Influence of structural relaxation on the magnetic permeability aftereffect of amorphous ferromagnetic alloys

0038-1098183 $3.00 + .OO Pergarcon Press Ltd.

Solid State Conmmnications, Vo1.47,No.12, pp.951-954,1983. Printedin Great Britain.

INFLUENCE OF STRUCTURAL RELAXATION ON THE MAGNETIC PERMEABILITY AFTEREFFE:CT OF AMORPHOUS FERROMAGNETIC ALLOYS* P. Allia, R. Sato Turtelli**, F. Vinai Istituto Elettrotecnico Nazionale "Galileo Ferraris", I-10125 Torino, Italy Gruppo Nazionale Struttura della Materia de1 CNR, u.r. 24, I-10125 Torino, Italy

A. Lovas Central Research Institute for Physics, H-1525 Budapest, Hungary (Received on February 11, 1983 by R. Fieschi) Room temperature measurements of the aftereffect of the magnetic permeability have been performed on amorphous Fe-(Cu-Cr)-B ribbons annealed at various temperatures. The results, in good agreement with the predictions of a new theory, give information on the effect of structural relaxation on the shear stress defects responsible for the magnetic aftereffect.

Introduction The after-effect, or disaccomodation, of the magnetic permeability of amorphous ferromagnetic alloys has been recently shown to arise from the magnetostrictive coupling of structural defects with the direction of the local magnetization vecto&. These defects have been described by Srolovitz et a1.2 as small regions(on the average composed of 10 + 20 atoms) where the atomic-level stresses (hydrostatic pressure and shear stress) have locally correlated, off-equilibrium values. The mechanism proposed for amorphous alloys, relating the magnetic after-effect to the directional ordering of a fraction of shear stress defects, is typically structural in nature, while in the case of crystalline ferromagnets the disaccomodation results from the ordering of specific impurity atoms or solute atom pairs3. The study of amorphous ribbons containing different amounts of Cr and Cu dissolved in a Fe-B matrix has been helpful in the verification of the absence of relevant contributions of specific solute atoms to the after-effect of these materials4. Further information on the validity of the prc?csed theory and the role of *Work suppoitad by CNR - Progetto Finaliz zato Metallurgia. **Permanent Address: Universidade Estadual de Campinas, Brazil

structural defects on the permeability after-effect Ap/p can be extracted from the analysis of the behaviour of Ap/p with annealing of ribbons. More specifical lY, the variation of the room temperaturevalue of Ap/p in Fe-(Cu,Cr)-B alloys annealed at different temperatures will be compared with the theoretical predictions, in order to get information about the effect of structural relaxation on the shear stress defects which are responsible for the magnetic disaccomodation. Experimental The after-effect of the magnetic peg meability, Apip , the saturation magnetization I, and the magnetostriction constant hs were measured at room temperature on amorphous ribbons of composition Fe80_x Crx B20s FegO x Cux B20,

Fe 85-x CrxB15

(O
952

MAGNETIC PERMEABILITY AFTEREFFECT OF AMORPHOUS FERROMAGNETIC ALLOYS

f e c t s due to the d i f f e r e n t p e r m e a b i l i t y o f s a m p l e s , b y m e a n s o f the s p e c i f i c p r o c e d u r e p r o p o s e d in a p r e v i o u s p a p e r l . In e x p e r i m e n t s in w h i c h the B l o c h w a l l s osc i l l a t e s l i g h t l y a r o u n d the e q u i l i b r i u m p o s i t i o n , the d i s a e c o m o d a t i o n is a f u n c tion of the w a l l d i s p l a c e m e n t ~, so that the v a l u e o f the a f t e r e f f e c t m e a s u r e d in a g i v e n s a m p l e b e t w e e n f i x e d t i m e s is obs e r v e d to c h a n g e b y s i m p l y v a r y i n g the am p l i t u d e o f the a.c. d r i v i n g f i e l d H e T , 8 -O n l y A ~ / ~ v a l u e s o b t a i n e d for e q u i v a l e n t w a l l d i s p l a c e m e n t s in d i f f e r e n t s a m p l e s c a n be c o m p a r e d . S i g n i f i c a n t e r r o r s c a n o c c u r b y u s i n g the s a m e a m p l i t u d e of H e to s t u d y d i f f e r e n t m a t e r i a l s , b e c a u s e the d i f f e r e n t p e r m e a b i l i t y of the r i b b o n s g i v e s rise to u n e q u i v a l e n t w a l l d i s p l a c e ments. The s a t u r a t i o n m a g n e t i z a t i o n w a s m e a -sured by a vibrating sample magnetometer, and the m a g n e t o s t r i c t i o n c o n s t a n t b y m e a n s of the s m a l l - a n g l e r o t a t i o n t e c h n i q u e 9. These different magnetic measurements were p e r f o r m e d on the same s a m p l e s to a v o i d errors due to c o m p o s i t i o n a l f l u c t u a t i o n s w i t h i n the same r i b b o n . Results

