INTRODUCTION TO THE STUDY OF DAMPING EFFECTS DUE TO MAGNETIC, ELECTRONIC PROPERTIES AND TO PHONONS INTERACTIONS

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INTRODUCTION TO THE STUDY OF DAMPING

EFFECTS DUE TO MAGNETIC, ELECTRONIC

PROPERTIES AND TO PHONONS INTERACTIONS

J. Degauque, A. Zarembowitch

To cite this version:

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JOURNAL

DE PHYSIQUE

Colloque C5, suppldment au nO1

7,

Tome 4 2 , octobre 1981

page

C5-607

INTRODUCTION T O T H E STUDY OF DAMPING EFFECTS DUE T O MAGNETIC,

ELECTRONIC PROPERTIES AND T O PHONONS INTERACTIONS

J . Degauque and A . ~arembowitch*

k b o r a t o i r e de Physique des Solides, associd au C.N.R.S.,

I.N.S.A.,

Avenue

de Rangueil, 31077 Toulouse Cedex, France

*kboral;oire de Dynamique

du

Rdseau e t Ultrasons, Universitd Paris V I ,

4 ,

place Jussieu, 75230 Paris-Cedes 05, France

A b s t r a c t . - T h i s i n t r o d u c t i o n t o theme V w i l l be devided i n t o two p a r t s . The f i r s t p a r t w i l l be devoted t o magnetic damping ( 7 p a p e r s ) ; i n t h e second p a r t t h e i n t e r e s t w i l l be focussed on e l e c t r o n i c p r o p e r t i e s and phonons i n t e r a c - t i o n s ( 7 p a p e r s )

.

When i t

i s

s u b j e c t t o a c y c l i c mechanical v i b r a t i o n , a ferromagnetic m a t e r i a l can ma- n i f e s t a damping of magnetic o r i g i n due t o h y s t e r e s i s e f f e c t s or/and a n e l a s t i c r e l a - x a t i o n e f f e c t s . The aim of t h i s a r t i c l e

i s

t o i n t r o d u c e t h e p a p e r s p r e s e n t e d i n s e s - s i o n V and which a r e more o r l e s s concerned w i t h t h i s damping. For t h i s purpose, a s h o r t summary o f t h e p h y s i c a l phenomena concerned i s b r i e f l y p r e s e n t e d .

I n most of t h e papers of t h e second p a r t , u l t r a s o n i c waves a r e used a s a s e n s i t i v e t o o l t o probe a p h y s i c a l phenomena s l i g h t l y coupled with mfchanical s t r e s s . The inves- t i g a t e d p h y s i c a l phenomena a r e : i n f l u e n c e of i m p u r i t i e s on f e r r o e l e c t r i c t r a n s i t i o n , anomalous behavior of some superconducting m a t e r i a l s , i n f l u e n c e o f a magnetic f i e l d on shallow donnors i n semiconductors, an u l t r a s o n i c Kondo e f f e c t , energy t r a n s f e r t between o p t i c a l phonons i n molecular c r y s t a l s

...

A l a r g e v a r i e t y of m a t e r i a l s i s i n v e s t i g a t e d : semiconductors, superconductors, f e r r o - e l e c t r i c s , molecular and ionic-molecular c r y s t a l s .

A f t e r d e s c r i b i n g b r i e f l y t h e p h y s i c a l phenomena concerned, t h e i n t e r e s t o f using an u l t r a s o n i c probe i s emphasized.

I . MAGNETIC E F ~ C T S .

-

Magnetomechanical h y s t e r e s i s

.-

Consider a homogeneous t e n s i l e s t r e s s V a p p l i e d t o a ferromagnetic m a t e r i a l . Let t h e r e be two magnetic domains with

-+

-C

magnetization v e c t o r s I I and I1 s e p a r a t e d by a domain w a l l ( D . W . ) ( F i g . I ) , making a n g l e s

3fl

and

o2

with t h e d i r e c t i o n o f t h e s t r e s s . There

r e s u l t s then

a

v a r i a t i o n o f m a g n e t o e l a s t i c energy, p e r u n i t volume :

A U

=

-

2

As

C ( C O S

2 y2

-

cOs2

yl)

+

where

As

: s a t u r a t i o n m a g n e t o s t r i c t i o n i n d i r e c t i o n s o f I

1 and

3.

