. Beyen

3)

E.T. REYEN

K. Agrawal

et al,

Phys. Rev. B4f3, 3152 ClS92>.

et al, Solid State et

a3, Phonon

89

Co-

71i, C1990) 2299.

p.346, edited

by

S. Humei

et al World Scientific CSlngapure). 4)

S. Swai

5)

M. Crawford

6)

J.W. Lynn et al, Phys. Rev. X.&As.

et al, Phya et al,

Rev. BIO, 2686

<1939>.

Phys. Rev. Bli, 3933<1990). 65,

C1991> 9l9.