Stress-induced anisotropy in LPE grown Ni(Fe,Al)2O4 films

Stress-induced anisotropy in LPE grown Ni(Fe,Al)2O4 films

Citation for published version (APA):

Straten, van der, P. J. M., & Metselaar, R. (1978). Stress-induced anisotropy in LPE grown Ni(Fe,Al)2O4 films.

Materials Research Bulletin, 13(11), 1143-1151. https://doi.org/10.1016/0025-5408(78)90201-5

DOI:

10.1016/0025-5408(78)90201-5

Document status and date:

Published: 01/01/1978

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S T R E S S - I N D U C E D A N I S O T R O P Y IN LPE G R O W N N i ( F e , A I ) 2 0 4 F I L M S P . J . M . v a n der S t r a t e n and R. M e t s e l a a r

L a b o r a t o r y of P h y s i c a l C h e m i s t r y , U n i v e r s i t y of T e c h n o l o g y , E i n d h o v e n , The N e t h e r l a n d s .

(Received September 8, 1978; Communicated by A. Rabenau)

A B S T R A C T P r e l i m i n a r y r e s u l t s are r e p o r t e d a b o u t the g r o w t h of s i n g l e c r y s t a l N i ( F e , A I ) 2 0 4 f i l m s , g r o w n by m e a n s of li- q u i d p h a s e e p i t a x y on ( ] ] ] ) M g O and on ( ] l ] ) Z n G a 2 0 4 s u b - s t r a t e s u s i n g a P b O - B 2 0 ~ - F e 2 0 3 s o l v e n t . W h i l e f i l m s g r o w n u p o n M g O s h o w s t r e s s r e l i e f at the g r o w t h t e m p e r a t u r e , f i l m s g r o w n u p o n Z n G a 2 0 4 p o s s e s s a t e n s i l e s t r a i n due to e l a s t i c d e f o r m a t i o n . S i n c e %]11 for N i F e 2 0 4 is s t r o n g l y n e g a t i v e a s t r e s s - i n d u c e d u n i a x i a l a n i s o t r o p y is p r e s e n t

in the films. S t r i p e d o m a i n s can be o b s e r v e d w i t h the B i t t e r t e c h n i q u e and w h e n a m a g n e t i c f i e l d is a p p l i e d p e r p e n d i c u l a r to the p l a n e of the film, m a g n e t i c b u b b l e s w i t h a d i a m e t e r of ~2 ~ m a p p e a r . A b u b b l e s t a b i l i t y fac- tor q e x c e e d i n g u n i t y is o b t a i n e d . F o r the f i r s t time m a g n e t i c b u b b l e s are f o u n d in L P E g r o w n s p i n e l f e r r i t e s .

I n t r o d u c t i o n

S i n g l e c r y s t a l l i n e o x i d i c b u b b l e m a t e r i a l s f o u n d and s t u d i e d so f a r are o r t h o f e r r i t e s , h e x a g o n a l f e r r i t e s , g a r n e t s and s p i n e l f e r r i t e s . The a p p l i c a b i l i t y of the o r t h o f e r r i t e s has f o u n d its l i m i t a t i o n s in the too l a r g e b u b b l e d i a m e t e r s (l). The p o s s i b i l i - ties of the h e x a g o n a l f e r r i t e s h a v e n o t b e e n s t u d i e d e x t e n s i v e l y but e x t r e m e l y low b u b b l e m o b i l i t i e s h a v e b e e n r e p o r t e d so far (2). W h i l e the o r t h o f e r r i t e s and the h e x a g o n a l f e r r i t e s are m a t e r i a l s p o s s e s s i n g a u n i a x i a l a n i s o t r o p y due to t h e i r c r y s t a l s y m m e t r y the g a r n e t s and s p i n e l s are i n t r i n s i c a l l y c u b i c w i t h f o u r e q u i v a - lent (]]I) m a g n e t i c axes. The p r e s e n c e of g r o w t h - i n d u c e d a n i s o t r ~ py in the g a r n e t s h o w e v e r , t o g e t h e r w i t h s t r e s s - i n d u c e d a n i s o t r o - py due to the l a t t i c e m i s m a t c h g i v e s a u n i a x i a l m a g n e t i c m a t e r i a l s u i t a b l e for m a g n e t i c b u b b l e a p p l i c a t i o n s . P r o b a b l y c a u s e d by the s u c c e s s of the g a r n e t s no e x t e n s i v e s t u d i e s h a v e b e e n m a d e of the s p i n e l f e r r i t e s in this r e g a r d , a l t h o u g h g r o w t h - i n d u c e d a n i s o t r o p i e s are r e p o r t e d for f l u x g r o w n s p i n e l f e r r i t e s (3). R e c e n t l y f i l m s of g o o d q u a l i t y h a v e b e e n g r o w n by CVD (4-6) and LPE (7-9) p r o c e d u r e s . S p i n e l f e r r i t e f i l m s s u p p o r t i n g m a g n e t i c b u b b l e s h a v e so far o n l y b e e n g r o w n by CVD m e t h o d s . P r e l i m i n a r y e x p e r i m e n t s i n d i c a t e that at l e a s t a s t r e s s i n d u c e d a n i s o t r o p y can be g e n e r a t e d in LPE g r o w n N i F e 2 _ x A l x O 4 f i l m s on ( ] ] l ) Z n G a 2 0 4 s u b s t r a t e s r e s u l t i n g in an e a s y axis of