distribution is an intrinsic feature of amorphous metallic systems 5. The behaviour of the product I s - He*" • ( A ~ / p ) is shown in Fig. 1 as a func tion of Xs2 for all ribbons studied both-in the as-cast condition (open symbols) and a f t e r 2 h o u r s a n n e a l i n g at T a = 3 0 5 ° C (full s y m b o l s ) . The e x p e r i m e n t a l p o i n t s of a s - c a s t s a m p l e s lie on a s t r a i g h t line of s l o p e unity, in a g r e e m e n t w i t h E q . ( 1 ) . The s p r e a d of the v a l u e s of I s - H e *. (Ap/ / ~ ) c a n be a s c r i b e d to the d i f f e r e n t rates o f q u e n c h i n g f r o m the m e l t of d i f f e r I^2U

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and Discussion

A

In Eq.

I

C

The e x p r e s s i o n f o r the m a g n e t i c p e r m e a b i l i t y a f t e r - e f f e c t , o b t a i n e d b y taking i n t o a c c o u n t the c o n t r i b u t i o n f r o m the d i r e c t i o n a l o r d e r i n g of s h e a r s t r e s s d e f e c t s , is I 2
Vol. 47, No. 12

/

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H s • Is A is a n u m e r i c a l

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con-

stant, d e p e n d e n t on the time i n t e r v a l used to s t u d y the p e r m e a b i l i t y a f t e r - e f fect, (A = 2.5 10 -2 in the p r e s e n t ease), k is the B o l t z m a n n c o n s t a n t , H e * is the e x t e r n a l f i e l d c o r r e s p o n d i n g to the m a x i m u m v a l u e of A p / p at the m e a s u r e m e n t temperature T i, < T 2 > is the s e c o n d m o m e n t of the s h e a r s t r e s s f l u c t u a t i o n s , whose value<~2> = 1 0 . 8 1 , i0 -3 (eV/A3) 2 is o b t a i n e d f r o m a m o d e l of a m o r p h o u s iron i0. F i n a l l y , < N > T is the n u m b e r p e r u n i t v o l u m e of s h e a r s t r e s s d e f e c t s w h i c h at the m e a s u r e m e n t t e m p e r a t u r e T, c a n f o ! low the r o t a t i o n o f I s w i t h r e v e r s i b l e i[ cal d i s p l a c e m e n t s , g i v i n g rise to the p e ~ m e a b i l i t y a f t e r - e f f e c t I. < N > T ' w h i c h is a c t u a l l y a f r a c t i o n of the total n u m b e r o f s h e a r s t r e s s d e f e c t s in the m a t e rial, i n v o l v e s an i n t e g r a t i o n o v e r a c o n tinuous distribution of activation energies f o r the local d i s p l a c e m e n t s of s t r u ~ rural d e f e c t s I. The e x i s t e n c e o f such a

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Fig. i - P l o t o f the p r o d u c t He* Is. (A~/ /~) v e r s u s ks 2 in Fe - ( C u , C r ) - B a m o r p h o u s a l l o y s . O p e n s y m b o l s : as c a s t ribbons. Full s y m b o l s : r i b b o n s a n n e a l e d , 2 h o u r s at T a = 305°C. S a m p l e s i d e n t i f i e d as f o l l o w s : l) F e ? 5 Cu 5 B 2 0 ; 2) F e 8 0 . 8 Cr4. 8 B 2 0 . 2

