Variation of domain structure with surface orientation for magnetoplumbite

Volume 8, n u m b e r 4

VARIATION

PHYSICS

OF

DOMAIN FOR

LETTERS

STRUCTURE WITH MAGNETOPLUMBITE

15 F e b r u a r y 1964

SURFACE

ORIENTATION

R. C A R E Y and E. D. ISAAC Lanchester College of Technology, Coventry R e c e i v e d 25 J a n u a r y 1964

T h e d o m a i n s t r u c t u r e of u n a x i a l m a g n e t i c m a t e r i a l s i s known to c o n s i s t of a r r a y s of 180 ° d o m a i n s m a g n e t i s e d in the e a s y d i r e c t i o n w i t h c e r t a i n v a r i a t i o n s in the s u b s i d i a r y s t r u c t u r e s f o r m e d at s u r f a c e s n o r m a l to the e a s y d i r e c t i o n . At s u c h s u r f a c e s , it h a s b e e n shown 3) t h a t t h e e f f e c t s of the d e m a g n e t i s i n g f i e l d s i s to p r o d u c e a r o t a t i o n of the m a g n e t i s a t i o n v e c t o r s a w a y f r o m the e a s y d i r e c t i o n (p* effect). T h u s , f o r s m a l l r o t a t i o n s , the m a t e r i a l i s a s s u m e d to h a v e an e f f e c t i v e p e r m e a b i l i t y , at r i g h t a n g l e s to the e a s y d i r e c t i o n , g i v e n b y p* = 1 + 2•I 2 / K , w h e r e I s i s the s a t u r a t i o n m a g n e t i s a t i o n of the m a t e r i a l and K i s the m a g n e t o c r y s t a l l i n e a n i s o t r o p y energy. F o x and T e b b l e 1) h a v e e x a m i n e d the c o n d i t i o n s u n d e r which a r e d u c t i o n in the d e m a g n e t i s i n g e n e r g y of an u n a x i a l c r y s t a l m a y b e b r o u g h t a b o u t by the ~* e f f e c t . T h e y c a l c u l a t e t h a t f o r m a t e r i a l s with high a n i s o t r o p y ( K > 2 ~ l s 2) the s u r f a c e e n e r g y of a s p e c i m e n with a K i t t e l s l a b d o m a i n s t r u c t u r e i s r e d u c e d by a factor, 2 X(~) - 1 + (1 +k*)½ ( l + k * s i n 2 q~)½ ' w h e r e k* = 2~I s 2 / K and q~ i s the a n g l e b e t w e e n the s u r f a c e and the c r y s t a l b a s a l p l a n e . U s i n g the c o l loid t e c h n i q u e t h e y e x a m i n e d the d o m a i n s t r u c t u r e on the c u r v e d s u r f a c e of a c o b a l t d i s c and found t h a t c l o s u r e d o m a i n s a r e f o r m e d when ~ ~< 57 o, c o r r e s p o n d i n g to X(q~) >/0.44. When the a n g l e b e t w e e n the s u r f a c e and the e a s y d i r e c t i o n i s l e s s than 33 ° , t h e r e i s no c l o s u r e d o m a i n s t r u c t u r e and any r e d u c -

tion in the d e m a g n e t i s i n g e n e r g y i s then b r o u g h t a b o u t by the ~* e f f e c t . H o w e v e r , a s F o x and T e b b l e p o i n t out, the e x p r e s s i o n f o r X(~o) i s v a l i d o n l y f o r m a t e r i a l s with k < 1, and t h i s i s not the c a s e for cobalt. F o r m a g n e t o p l u m b i t e (/s = 350 e m u / g , K = 3 x 106 e r g / c m ) , k* ~ 0.25, and the e x p r e s s i o n f o r ~(~) w i l l t h e r e f o r e be v a l i d f o r s u r f a c e s a t w h i c h K i t t e l s l a b s t r u c t u r e s e x i s t . U s i n g the c o l l o i d t e c h n i q u e , we h a v e e x a m i n e d the d o m a i n s t r u c t u r e s at s u r f a c e s on a s i n g l e c r y s t a l of m a g n e t o p l u m b i t e , f o r the r a n g e of o r i e n t a t i o n 0< q~< 90 ° C l o s u r e d o m a i n s a r e found f o r s u r f a c e s c o r r e s p o n d i n g to ~ --< 73 ° and at q~ = 73 o, a t r a n s i t i o n t a k e s p l a c e f r o m a c l o s u r e d o m a i n s t r u c t u r e to one of K i t t e l s l a b s . T h i s m e a n s t h a t f o r q~ ~< 73 °, r e d u c t i o n s in the m a g n e t o s t a t i c e n e r g y o c c u r both by the p* e f f e c t and b y the f o r m a t i o n of c l o s u r e d o m a i n s and, in t h i s r a n g e of o r i e n t a t i o n s , the e x p r e s s i o n f o r ~ (~) d o e s not a p p l y . F o r bulk s p e c i m e n s of m a g n e t o p l u m b i t e t h e r e f o r e , the r a n g e of o r i e n t a t i o n s o v e r w h i c h the e x p r e s s i o n f o r ~ (~) m a y be a p p l i e d i s s m a l l (though it m a y b e a p p l i e d in c a l c u l a t i o n s f o r v e r y thin s p e c i m e n s w h e r e the s l a b s t r u c t u r e e x i s t s f o r any s u r f a c e o r i e n t a t i o n 2)) and f o r m a t e r i a l s with k* < 0.25, the r a n g e w i l l be e v e n s m a l l e r .

References 1) M. Fox and R.S.Tebble, Proc. Phys. Soc.72 (1958) 765. 2) C.Kooy, Philips Techn.Rev. 19 (1958) 286. 3) H . J . W i l l i a m s , R.M. Bozorth and W. Shockley, Phys. Rev. 75 (1949) 155.

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