When and

3

a r e p a r a l l e l ,

A U

i s z e r o : t h e

s t r e s s d has no i n f l u e n c e on a 180° D.W. On t h e o t h e r hand, I

f o r a 90°D.W. ( b . c . c . m a t e r i a l s with e a s y magnetization i n F i g . 1

t h e

[loo]

d i r e c t i o n , e . g Fe) and f o r 71° o r 109' D.W.s ( f . c . c . m a t e r i a l s w i t h e a s y ma- g n e t i z a t i o n i n t h e

El11

d i r e c t i o n , e . g . N i ) , t h e s t r e s s e f f e c t induces a v a r i a t i o n o f n u and a displacement of the D.W. Consequently, t h i s s t r e s s e f f e c t s i m u l a t e s a

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C5-608 JOURNAL

DE

PHYSIQUE

magnetic f i e l d H b which, i n t h e absence o f r o t a t i o n of

7

and

3

i s , roughly :

H q N

- -

( w i t h I s =

1 1 ~ 1

=

1 1 ~ 1 ) .

The d i f f e r e ~ t behaviour of 180' and 90"

2 ' 1%

D.W., s u b j e c t e d - t o s t r e s s e f f e c t can be a l s o understand i f we suppose a c u b i c f e r r o - magnetic sample cooled from paramagnetic s t a t e . Owing t o m a g n e t o s t r i c t i o n , on p a s s i n g through t h e Curie temperature, a c u b i c l a t t i c e s t r a i n occurs i n d i r e c t i o n s determined by t h e d i r e c t i o n of spontaneous magnetization. Those s t r a i n s being along one o r o t h e r o f two p a r a l l e l d i r e c t i o n s of a 180° D.W., no s t r a i n i s s e t up a l o n g

t h i s w a l l while i n t h e 90° D.W. c a s e , a n e t d i s t o r t i o n appears along t h e w a l l . When a s h e a r s t r e s s e s

?

a r e i n t r o d u c e d i n a rod by t o r s i o n , t h e y a r e e q u i v a l e n t t o a combination of t e n s i o n ( +

6 )

and compression ( -

6 )

s t r e s s e s of e q u a l s t r e n g t h and a t r i g h t a n g l e s t o each o t h e r . I n t h i s c a s e , i f ? i s a p p l i e d t o a ferromagnetic sam- p l e , t h e r e w i l l be a p r e f e r e n t i a l d i s t r i b u t i o n

of magnetic domains o r i e n t e d i n t h e + U d i r e c -

I

Sample

axis

t i o n i f

A>

0 (Fe)

,

o r i n t h e

- a

d i r e c t i o n

I

i f A s < O ( N i ) ( P i g . 2)

.

Therc w i l l be r s s o -

I

c i a t e d with such a d i s t r i b u t i o n , a magneto-

s t r i c t i v e s h e a r s t r a i n

I s

which

i

_I

xG

adds t o t h e e l a s t i c s t r a i n

Ie

and which

1

reaches a s a t u r a t i o n value ( ) f o r high

2 .

1 r m

s

Owing t o t h e i r r e v e r s i b l e n a t u r e of t h e 90'

1

D.W. movements, when r e t u r n s t o z e r o , a rema-

1

n e n t m a g n e t o s t r i c t i v e s t r a i n

Tr

remains. The v a r i a t i o n

ym

= f ( r ) d e s c r i b e s a magnetome-

I

J+G

I

c h a n i c a l h y s t e r e s i s loop w i t h energy l o s s

A W

1 \-c

which a r e p r o p o r t i o n a l t o

2".

When i n c r e a s -

I

s e s from t h e z e r o v a l u e , n d e c r e a s e s c0ntir.u-

I

o u s l y from n = 3 (Rayleigh r e g i o n f o r s m a l l

Z )

I

pqf

t o n = 0 ( s a t u r a t i o n ) . The l o s s e s a t s a t u r a t i o n

.