(high

Fe75~ .S Cr4.8

B19.9

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Vol. 47, No. 12

953

MAGNETIC PERMEABILITY AFTEREFFECT OF AMORPHOUS FERROMAGNETIC ALLOYS

e n t m a t e r i a l s II, as c l e a r l y s h o w n in the p r e s e n t c a s e b y two r i b b o n s ( p o i n t s 3 a n d 4 in Fig. I) h a v i n g the s a m e c o m p o s i t i o n but produced by different wheel velocities. A c c o r d i n g to Eq. (i), the s c a t t e r o f the v a r i o u s I s - He*- ( A ~ /~ ) v a l u e s p l o t ted a g a i n s t As2 m a y be a t t r i b u t e d to the-f l u c t u a t i o n s o f the p r o d u c t < N >T" f r o m m a t e r i a l to m a t e r i a l . S i n c e the v a lue o f < T 2 > is n o t m o d i f i e d b y s m a l l c h a n ges in the a l l o y ' s rate of q u e n c h i n g f r o m the m e l t i0 it c a n be c o n c l u d e d that the v a r i a t i o n o f A ~ / ~ in s a m p l e s p r o d u c e d w i t h d i f f e r e n t q u e n c h i n g r a t e s is m a i n l y r e l a t e d to c h a n g e s o f < H > T " If a c o m p o s i t i o n a l c o n t r i b u t i o n to A W / ~ is p r e s e n t , it is s m a l l e r t h a n the experimental scattering of data w h i c h is, as u s u a l , r a t h e r large, o w i n g to d i f f e r e n c e s i n the c o o l i n g r a t e s a n d in the p r e p a r a t i o n c o n d i t i o n s of r i b b o n s . A s s h o w n in Fig. I, a n n e a l i n g of s a m p l e s m e r e l y res u l t s in a c o h e r e n t d e c r e a s e o ~ the p r o duct I s H e * ( A ~ / ~ ), w h i c h is s l i g h t l y m o r e p r o n u n c e d f o r r i b b o n s c o n t a i n i n g 15 at % B. E q u a t i o n (i) is v e r i f i e d to h o l d e v e n in the c a s e of a n n e a l e d r i b b o n s . No difference between materials containing Cr a n d Cu is found. S i n c e < T2 > is u n a f f e c t e d b y s t r u c t u ral r e l a x a t i o n iO the d e c r e a s e o f the permeability after-effect after annealing is a t t r i b u t e d to the v a r i a t i o n of the h u m b e r < N > T of s h e a r s t r e s s d e f e c t s w h i c h are a c t i v a t e d at r o o m t e m p e r a t u r e . H o w e v e r , to get s i g n i f i c a n t i n f o r m a t i o n on the b e h a v i o u r of < N > with struc T r u r a l r e l a x a t i o n , s p u r i o s e f f e c t s due to p o s s i b l e v a r i a t i o n s o f H e *, k s , I s w i t h t h e r m a l t r e a t m e n t of s a m p l e s m u s t be p r o p e r l y e l i m i n a t e d . C o n s e q u e n t l y , it w o u l d be c o n v e n i e n t to s t u d y the d e p e n d e n c e o n a n n e a l i n g o f the p r o d u c t P ( T a, T) = ((AF/ /~ ) • (I s • H e */ Xs2)), w h i c h is p r o p o r t i o n a l to < N > T The r o o m t e m p e r a t u r e v a l u e s o f R e x p = = (P(Ta)) a n n / ( P ( T a )) as c a s t = < N > T / < N > T as c a s t f o r the r i b b o n s e r i e s

ann / con-

t a i n i n g 20 at % a n d 15 at % B are r e s p e c t i v e l y s h o w n in F i g u r e s 2 a n d 3 as funct i o n s of the a n n e a l i n g t e m p e r a t u r e T a. The results indicate thatT is a m o n o t o n i c a l l y d e c r e a s i n g f u n c t i o n of T a. H o w e v e r , the a f t e r - e f f e c t a p p e a r s to be p r e s e n t ev e n a f t e r h i g h t e m p e r a t u r e a n n e a l i n g s , in a g r e e m e n t w i t h the r e s u l t s t y p i c a l l y obt a i n e d on v a r i o u s m a g n e t o s t r i c t i v e amorp h o u s a l l o y s 12 The d e c r e a s e of P (T a) is, w i t h i n the e x p e r i m e n t a l e r r o r s , i n d e p e n d e n t o f

the a c t u a l a l l o y c o m p o s i t i o n . In t h e s e m a t e r i a l s , no i n c r e a s e o f P ( T a) h a s b e e n o k s e r v e d in the s c a n n e d r a n g e o f a n n e a l i n g t e m p e r a t u r e s , d i f f e r e n t f r o m the c a s e o f a z e r o m a g n e t o s t r i c t i o n alloy, w h i c h w a s h o w e v e r s u b m i t t e d to a d i f f e r e n t a n n e a l ing p r o c e d u r e 8.