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m a g n e t i z a t i o n p e r p e n d i c u l a r to the p l a n e of the film. S t r i p e do- m a i n s and c i l y n d r i c a l d o m a i n s ( b u b b l e s ) can be o b s e r v e d .

T h e o r y

F o r the e x i s t e n c e of s t a b l e i s o l a t e d b u b b l e d o m a i n s a u n i q u e axis of m a g n e t i z a t i o n p e r p e n d i c u l a r to the p l a n e of the f i l m m u s t be r e a l i z e d in s u c h a w a y that the s t a b i l i t y f a c t o r q is g r e a t e r t h a n u n i t y . (q = K u / 2 ~ M ~ , w h e r e K u is the u n i a x i a l a n i s o t r o p y c o n s t a n t and M s the s a t u r a t i o n m a g n e t i z a t i o n ) . In o r d e r to

a c h i e v e this the u s e of low m o m e n t s p i n e l f e r r i t e s is f a v o u r a b l e . L o w 4 ~ M s v a l u e s can be o b t a i n e d w h e n a p a r t of the Fe ions is s u b s t i t u t e d by AI ions. The e x i s t e n c e of a c o m p e n s a t i o n p o i n t in the 4 ~ M s - c o m p o s i t i o n d i a g r a m is v e r y h e l p f u l (as w i t h the g a r n e t ~ in this r e g a r d ; l o w m o m e n t m a t e r i a l s w i t h r e l a t i v e l y h i g h C u r i e t e m p e r a t u r e s are o b t a i n e d w h e n f e w Fe ions are s u b s t i t u t e d by AI ions. C o m p e n s a t i o n p o i n t s are k n o w n in s e v e r a l s p i n e l s y s t e m s e.g. N i F e 2 _ x A l x O 4 , N i F e 2 - x V x 0 4 and L i 0 . S F e 2 . 5 - x A l x O 4. In t a b l e I the r o o m t e m p e r a t u r e c o m p e n s a t i o n p o i n t s t o g e t h e r w i t h the C u r i e t e m p e r a t u r e s and l a t t i c e c o n s t a n t s are g i v e n . In this s t u d y we h a v e p a i d a t t e n t i o n to the N i F e 2 _ x A l x O 4 s y s t e m . N i F e 2 0 4 is an i n v e r s e s p i n e l : F e [ N i F e ] O 4. W h e n p a r t of the Fe ions are s u b s t i t u t e d by AI ions, this s u b s t i t u t i o n is p r e - d o m i n a n t l y m a d e on o c t a h e d r a l s i t e s (13). F o r x = 0.7 the c a t i o n d i s t r i b u t i o n can be w r i t t e n as F e 0 . 9 A I 0 . 1 [ N i F e 0 . 4 A I 0 . 6 ] O 4.

The u n i a x i a l a n i s o t r o p y can be b o t h s t r e s s and g r o w t h i n d u - ced. The s t r e s s - i n d u c e d a n i s o t r o p y of a (111) f i l m can be c a l c u - l a t e d f r o m 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 (%111) and the s t r e s s (6) in the f i l m a c c o r d i n g to K~ = - 3 / 2 . % 1 1 l.~. B e s s e r c.s. (14) h a v e d e v e l o p e d a s t r e s s m o d e l for h e t e r o - e p i t a x i a l m a g n e t i c o x i d e f i l m s : F o r s m a l l m i s f i t v a l u e s the s t r e s s is c a u s e d by e l a s t i c d e f o r m a t i o n of the f i l m at the d e p o s i t i o n t e m p e r a t u r e re- s u i t i n g in a s t r e s s ; E a s - af

