SOFT PHONONS AND MAGNETIC ORDERING IN THE γ-PHASE TRANSITION METAL ALLOYS Fe1-xPdx

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SOFT PHONONS AND MAGNETIC ORDERING IN

THE γ-PHASE TRANSITION METAL ALLOYS

Fe1-xPdx

M. Sato, B. Grier, S. Shapiro, H. Miyajima

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque

C6,

suppZe'rnent au no

12,

Tome

42,

de'cenbre

1981

page

C6-770

SOFT PHONONS AND MAGNETIC ORDERING IN THE Y-PHASE TRANSITION METAL

ALLOYS

Fel-xPdx

X li X X*

M. Sato

,

B.H. ~ r i e r * , S.M. Shapiro and H. Miyajima

X

Brookhaven National Laboratory, Upton, New York

11 973, U .

S.A.

St*

The Institzrte for SoZid State Physics, the University of Tokyo, Roppongi,

7-22-1,

Minato-ku, Tokyo

106,

Japan

A b s t r a c t .

-

Neutron i n e l a s t i c s c a t t e r i n g measurements have been performed on two s i n g l e c r y s t a l s of t h e t h e r m a l l y quenched y-phase ( f c c ) a l l o y , Fel-,PdX with x = 0.28 and x = 0.37. The x = 0.28 sample which o r d e r s ferromagneti- c a l l y a t Tc = 575 K e x h i b i t s a smeared s t r u c t u r a l t r a n s i t i o n i n t o a n f c t phase n e a r TM = 265 K. An anomalous d i s p e r s i o n of t h e [<SO]TAl branch due t o t h e d e c r e a s e of t h e phonon energy around t h e r p o i n t develops below Tc. A s t h e temperature d e c r e a s e s , t h e branch d e c r e a s e s i n energy. The anomalous p a r t of t h e e l a s t i c c o n s t a n t , A(Cll-C12)/2, f o l l o w s t h e same temperature dependence a s t h e s q u a r e of t h e magnetization. On t h e x = 0.37 sample which h a s no s t r u c - t u r e t r a n s i t i o n , t h e phonon anomaly i s much weaker. For both c r y s t a l s t h e o t h e r branches e x h i b i t normal behavior.

The iron-based I n v a r a l l o y s , Fel-xNix, Fel-xPtx, and Fel-xPdx undergo a marten- s i t i c f c c t o bcc f i r s t - o r d e r phase t r a n s f o r m a t i o n a t temperature TM w e l l below t h e magnetic o r d e r i n g temperature T

.

The l a t t i c e dynamics of Fe N i ar,d Fe P t

1-x x 1-x x a l l o y s have been e x t e n s i v e l y st:died by u l t r a s o n i c l s 2 and i n e l a s t i c n e u t r o n s c a t t e r - ing

technique^^'^

w i t h t h e g o a l of understanding t h e r e l a t i o n s h i p between t h e I n v a r p r o p e r t i e s , t h e magnetization M and t h e m a r t e n s i t i c t r a n s i t i o n . I n Hausch's u l t r a -

1 2

s o n i c s t u d y of Fel-xNix and Fe P t h e observed an anomalous d e c r e a s e of t h e e l a s t i c

3 ₂

c o n s t a n t s C44 and ~ ( c ~ ~ - c ~ ~ ) , which h a s t h e same temperature dependence a s M

.

This was e x p l a i n e d a s due t o a s t r a i n dependent exchange coupling i n t h e Heisenberg s p i n

1

system. Bndoh e t a l s o observed an anomalous behavior of T(C11-C12) i n Fel_NiX by n e u t r o n s c a t t e r i n g measurements, b u t emphasized t h a t t h e anomalous p a r t of 1

-(C _{2 11 12}-C ) v a r i e s l i n e a r l y i n

M.

T h e i r e x p l a n a t i o n was based more on t h e dynamical response of t h e conduction e l e c t r o n s t o t h e s t r a i n .

Recent

measurement^^'^

on Fe _1-xPd _xa l l o y s have shown t h a t a n o t h e r phase, a face- c e n t e r e d t e t r a g o n a l ( f c t ) phase, e x i s t s between t h e f c c and bcc phases. I n t h i s paper, we r e p o r t on t h e l a t t i c e dynamics of Fe _lix Pd _xs t u d i e d by i n e l a s t i c n e u t r o n s c a t t e r i n g and show t h a t t h e anomalous p a r t of ?(Cll-C12) f o l l o w s t h e temperature

2

dependence of M

.