Rexp

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Fig.

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I

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2 - Plot

I

Ta

200

300

of:

R e x p = ( P ( T a ) ) a n n / ( P ( T a ) ) a s c a s t as a f u n c t i o n o f the a n n e a l i n g t e m p e r a t u r e T a f o r r i b b o n s c o n t a i n i n g 20 at % B. A: h i g h q u e n c h i n g rate; B: low q u e n c h i n g rate.

I

\

R exp

\

\

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o \

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200

3 - The same as in Fig. c o n t a i n i n g 15 at % B.

I

Ta 2 for

300 rib-

By c o m b i n i n g the h y p o t h e s i s on < T 2 > w h i c h , a c c o r d i n g to the k n o w n m o d e l s I0, is n o t a f f e c t e d b y s t r u c t u r a l r e l a x a t i o n , a n d the o b s e r v a t i o n that P ( T a ) d e c r e a s e s a f t e r s u i t a b l e t h e r m a l t r e a t m e n t s , it c a n be c o n c l u d e d that the m a j o r e f f e c t o f ann e a l i n g o n the s h e a r s t r e s s d e f e c t s is a reduction of their mobility, rather than a r e d u c t i o n o f t h e i r t o t a l n u m b e r . The p a r t i a l f r e e z i n g of t h o s e s h e a r s t r e s s defects which can perform local displac e m e n t s in the as c a s t m a t e r i a l , c o u l d

954

MAGNETIC PERMEABILITY AFTEREFFECT OF AMORPHOUS FERROMAGNETIC ALLOYS

p o s s i b l y be related to the decrease of the alloy's macroscopic free volume V F with structural relaxation. The existence of a close relation betweenT and V F has been indeed verified by direct comparison of the data of magnetic after-effect and electrical resistivity, taken on similar ribbons 13. In conclusion, the after-effect of the magnetic p e r m e a b i l i t y of ferromagnetic metallic glasses turns out to be, within the experimental errors, in agreement with the p r o p o s e d theory (Equation (i) ), both in as-cast and annealed ribbons. This result supports the interpre-

V o l . 47, No. 12

tation of the d i s a c c o m o d a t i o n in amorphous ferromagnets as a genuine structural process. The b e h a v i o u r of A#/~ in annealed samples can be accounted for as due to the v a r i a t i o n o f < N >T, the fraction of shear stress defects w h i c h give rise to the after-effect. The decrease ofT with increasing a n n e a l i n g temperature suggests that the reduction of the m o b i l i t y of shear stress defects can be e x p l a i n e d in terms of atomic rearrange merits, associated with a reduction of the macroscopic free volume, occurring in glassy alloys as a consequence of thermal treatments.

References i. P. Allia and F. Vinai,

Phys. Rev. B26,

6186 (1982) 2. D. Srolovitz, K. Maeda, V. Vitek and T. Egami, Phil. Mag. A44, 847 (1981) 3. J.C. Slonczewsky, in: Magnetism, G. Rado, H. Suhl, eds. (Academic, New York 1963), Vol. I, p. 205 4. P. Allia, A. Lovas, R. Sato Turtelli, G.P. Soardo, and F~ Vinai, J. Appl. Phys. 5__33, 7849 (1982) 5. P. Allia, P. Mazzetti, G.P. Soardo, and F. Vinai, J. Magn. Mat. 15-18,

1361 (1980) 6. P. Allia, J. Magn. 7. P. A l l i a Magnetics

P. Mazzetti, and F. Vlnai, Magn. Mat. i~9, 281 (1980) and F. Vinai, IEEE Trans. on MAG 17, 1481 (1981)

8. T. Jagielinski, J. Appl. Phys. 5__33, 7852 (1982) 9. K. Narita, J. Yamasaki, and H. Fukuna ga, IEEE Trans. on M a g n e t i c s MAG-16,

435 (1980) i0. T. Egami and D. Srolovitz, J. Phys. F (in p r e s s ) F l 2 , 2141 (1982) ii. P. Allia, F.E. Luborsky, R. Sato Turtelli, G.P. Soardo, and F. Vinai, IEEE Trans. on M a g n e t i c s MAG-17, 2615 (1981) 12. P. A l l i a and F. Vinai, J. Physique 4__~i,

C8-654 (1980) 13. P. Allia, G. Riontino, R. Sato Turtel li, and F. Vinai, Solid State Comm.

4,3, 821 (1982)