0"1

: 1 - ~ af E is Y o u n g s m o d u l u s , ~ the P o i s s o n c o n s t a n t , a s the s u b s t r a t e l a t t i c e p a r a m e t e r and af the u n s t r a i n e d f i l m l a t t i c e p a r a m e t e r . F o r h i g h e r m i s f i t v a l u e s at the d e p o s i t i o n t e m p e r a t u r e the s t r e s s is p r o b a b l y r e l i e v e d by the f o r m a t i o n of m i s f i t d i s l o c a t i o n s at the s u b s t r a t e - f i l m i n t e r f a c e (15) r e s u l t i n g in a b u l k l a t t i c e c o n s t a n t of the film. T h e s t r e s s of the f i l m at r o o m t e m p e r a t u r e t h e n r e s u l t s f r o m the d i f f e r e n c e s in e x p a n s i o n c o e f f i c i e n t s of T a b l e I R o o m t e m p e r a t u r e c o m p e n s a t i o n p o i n t s of s p i n e l f e r r i t e s y s t e m s t o g e t h e r w i t h C u r i e t e m p e r a t u r e s (8c) and l a t t i c e c o n s t a n t s . s y s t e m x 0 c ( O C ) a o ( ~ ) Ref. N i F e 2 - x A l x O 4 N i F e 2 - x R h x O 4 N i F e 2 - x V x O 4 L i 0 . s F e 2 . 5 - x A l x O 4 L i 0 . s F e 2 . 5 - x R h x O 4 0 . 6 8 300 8 . 2 3 ( 1 0 ) 0 . 6 0 400 8 . 3 6 ( I I ) 0 . 7 0 400 8 . 3 4 ( I I ) 0 . 7 0 350 8 . 2 6 (12) 0 . 8 0 50 8 . 4 O ( 1 1 )

f i l m ( a f ) a n d s u b s t r a t e ( a s ) a n d f r o m t h e t e m p e r a t u r e d i f f e r e n c e A T b e t w e e n d e p o s i t i o n t e m p e r a t u r e a n d r o o m t e m p e r a t u r e g i v i n g o - E 2 - I-~ (af - a s ) A T . In t h e c a s e of N i F e 2 0 4 d e p o s i t e d o n M g O s u b s t r a t e s t h e f i l m s a r e p r e d i c t e d to b e in t e n s i o n (o-1>0) w h e n e l a s t i c d e f o r m a t i o n o c c u r s a n d in c o m p r e s s i o n ( o ~ < 0 ) w h e n s t r e s s r e l i e f o c c u r s at t h e g r o w t h t e m p e r a t u r e . W h e n o n l y e l a s t i c d e f o r m a t i o n o c c u r s t h e s t r e s s - i n - d u c e d u n i a x i a l a n i s o t r o p y f o r ( 1 1 1 ) f i l m s c a n b e w r i t t e n as: K s = _ 3 / 2 . % I E a s - af u 11 1 - ~ af F o r N i F e 2 0 4 %111 = 2 1 . 1 0 - 6 ( 1 6 ) , w h i l e f o r N i 0 . 8 F e 2 . 2 0 4 %111 = - 4 . 1 0 - 6 ( 1 7 ) . T h i s m e a n s t h a t n i c k e l f e r r i t e f i l m s g r o w n i n t e n - s i o n o n ( 1 1 1 ) s u b s t r a t e s w i l l h a v e a p o s i t i v e s t r e s s - i n d u c e d a n i - s o t r o p y . F o r e x a m p l e N i F e 2 0 4 w i t h a f i r s t o r d e r a n i s o t r o p y c o n - s t a n t K 1 o f - 0 . 7 1 0 5 e r g / c m B g i v e s a K~ v a l u e o f a b o u t + 6 . 5 105 e r g / c m 3 w h i l e t h e d e m a g n e t i z a t i o n e n e r g y ~ M ~ i s a b o u t 4 . 5 105 e r g / c m 3 . H e r e we h a v e a s s u m e d E = 1 . 6 101 d y n e / c m 2 a n d ~ = 0 . 3 ( 1 8 ) . I n v i e w o f t h i s c o n s i d e r a t i o n o n e m a y e x p e c t s t a b l e b u b b l e s i n N i F e 2 _ x A l x O 4 f i l m , a s s u m i n g t h a t s t r e s s r e l i e f c a n b e s u p p r e s - s e d . E x p e r i m e n t a l LPE g r o w t h o f N i F e 2 _ x A l x O 4 l a y e r s i s p e r f o r m e d a c c o r d i n g t o s t a n d a r d LPE p r o c e d u r e s d e s c r i b e d p r e v i o u s l y ( 8 ) . T h e v e r t i c a l w a y o f d i p p i n g w a s u s e d w i t h o u t s u b s t r a t e r o t a t i o n . MgO w i t h 2 a o = 8 . 