The measurements were performed on two s i n g l e c r y s t a l s of Fe Pd w i t h x = 1-x x

0.37 ?r 0.01 ( c r y s t a l 1 ) and x = 0.28 f 0.01 ( c r y s t a l 2 ) . The c o n c e n t r a t i o n of crys- t a l 1 is such t h a t i t does n o t e x h i b i t any s t r u c t u r a l phase t r a n s f o r m a t i o n below t h e Curie p o i n t . C r y s t a l 2 e x h i b i t s a n f c c t o f c t t r a n s i t i o n n e a r TM = 265 K but because of c o n c e n t r a t i o n g r a d i e n t s t h e t r a n s i t i o n i s smeared o u t over 35 K. I n a d d i t i o n , a "on l e a v e from t h e I n s t i t u t e f o r S o l i d S t a t e P h y s i c s , The U n i v e r s i t y of Tokyo, 7-22-1,

Roppongi, Minato-ku, ~ o k ~ o 106, Japan

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(0.15,0.15,01 TA I

0 2 4

ENERGY TRANSFER (meV)

Fig. 1. Examples of the observed pro- files of the [SSOITAl soft phonon branch.

Fig. 2. Dispersion of the [<SO]TAl phonon branch at various temperatures.

bcc phase also appears at lower temperatures. Because of this, it was not possible to study any of the details of the critical dynamics associated with the martensitic transition near T

M -

Fig. 1 shows the observed spectra of the [5SO]TAl phonons for 5= 0.15 measured

1

at several temperatures. This branch corresponds to the elastic constant -(C -C ) .

2 11 12

At T = 676 K, which is greater than

T

= 575 K, the spectrum is symetric and rela-

tively narrow. As T is lowered, the frequency decreases and the linewidth increases. This is opposite to that expected from normal anharmonic processes. The small q por- tion of the dispersion curve for this branch is shown in Fig. 2. Above Tc, the dis-

persion curve is linear.

As

T decreases, an anomalous upward curvature develops.

1

We can compare the anomalies in ;?(Cll-C12) to the magnetization by defining the

quantity 6' =

5

i

w2 (T>Tr)-w2

(T)

_where_w_{(T) is the (<<O]TAl phonon energy. The extra-}

~VT>T,)

5

I

polation of ti2 to <=0,

IS^,

is the amount that the elastic constant changes below

T

c' Fig. 3 shows the behavior of 62 as a function of temperature. This is compared with

M(T) and M~(T) and it can be seen that the anomalous contribution to

?(c11-c12)

has

the same temperature dependence as

M~(T).

This agrees with the results of Hausch

for Fe Ni and FejPt, but differs from thosof Endoh et al. on Fe0.65Ni0.35 where

1-x x

62 % M(T).

When the quantity 62 approaches 1, the elastic constant

% ( c ~ ~ - c ~ ~ )

goes to 0. In

Fig. 3, the extrapolation of 62 to unity occurs at a temperature very near the martensitic transition temperature. This implies that the coupling to the magnetization which is responsible for the phonon softening is intimately related to the driving mechanism of the fcc-fct transition. Evidence to support this comes from the fact

that in crystal 1, x = 0.37, no martensitic (fcc-fct) transition occurs and the

anomalous phonon behavior is much weaker.

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C6-772 JOURNAL DE PHYSIQUE

Fig. 3. The amount of the softening of the elastic constant 1/2(Cll-C12) norma- lized by the values above Tc is shown. This is determined by the extrapolation of 6-2=[l-u2(~)/u2(~>~C)]11 to 5x0. The

temp5rature dependence of

M

and

M~

is

shown by the broken lines.

the [SLO]TAl phonons as

T

decreases be-

low Tc. This cannot be explained by a

macroscopic inhomogeneity of x. However

a coupling of the phonons to some other fluctuations, such as spin fluctuations

oh

,do

2& 3&-,

4A0

5;0

\AO

or charge density waves, can explain the

+

T ( K ) T and q dependences of the linewidth.

The detailed study of the linewidth remains a future problem.

Acknowledgments

-

The authors are indebted to

M.

Matsui for providing them with use-

ful information. They are grateful to G. Shirane for his support and to S. K.Sinha for useful discussions. Work at Brookhaven was supported by the Division of Basic Energy Sciences, U. S. Department of Energy, under Contract no. DE-AC02-76CH00016. References-

1.

G.

Hausch, phys. stat. sol. (a)

2,

501 (1973).

2.

G.

Hausch,

J.

Phys. Soc. Jpn

3,

819 (1974).

3.

K.

Tajima, Y. Endoh, Y. Ishikawa, and W. G. Stirling, Phys. Rev. Lett.

37,

519

(1976).

4. Y. Endoh and

Y.

Noda,

J.

Phys. Soc. Jpn

66,

806 (1979).

5.

M.

Matsui, T. Shimizu, H. Yamada, and K. Adachi,

J.

Magn.Mag. Mat. =,1201

(1980).

6.

M.

Matsui, H. Yamada, and K. Adachi, J. Phys. Soc. Jpn

48,

2161 (1980).

7.

S.

K.

Sinha, Dynamical Properties in Solids, ed.

G.

K. Horton and A. A.