,

A<o

I

a r e a t t a i n e d when a l l of t h e 90' D.W. i r r e v e r -

s i b l e jun~ps have taken p l a c e . Under a c y c l i c v i b r a t i o n , t h e ferromagnetic m a t e r i a l m a n i f e s t I

a magnetomechanical damping Q-'

.

independent Fig. 2 : P r e f e r e n t i a l d i s t r i b u - ma9 t i o n o f magnetic domains, under on t h e frequency and which, when measured a s a s h e a r - s t r e s s e f f e c t .

f u n c t i o n of

?

( o r s h e a r s t r a i n ] )

,

shows a maximum f o r n nearby of 2 .

The importance of Q-I depends on t h e magnetic domain c o n f i g u r a t i o n and i n p a r t i c u - mag

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magnetic behaviour (mainly i n f l u e n c e d by 180' D.W.s) and t h e magnetomechanical beha- v i o u r vary i n o p p o s i t e d i r e c t i o n s . This r e s u l t which i s e a s y t o understand,

i s

q u i t e o r i g i n a l because more o f t e n t h a n n o t , i n m a t e r i a l s s t u d i e d by o t h e r workers, t h e va- r i a t i o n u s u a l l y t a k e s p l a c e i n t h e same s e n s e .

The magnitude, t h e shape and t h e p o s i t i o n o f t h e magnetomechanical damping maximum

-

1

Q m a g ( r ) depend a l s o on t h e i n t e n s i t y and d i s t r i b u t i o n of l o c a l i n t e r n a l s t r e s s e s

dloc

which oppose t h e 90° D.W. displacements.

Associated with such a 90' D.W. jump a g a i n s t t h e b a r r i e r

dloc,

t h e r e

i s

a l o c a l energy l o s s

Auloc.

On t h e assumption of a s t a t i s t i c a l d i s t r i b u t i o n of i n t e r n a l s t r e s s

clot,

Smith and Birchak

[l]

have c a l c u l a t e d t h e t o t a l magnetomechanical l o s - s e s . Depending on t h e d i s t r i b u t i o n f u n c t i o n c o n s i d e r e d [Nl

(qOc)

o r

N2

I

rlOc)

[lg, t h e y deduce two p o s s i b l e e x p r e s s i o n s f o r t h e magnetomechanical maximum :

6 T - \ I

w i t h x = - = - - -

.

6

(used f o r a tension-compression v i b r a t i o n ) ,

7

and r c o r -

6.

p i .

T i

respond t o t h e maxlmum magnetomechanical damping.

Ci

i s

t h e average e f f e c t i v e i n t e r - n a l s t r e s s which t h e 90' D.W.s have overcome t o o b t a i n t h e magnetomechanical loop s a - t u r a t i o n . Under t o r s i o n a l v i b r a t i o n ,

ri

i s r e l a t e d t o

bi

by =

ri$&ri

= $ G

\6,;

E and G a r e young and s h e a r moduli r e s p e c t i v e l y , K i s a shape c o e f f i c i e n t f o r t h e ma-

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and

p;'(])

e x h i b i t a m a x i m u m £or X = 0.7226 and gnetomechanical loop. Q-I

X = 1.092 r e s p e c t i v e l y .

Owing t o t h e a d d i t i o n o f t h e m a g n e t o s t r i c t i v e s t r a i n t o t h e o r d i n a r y e l a s t i c s t r a i n , t h e s h e a r modulus f o r t h e s a t u r a t e d c o n d i t i o n Gs ( o r Es f o r t h e tension-compression experiment) i s l a r g e r t h a n f o r any o t h e r l e v e l o f magnetization. The modulus e f f e c t

i s

a l s o given by t h e Smith and B i r c h a k ' s model :

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C5-6 10

JOURNAL DE PHYSIQUE

F i g . 3 : Comparison between experimental and t h e o r e t i c a l v a r i a t i o n s of magne tomecha- n i c a l damping Q - ~ and modulus e f f e c t A ( I / G )

[z]

.