4 2 % a n d Z n G a 2 0 4 w i t h a o = 8 . 3 3 ~ a r e u s e d a s s u b s t r a t e s . T h e ( 1 1 1 ) MgO w a f e r s w e r e c u t f r o m a b o u l e o f MgO w i t h i n 0 . 5 o o f t h e d e s i r e d p l a n e a n d a f t e r w a r d s g r o u n d w i t h S i C a n d p o l i s h e d w i t h s y t o n . T h e Z n G a 2 0 4 s u b s t r a t e s w e r e g r o w n f r o m a P b 2 P 2 0 7 f l u x ( 1 9 ) a n d w e r e u s e d i n t h e a s - g r o w n s t a t e h a v i n g { 1 1 1 } f a c e t s m e a s u r i n g a b o u t 5 - 6 mm a l o n g t h e e d g e . T h e f l u x i s b a s e d o n P b O , B 2 0 3 , N i O , F e 2 0 3 a n d A 1 2 0 3 a l l r e a g e n t g r a d e . T h e f l u x c o m p o s i t i o n f o r t h e g r o w t h o f p u r e N i F e 2 0 4 i s n e a r l y i d e n t i c a l t o t h e o n e u s e d b y R o b e r t s o n ( 7 ) f o r t h e LPE g r o w t h o f N i F e 2 0 4 . T h e NiO c o n t e n t i s m u c h l o w e r h o w e v e r t h a n u s e d b y R y b a l ' s k a y a i n h i s s o l u b i l i t y s t u d y ( 2 0 ) . T h e s a t u - r a t i o n t e m p e r a t u r e o f t h e m e l t i s s t r o n g l y d e p e n d e n t o n t h e NiO a n d B 2 0 3 c o n t e n t s w h i c h c a n b e v a r i e d o v e r w i d e r a n g e s . T h e m e l t c o m p o s i t i o n s u s e d b y R o b e r t s o n a n d b y R y b a l ' s k a y a a n d t h e c o m p o - s i t i o n s u s e d i n t h i s s t u d y a r e c o l l e c t e d i n t a b l e I I . T h e s a t u r a t i o n t e m p e r a t u r e s o f t h e m e l t s w e r e n o t a c t u a l l y d e t e r m i n e d . A t e m p e r a t u r e i n d i c a t i o n w a s f o u n d b y o b s e r v i n g t h e s u r f a c e o f t h e m e l t w h e n t h e t e m p e r a t u r e w a s l o w e r e d a t a r a t e o f a b o u t 2 ° C / m i n a f t e r s t i r r i n g a t e l e v a t e d t e m p e r a t u r e s . When c r y s - t a l s w e r e o b s e r v e d f l o a t i n g o n t h e s u r f a c e o f t h e m e l t t h e c o r - r e s p o n d i n g t e m p e r a t u r e T c w a s t a k e n a s t h e l o w e s t t e m p e r a t u r e a t w h i c h LPE g r o w t h w a s t o b e p e r f o r m e d . T h e a c t u a l g r o w t h t e m p e r a - t u r e s w e r e c h o s e n b e t w e e n T c a n d T c + 4 0 ° C . T h e d e p o s i t i o n t i m e s w e r e v a r i e d b e t w e e n 5 a n d 10 m i n u t e s r e s u l t i n g i n f i l m t h i c k n e s - s e s f r o m a b o u t 1 Bm t o o v e r 10 Bm. T h e l a t t i c e c o n s t a n t s o f t h e s p i n e l f e r r i t e f i l m s w e r e d e - t e r m i n e d b y x - r a y d i f f r a c t i o n b y m e a s u r i n g t h e B r a g g ' s a n g l e f r o m p l a n e s p a r a l l e l t o ( 1 1 1 ) u s i n g t h e s u b s t r a t e a s i n t e r n a l s t a n d a r d . T h e c o m p o s i t i o n s o f t h e f i l m s w e r e c a l c u l a t e d f r o m e l e c t r o n

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P . J . M . VAN DER STRATEN, et al.

Vol. 13, No. 11

T a b l e II

M e l t c o m p o s i t i o n s u s e d by R o b e r t s o n (7) a n d R y b a l ' s k a y a (20) a n d the c o m p o s i t i o n s u s e d in this s t u d y , t o g e t h e r w i t h the o b s e r v e d T c v a l u e s ( c o n s u l t t e x t ) . C o m p o s i t i o n s n o r m a l i z e d to 250 g PbO. M e l t P b O B 2 0 3 F e 2 0 3 A I 2 0 3 N i O Tc (°C) R o b e r t s o n 250 8 . 3 3 1 8 . 5 8 - 0 . 8 7 - R y b a l ' s k a y a 250 5 . 2 6 1 8 . 2 1 - 8.51 - A 250 10 17 - 1 930 B 250 |0 17 1 1 9 4 0 C 250 I0 17 3 1 965 D 250 15 17 5 1 985 E 250 15 17 6 1 995 F 250 20 ]7 6 1 930 G 250 25 17 6 I 885 H 250 30 17 6 I 855 I 250 35 17 6 1 830 m i c r o p r o b e d a t a u s i n g N i F e 2 _ x A l x O 4 s t a n d a r d s w i t h x = 0, 0 . 5 a n d 1.0. T h e a c c u r a c y a p p e a r e d to be b e t t e r t h a n 0 . 0 2 a t o m s p e r f o r - m u l a u n i t . S i n c e N i F e 2 0 4 is n o t t r a n s p a r e n t to v i s i b l e l i g h t d o m a i n s t r u c t u r e s w e r e i n v e s t i g a t e d w i t h the a i d of the B i t t e r t e c h n i - que. A m a g n e t i c f i e l d r e a c h i n g up to I 0 0 0 Oe c o u l d be a p p l i e d p e r p e n d i c u l a r to the p l a n e of the f i l m u s i n g an e l e c t r o m a g n e t . R e s u l t s a n d d i s c u a s i o n F i l m p a r a m e t e r s A l l f i l m s w e r e s h o w n to be p u r e s p i n e l s w i t h a Ni c o n t e n t of 0 . 9 9 ~ 0 . 0 2 a t o m s p e r f o r m u l a u n i t . F i l m s g r o w n u p o n M g O s u b s t r a - tes e x h i b i t m o r e c r a c k s t h a n f i l m s g r o w n u p o n Z n G a 2 0 4 s u b s t r a t e s . W h e n the AI c o n t e n t of t h e f i l m s i n c r e a s e s , c r a c k i n g b e c o m e s m o r e s e v e r e . W h e n a h i g h s u p e r s a t u r a t i o n is u s e d d u r i n g the g r o w t h , s p i r a l g r o w t h a n d g r o w t h h i l l o k s c a n be o b s e r v e R (Fig. I). By r a i s i n g the AI c o n t e n t of the m e l t ( c o m p o s i t i o n s A - E ) the AI c o n - t e n t of the f i l m i n c r e a s e s . T h e s a t u r a t i o n t e m p e r a t u r e c a n be d e - c r e a s e d c o n s i d e r a b l y by a d d i n g B 2 0 3 to the m e l t . T h i s r e s u l t s in a d e c r e a s e of the AI c o n t e n t of the f i l m s , as is s h o w n f o r c o m - p o s i t i o n s E - I in F i g . 2. ( a l s o cf. T a b l e II). T h e Pb c o n t e n t of the f i l m d e c r e a s e s w i t h i n c r e a s i n g g r o w t h t e m p e r a t u r e f r o m 0 . 0 2 a t o m s Pb p e r f o r m u l a u n i t at 8 4 0 ° C to less t h a n 0 . 0 0 5 a t o m s Pb at I 0 2 0 o c .

W h e n the AI c o n t e n t of the f i l m s is p l o t t e d v e r s u s the s t r a i n e d f i l m l a t t i c e c o n s t a n t s as in Fig. 3, all p o i n t s a r e c l o s e to a s t r a i g h t l i n e r e s e m b l i n g V e g a r d ' s r e l a t i o n s h i p b e t w e e n u n s t r a i n e d ( b u l k ) l a t t i c e c o n s t a n t s a n d AI c o n t e n t s in N i F e 2 - x A l x O 4 as r e p o r t e d by S c h u l k e s c.s. (12). T h e s e b u l k v a l u e s w e r e c o n f i r m e d by o u r o w n m e a s u r e m e n t s . B e c a u s e t h e r e a r e d i s t i n c t d e v i a t i o n s f r o m V e g a r d ' s r e l a t i o n d e p e n d i n g b o t h on the t y p e of s u b s t r a t e u s e d a n d on the AI c o n r t e n t of the f i l m , we w i l l c o m p a r e o u r d a t a w i t h c a l c u l a t e d v a l u e s a s s u m i n g e i t h e r 100% e l a s t i c d e f o r m a t i o n or 100% s t r e s s r e l i e f at the d e p o s i t i o n t e m p e r a t u r e . U s i n g a P o i s s o n c o n s t a n t of 0 . 3 f o r the N i F e 2 - x A l x O 4 s y s t e m

a n d x = 0 . 6 (a o = 8 . 2 4 9 ~) the s t r a i n e d l a t t i c e c o n s t a n t , a s s u - m i n g 100% e l a s t i c d e f o r m a t i o n , w o u l d be 8 . 0 8 ~ on M g O a n d 8 . 1 8 on Z n G a 2 0 4 s u b s t r a t e s . T h e c o n n e c - t i o n b e t w e e n the s t r a i n e d l a t t i c e c o n s t a n t s a n d the AI c o n t e n t is d r a w n in F i g . 3 for M g O a n d Z n G a 2 0 4 s u b s t r a t e s . W h e n s t r e s s r e l i e f o c c u r s at the g r o w t h t e m p e r a t u r e the r e s u l - t i n g r o o m t e m p e r a t u r e s t r e s s ~- 2 F I G . I. c a n be c a l c u l a t e d f r o m the k n o w n e x p a n s i o n c o e f f i c i e n t s f o r M g O S u r f a c e m o r p h o l o g y of a (8), N i F e 2 0 4 (17) a n d Z n G a 2 0 4 (]8) N i F e 2 x A l 0 f i l m w i t h x = 0.26 of r e s p e c t i v e l y 1.34 ]0 -5 , ] . 0 0 g r o w n - o n ~ ] ~ ] ) Z n G a 2 0 4 f r o m 10 -5 a n d 0 . 9 5 |0 -5 ° C - 1 ( 2 0 - 9 0 0 ° C ) . m e l t G d u r i n g 5 m i n u t e s at 894 F i l m s g r o w n u p o n M g O w i l l be in °C. S m a l l c r a c k s a n d s p i r a l c o m p r e s s i o n w h i l e f i l m s g r o w n u p o n g r o w t h c a n be o b s e r v e d . Z n G a 2 0 4 w i l l be in t e n s i o n . If o n e a s s u m e s t h a t in the s t r e s s r e l i e - v e d f i l m e l a s t i c d e f o r m a t i o n o c - c u r s d u r i n g c o o l i n g to r o o m t e m p e - ~ 10 r a t u r e the s t r a i n e d l a t t i c e c o n - ! s t a n t s c a n be c a l c u l a t e d . U s i n g a AT of 9 0 0 ° C (a s - af) ~ for M g O ~