I , , I : I

0 5 70. !5 . 0 5

---

n

-105y

-

lo5-,

-

f e c t i v e i n t e r n a l s t r e s s which opposes t h e 90' D.W.s i r r e v e r s i b l e jumps. With measurements made by t o r s i o n , t h i s method i s a p p l i e d i n two p a p e r s p r e s e n t e d i n theme 5 :

-

t o e s t i m a t e

Ci

and

As

i n d i s o r d e r e d s t a t e o f a Co-Pt a l l o y (B. Augustyniak, W . Chomka). I t i s a l s o observed t h a t a n ordered o r p a r t i a l l y o r d e r e d s t a t e d r a s t i c a l - l y d i m i n i s h e s t h e i r r e v e r s i b l e motion of t h e D.W.s ;

-

t o s t u d y t h e e v o l u t i o n o f

Cf.

d u r i n g cold-work o f p u r e i r o n (B. sti id, J. ~ e g a u q u e )

I t i s t h e n p o s s i b l e t o determine t h e i n f l u e n c e o f t h e d i f f e r e n t d i s l o c a t i o n s s t r u c - t u r e s (observed by e l e c t r o n i c microscopy) on 90° D.W. s i r r e v e r s i b l e jumps.

Magnetomechanical h y s t e r e s i s h a s a t e c h n o l o g i c a l a p p l i c a t i o n i n t h e use o f h i g h dam- p i n g c a p a c i t y m a t e r i a l s . Such m a t e r i a l s a r e employed i n themachine p a r t s s u b j e c t t o high v i b r a t i o n t o reduce v i b r a t i o n and n o i s e p o l l u t i o n [ 3 ] . For such p u r p o s e s , t h e s e m a t e r i a l s must have a h i g h mechanical s t r e n g h t , a e a s y w o r k a b i l i t y and a high damping c a p a c i t y a s s t i l l h i g h e r temperatures. Non m e t a l l i c m a t e r i a l s ( p l a s t i c , rubber) have a disadvantage because o f l a c k o f high mechanical s t r e n g t h and high temperature en- durance ; non f e r r o u s a l l o y s (Cu-Mn, Ni-Ti) have a high damping c a p a c i t y n e a r room temperature o n l y . A c e r t a i n number of ferromagnetic Fe and N i base a l l o y s may have t h e d e s i r e d mechanical p r o p e r t i e s . Usually, high damping m a t e r i a l s a r e c h a r a c t e r i z e d

Aw

-

A;

-

A?+,

by t h e i r s p e c i f i c damping c a p a c i t y (S .D.C.) : P =

-

W

2

np-l,

where A$

An, An+l a r e v i b r a t i o n a l amplitudes f o r s u c e s s i v e s c y c l e s i n a f r e e decay damping t e s t ; t h e maximum a v a i l a b l e energy i n a c y c l e i s W and t h e energy d i s s i p a t e d i n t h a t

1

Of

c y c l e

i s A ~ .

On u s i n g t h e r e s o n a n t method t h e y a r e c h a r a c t e r i z e d by Q-' =

-

f r ' w h e r e n f i s t h e h a l f - w i d t h of a resonance peak of r e s o n a n t frequency f r .

By c a n t i l e v e r and r e s o n a n t b a r method, Schneider e t a l . (Lausanne, 1 9 8 1 ) , i n a Fe-12- 14 % C r observe a r e c o r d value o f P compared t o t h e maximum v a l u e s measured on o t h e r s ferromagnetic a l l o y s , i n t h e Table I .

This high P v a l u e d e c r e a s e s d r a m a t i c a l l y with a s m a l l v a r i a t i o n o f c o n c e n t r a t i o n of

C r because of t h e appearance of a phase which reduces t h e D.W. m o b i l i t y a s shown by t h e high v a l u e of t h e c o e r c i v e f i e l d . The i n f l u e n c e of t e r n a r y elements on P v a r i a - t i o n s a r e a l s o i n v e s t i g a t e d and compared t o mechanical p r o p e r t i e s .

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Used method Alloys

1

S.D.C. Fe- (12-14) C r ' 0.80 (Lausanne 1981) C a n t i l e v e r beam S i n t e r e d a l l o y s ; [4]

1

Fe-16 C r I T o r s i o n a l

t53

4

Table I : Maximum c a p a c i t y damping o b t a i n e d i n Fe-based a l l o y s a f t e r a h e a t t r e a t e d a t 1200°C ( 1 h)

.