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the g r o w t h t e m p e r a t u r e . T h e m e a - s u r e d v a l u e s f o r (a s - af) ~ a r e a b o u t - 0 . 0 1 ~, c o m p a r e d to - 0 . 0 4 7 E 02 t h e o r e t i c a l l y . O b v i o u s l y s o m e o s t r a i n is r e l e a s e d by c r a c k i n g of the f i l m . In the c a s e of Z n G a 2 0 4 0 s u b s t r a t e s o u r d a t a a r e c o n s i s t e n t w i t h the v a l u e s c a l c u l a t e d a s s u - m i n g 1 0 0 % e l a s t i c d e f o r m a t i o n up to x = 0 . 1 6 in N i F e 2 _ x A l x O 4. T h i s c o r r e s p o n d s w i t h a r o o m t e m p e r a - t u r e m i s m a t c h of 0 . 0 2 ~ in t e n - s i o n . F o r g r e a t e r m i s f i t v a l u e s ( x > 0 . 1 6 ) s t r e s s r e l i e f o c c u r s at t h e d e p o s i t i o n t e m p e r a t u r e a n d f i l m c r a c k i n g is a l s o o b s e r v e d w h i c h e x p l a i n s t h e f a c t t h a t o u r l I I t A I I I I

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F I G . 2. AI c o n t e n t v e r s u s g r o w t h t e m - p e r a t u r e f o r N i F e 2 _ x A l x O 4 f i l m s g r o w n on (Ill) Z n G a 2 0 4 ; E - I i n d i c a t e ~ m e l t s w i t h i n c r e ~ s i n g B 2 0 3 c o n t e n t . d a t a a r e a l i t t l e h i g h e r t h a n a c c o r d i n g to a 1 0 0 % s t r e s s r e l i e f m o d e l . T h e f i l m s g r o w n u p o n Z n G a 2 0 4 w i t h x = 0 . 7 8 a n d 0 . 9 4 a r e g r o w n at r e l a t i v e l y h i g h t e m p e r a t u r e a n d as a c o n s e q u e n c e i n t e r - d i f f u s i o n b e t w e e n f i l m a n d s u b s t r a t e c a n o c c u r r e s u l t i n g in a h i g h e r f i l m l a t t i c e c o n s t a n t . ( T h e o c c u r e n c e of i n t e r d i f f u s i o n c a n be s h o w n by a n n e a l i n g a N i F e 2 0 4 f i l m on a M g O s u b s t r a t e at l l 0 0 ° C : A s o l i d s o l u t i o n of N i F e 2 0 4 a n d M g F e 2 0 4 is f o r m e d w i t h a h i g h e r l a t t i c e c o n s t a n t t h a n p u r e N i F e 2 0 4 ) .

1148 P . J . M . V A N D E R S T R A T E N , e£ al. Vol. 13, No. ii D o m a i n s t r u c t u r e As e x p e c t e d f r o m the s t r e s s c o n s i d e r a t i o n s no d o m a i n s t r u c t u - re c o u l d be m a d e v i s i b l e on f i l m s g r o w n u p o n

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u p o n Z n G a 2 0 4 s h o w e d a p a t t e r n ty- a3c p i c a l l y c a u s e d by the f i r s t o r d e r c r y s t a l a n i s o t r o p y (Fig. 4), A I - s u b s t i t u t e d N i - f e r r i t e f i l m s g r o w n in t e n s i o n u p o n (111) Z n G a 2 0 4 s u b s t r a t e s e x h i b i t s t r i p e a2s d o m a i n s r e s e m b l i n g the p a t t e r n s o b s e r v e d on u n i a x i a l g a r n e t films. T h e b e s t d e v e l l o p e d p a t t e r n s are f o u n d for N i F e 2 - x A l x O 4 f i l m s w i t h x = 0.11 a n d 0 . ] 6 ; f i l m s w h i c h 820 are e l a s t i c a l l y d e f o r m e d . F i l m s w i t h x = 0 . 2 6 and x = 0 . 4 4 a l s o s h o w s h a r p s t r i p e d o m a i n s b u t n o t o v e r the e n t i r e s u r f a c e ; in the n e i g h b o u r h o o d of c r a c k s the s t r u c - t u r e d i s a p p e a r s . T h e s t r i p p e r i o d r a n g e s f r o m 1.6 ~ m for x = 0.]1

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AI c o n t e n t v e r s u s the s t r a i n e d to 2.3 ~ m for x = 0 . 4 4 . F i l m s l a t t i c e c o n s t a n t s of N i F e 2 _ x A l x w i t h h i g h e r AI c o n t e n t s s h o w m o r e 04 f i l m s g r o w n on (111) M g O (=) d i f f u s e d o m a i n p a t t e r n s . W h e n a or (I]I) Z n G a 2 0 4 (o). A l s o the m a g n e t i c f i e l d is a p p l i e d p e r p e n - d i c u l a r to the p l a n e of the f i l m the s t r i p w i d t h i n c r e a s e s w i t h i n c r e a s i n g f i e l d . S t r i p e d o m a i n s m e a s u r e d u n s t r a i n e d l a t t i c e c o ~ s t a n t s (x) are p l o t t e d . S o l i d l i n e r e p r e s e n t V e g a r d ' s r e l a - t i o n s h i p , w h e r e a s the d a s h e d - o c c u r r i n g in f i l m s w i t h x = 0.61 d o t t e d l i n e and d a s h e d l i n e re- (Fig. 5) a n d x = 0 . 7 8 c a n be c o n - p r e s e n t c a l c u l a t e d v a l u e s of t r a c t e d to c y l i n d r i c a l d o m a i n s , s t r a i n e d l a t t i c e c o n s t a n t s for F o r x = 0.61 b u b b l e s w i t h a d i a - r e s p e c t i v e l y f i l m s on M g 0 and m e t e r of ~ 2 ~ m a p p e a r at a b o u t on Z n G a 2 0 4 a s s u m i n g ]00% e l a s - 550 Oe b i a s f i e l d and w h e n this tic d e f o r m a t i o n .

f i e l d is i n c r e a s e d f u r t h e r to a b o u t 600 Oe the b u b b l e s c o n t r a c t to a b o u t 75% of t h e i r o r i g i n a l d i a m e t e r a n d c o l l a p s e . F o r the f i l m w i t h x = 0 . 7 8 t h e s e v a l u e s a r e r e s p e c t i v e l y 350 a n d 400 Oe. B u b b l e o b s e r v a t i o n s in the f i l m s w i t h x $ 0 . 4 4 (Fig. 6) c o u l d n o t be m a d e . W i t h a b i a s f i e l d l a r g e r t h a n 600 Oe the h a l f d o m a i n p e r i o d b e c o m e s too s m a l l a n d the d o m a i n b o u n d a r y b e c o m e s too d i f f u s e to FIG. 4. f o l l o w f u r t h e r c o n t r a c t i o n . D o m a i n p a t t e r n o b s e r v e d on a In Fig. ~ w e h a v e p l o t t e d (111) N i F e 2 0 4 f i l m g r o w n on the AI c o n t e n t of N i F e 2 - x A l x 0 4 ~ _ _ Z n G a 2 0 4 . T h e f i l m e x h i b i t s a v e r s u s c a l c u l a t e d v a l u e s of 2 , s m a l l c o m p r e s s i v e s t r a i n ( 0 . 0 0 3 K ~ (ED) (due to e l a s t i c d e f o r m a - ~ in c o m p r e s s i o n ) . t l o n ) and K~ (SR) ( a s s u m i n g

s t r e s s r e l i e f at the d e p o s i t i o n t e m p e r a t u r e a n d s u b s e q u e n t e l a s - tic d e f o r m a t i o n d u r i n g c o o l i n g ) . T h e v a l u e s of K s a r e c a l c u l a t e d u s i n g t h e v a l u e of