3

phase ( f . c. c . ) and whose r a t i o v a r i e s with composition. The l a r g e values o f S.D.C. could be e x p l a i n e d by t h e s t r e s s induced r e o r i e n t a t i o n o f a n t i f e r r o m a q n e t i c domain boundaries (micro-twins b o u n d a r i e s ) . I n t h e p r e s e n t p a p e r , t h e S.D.C. measu- r e d by f l e x u r a l and t o r s i o n a l v i b r a t i o n o f t h e

T

phases of Mn-Ni and Mn-Fe-Cu a l l o y s

i s

examined a s a f u n c t i o n of temperature, s t r a i n amplitude, frequency and a l l o y com- p o s i t i o n . Near 250 K , t h e S.D.C. a s a f u n c t i o n o f temperature, i n high manganese a l - l o y s shows a " r e l a x a t i o n " peak ( P N 0.1 ; a c t i v a t i o n energy 5 x lo4 ~ / m o l ) which

i s

a s s o c i a t e d w i t h m i g r a t i o n o f a n t i f e r r o m a g n e t i c domain boundaries ( t w i n boundaries)

.

Magnetic r e l a x a t i o n mechanism.- Magnetomechanical l o s s e s and t h e a ~ e f f e c t of f e r - romagnetic m a t e r i a l s , i n v o l v e a l s o a r e l a x a t i o n mechanism due t o eddy c u r r e n t e f f e c t s and/or o r d e r i n g e f f e c t s . The eddy c u r r e n t e f f e c t s (whose c o n t r i b u t i o n

i s

a b s e n t under c o n d i t i o n s o f magnetic s a t u r a t i o n ) a r e important a t high v i b r a t i o n a l frequency and may be d i v i d e d i n t o "microscopic" and "macroscopic" components. The former i s asso- c i a t e d w i t h l o c a l motion o f D.W.s and may be seen most c l e a r l y i n t h e demagnetized s t a t e . The l a t t e r i s a s s o c i a t e d w i t h s t r e s s - i n d u c e d changes i n t h e n e t magnetization of t h e sample ; it i s z e r o i f t h e magnetization i s z e r o and depends s t r o n g l y on t h e m a t e r i a l m a g n e t i z a t i o n a s can be seen i n t h e p a p e r of Schneider e t a l . (Lausanne,

1981) a l r e a d y mentioned.

Magnetic o r d e r i n g e f f e c t s a r e due t o t h e e x i s t e n c e o f a c o u p l i n g between magnetiza- t i o n and t h e e q u i l i b r i u m s t a t e of s h o r t range o r d e r . For example, a f t e r demagnetiza- t i o n of t h e m a t e r i a l , t h e r e d i s t r i b u t i o n of p o i n t d e f e c t s whose symmetry i s lower t h a t of t h e h o s t l a t t i c e i n t o e n e r g e t i c a l l y f a v o r a b l e p o s i t i o n s causes t h e d e c r e a s e of t h e m o b i l i t y of D . W . s . Then, a s a f u n c t i o n of times and f o r s u i t a b l e measurements f r e q u e n c i e s , one observes a decrease o f amplitude-dependent maqnetomechanical dam- p i n g [ 6 , 7 1 (magnetomechanical a f t e r e f f e c t ) and an i n c r e a s e of t h e r e l u c t a n c e (magne-

1

t i c a f t e r e f f e c t ) . The measurement of r e l u c t a n c e r =

-

(where

xi

i s t h e i n i t i a l

X i

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JOURNAL

DE PHYSIQUE

Pying different ''interstitial'' sites, respectively. It is proposed that the reorien- tation processus may be favored by the presence of free volume.

In Ersoy's paper (Lausanne, 1 9 8 1 ) , propagation of a plane wave in a deformable, thermo-electric media, in the presence of external magnetic field is investigated. Some limiting values of the phase velocities and of attenuation constants of the plane wave are obtained and discussed.