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f o r x = 0. Up to x = 0 . I ~ K ~ (ED) is v a - lid a n d a s t a b i l i t y f a c t o r q of 0 . 5 4 is f o u n d f o r x = 0 . 1 6 . F o r x g 0 . 4 4 at w h i c h s t r e s s r e l i e f o c c u r s at the g r o w t h t e m p e r a t u r e , we c a l c u l a t e f r o m K ~ (SR) a v a l u e of q = ].7 f o r x = 0 . 4 4 a n d a b o u t 7 f o r x = 0 . 6 1 , b u t an u n c e r t a i n t y d u e to the f a c t t h a t %111 = f ( x ) m u s t be k e p t in m i n d . T h e o c c u r r e n c e of s t r e s s r e l i e f in f i l m s g r o w n on M g O m a y a l s o h a v e c o n s e q u e n c e s for the i n t e r p r e t a t i o n of o u r r e s u l t s on C u F e 2 0 A f i l m s r e p o r t e d in ref. (9). T h e r e p o r t e d c a l c u l a t e d v a - l u e s o~ t h e s t r e s s - i n d u c e d a n i s o t r o p y c o n s t a n t s m i g h t be in e r r o r s i n c e w e d i d n o t a c c o u n t f o r s t r e s s r e l i e f . C o n c l u s i o n s We h a v e s h o w n t h a t s t o i c h i o m e t r i c N i F e 2 _ x A l x O 4 f i l m s c a n be d e p o s i t e d on (111) M g O a n d on (ill) Z n G a 2 0 4 s u b s t r a t e s . F i l m s g r o w n u p o n M g O a r e s u f f e r i n g f r o m s e v e r e s t r e s s r e l i e f a n d as a c o n s e q u e n c e M g O s u b s t r a t e s a r e e n t i r e l y u n s u i t a b l e f o r g r o w t h of A l - s u b s t i t u t e d n i c k e l f e r r i t e f i l m s w i t h b u b b l e a p p l i c a t i o n s . F i l m s g r o w n u p o n Z n G a 2 0 @ a r e m u c h b e t t e r in t h i s r e g a r d ; up to 0 . 0 2 ~ in t e n s i o n e l a s t l c d e f o r m a t i o n o c c u r s . F i l m s g r o w n in t e n - s i o n w i t h

~III

< 0 h a v e a u n i a x i a l a n i s o t r o p y p e r p e n d i c u l a r to the p l a n e of t h e f i l m . D u e to the e x i s t e n c e of a c o m p e n s a t i o n p o i n t l o w - m o m e n t f i l m s c a n be g r o w n w i t h a s t a b i l i t y f a c t o r e x - c e e d i n g u n i t y . S t r i p e d o m a i n s c a n be o b s e r v e d w i t h the B i t t e r t e c h n i q u e . By a p p l y i n g a m a g n e t i c f i e l d p e r p e n d i c u l a r to the p l a n e of t h e f i l m m a g n e t i c b u b b l e s c a n be g e n e r a t e d . S i n c e t h e r e s u l t s o b t a i n e d so f a r a r e v e r y e n c o u r a g i n g the w o r k on the n i c k e l f e r r i t e s y s t e m is e l a b o r a t e d f u r t h e r . O n Z n ( G a , A I ) 2 0 4 s u b s t r a t e s w i t h l a t t i c e c o n s t a n t s r a n g i n g f r o m 8 . 2 8 - 8 . 2 3 ~ it s h o u l d be p o s s i b l e to d e p o s i t e l a s t i c a l l y d e f o r m e d N i F e 2 _ x A l x O 4 f i l m s w i t h a b u b b l e s t a b i l i t y f a c t o r q r e a c h i n g up to 5 or e v e n h i g h e r . T h e d e p o s i t i o n p r o c e s s i t s e l f c a n c e r t a i n l y be i m p r o v e d : By l o w e r i n g the N i O c o n t e n t or by i n c r e a s i n g the B 2 0 3 c o n t e n t of t h e f l u x the s a t u r a t i o n t e m p e r a t u r e c a n be d e c r e a s e d c o n s i d e r a b l y . F i l m g r o w t h at l o w e r t e m p e r a t u r e s is l e s s i n f l u e n c e d by d i f f e r e n - ces in e x p a n s i o n c o e f f i c i e n t s of f i l m a n d s u b s t r a t e . A l s o p r o - b l e m s a r i s i n g f r o m i n t e r d i f f u s i o n b e t w e e n s u b s t r a t e a n d f i l m a r e

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1150 P . J . M . VAN DER STRATEN, et al. Vol. 13, No. 11 e l i m i n a t e d w h e n low t e m p e r a - t u r e s c a n be u s e d . K n o w l e d g e of the e x p a n - s i o n c o e f f i c i e n t s of f i l m and s u b s t r a t e a n d k n o w l e d g e of 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 s of the N i F e 2 _ x A l x O 4 s e r i e s are e s s e n t i a l xn o r d e r to c a l c u l a t e the s t r e s s - i n d u c e d a n i s o t r o p y .

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FIG. 6. ~)omain p a t t e r n o b s e r v e d on a l ] i F e 2 - x A l x 0 4 f i l m w i t h x = 0 . 4 4 g r o w n on (I]I) Z n G a 2 0 4 . A m a g - n e t i c f i e l d is p r e s e n t p e r p e n - d i c u l a r to the p l a n e of the film: a) 0 Oe, b) 250 Oe and c) 500 Oe. FIG. 7. 2 ~ (10) a n d K~ v e r s u s the AI c o n t e n t of N i F e 2 _ x A l x O 4 f i l m s . K~ (ED): c a l c u l a t e d a s s u m i n g I~0% e l a s t i c d e f o r m a t i o n . K~ (SR): c a l c u l a t e d a s s u m i n g ]00% s t r e s s r e l i e f . C a l c u l a - t i o n s are p e r f o r m e d u s i n g X l l l for p u r e N i F e 2 0 4 for all c o m - p o s i t i o n s .

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