11. ULTRASONIC ATTENUATION DUE TO ELECTRONIC PROPERTIES AND TO PHONONS INTERACTIONS. Almost all the physical phenomena are

s t r e s s s e n s i t i v e .

Consequently, the interaction of stress waves with particules or with excitations in solids has a uni- versal character.

Thus, the measurement of ultrasonic attenuation and sound velocity is a very powerful tool for investigating the physical properties of solids.

The

universality

of the tool

is illustrated by the variety of subjects covered in this session. In the following papers, the phonon electron interaction will be studied in various situations (semi-conductors, super-conductors, amorphous films, high purity cristals

. . . I

; the phonon-phonon interaction will be examined in ferroelectrics, molecular crystals, ionic-molecular crystals.

Obviously, the larger the range of frequencies, the more powerful the tool is. Thus, since the last conference the inflation rate for the frequency range of ultrasonic waves has been important. Frequency as high as 1 GHz are now currently used ; sometimes, 3 GHz ultrasonic experiments are reported.

From this point of view, we may notice that if pulse echo,pulse-overlap techniques remain traditionnal, surface acoustic waves and optical techniques are used in some cases.

In metallic crystals, at low temperature, the ultrasonic attenuation is mainly determined by dislocations and by phonon-electron interaction. Using

y

irradiation for pinning the dislocations, the phonon-electron interaction can be carefully studied and the PIPPARD formula 181 can be verified in a large range of values for ql (q = wave number ; 1 = mean free path length). This has been done by SCHREY et a1 (Lausanne 1981) in copper crystals with samples of different purity levels

(20

<

R.R.R

<

20 000).

In crystals doped with paramagnetic impurities (Fe

-

Mn) an "Ultrasonic Kondo effect" is observed.

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Similary, in CHEEKE et a1 paper, by using a magnetic field in a piezoelectric semi-conductor, the evidence for a magnetic field dependent relaxation time is given. A clever analysis of the selection rules for this interaction is made. For superconducting materials, the principal effect (transition effect) is examined in theme 7. Here, some particular behaviour are studied : anormalous anelastic contributions surimposed on the normal temperature dependence are observed below

lo

K both in the superconducting state and normal conducting states. Interesting similarities of ultrasonic attenuation with the classical two levels system are pointed out. (S. EWERT et al).

Spectacular influence of thickness on the ultrasonic attenuation of surface acoustic waves in superconducting thin films of amorphous Bi are reported

(M. TOGUCHI)

.

In molecular crystals, in contrast to metallic or semi-conducting crystals, the basic mechanism of ultrasonic attenuation is still not well understood. Following LIEBERMANN 1101, an extension to molecular crystals of a mechanism well known in molecular liquids and gases is proposed in two papers : the slow transfer of energy from internal to external degrees of freedom of the molecules ; the experimental evidence for relaxation process in some ionic-molecular crystals is given by

MICHARD; a unified theory including classical mechanism of ultrasonic attenuation (AKHIESER process, thermal conduction process) and Liebermann process is given by PERRIN.

Ferroelectric solids are studied in one paper by NAITHANI et a1 who propose a theoritical approach for investigating the sound attenuation in ferroelectrics.

References

1 Smith

G.W.,

Birchak J.R., J. Appl. Phys.,

40,

5174 (1969) and 41, 3315 (1970)

-

2 Degauque J., Astid B., Kubin L.P., Phys. Stat. SOL. (a),

45,

493, (1978)

Sugimoto

K.,

(1978), Mem. Inst. Sci. Ind. Res., Osaka Univ., E , 3 1 Suzuki

K.,

T. Fujita, Masebe M., (1977), Int. Friction Ultra. ATT.

in Solids, ICIFUAS 6, Univ. Tokyo Press 757 (1977) Masumoto H., Sawaya S., Minai M., (1979), Trans. Jap. Inst. Met.,

20, 409 (1979).

-

Maringer R.E., (1964), J. Appl.,

35,

8, 2375

Astie B., Degauque J., Peyrade J.P. (1980), Proceedings of third European Conf. on Int. Friction, 211 (Pergamon Press) Pippard A.B., Phil Mag.,

46,

1104 (19551

Herring C., and Vogt E., Phys Rev., 101 (1956) 44