Measurement of domain wall mobility in GdIG
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w h e r e Vwall is the n o r m a l v e l o c i t y of a d o m a i n w a l l and Hexcess is the value of the t o t a l f i e l d a c t i n g on the w a l l in e x c e s s of that f i e l d j u s t r e q u i r e d to change the p o s i t i o n of the wall. With an a r r a y of bubble d o m a i n s , the m o b i l i t y m e a s u r e m e n t should be e a s y to i n t e r p r e t b e c a u s e the individual d o m a i n s can be s h r u n k j u s t to the point of c o l l a p s e with an applied f i e l d p u l s e and when the p u l s e is r e m o v e d the p a t t e r n w i l l r e v e r t to its o r i g i n a l s t a t e . The n u m b e r of d o m a i n s mad the total w a l l l e n g t h is the s a m e f o r e a c h p u l s e as long as none of the bubbles c o l l a p s e . The applied f i e l d i s u n i f o r m so t h e r e w i l l be no l a t e r a l g r a d i e n t which would tend to change the p o s i t i o n of the d o m a i n s . T h i s is in c o n t r a s t to the many m o b i l i t y m e a s u r e m e n t s in which l o c a t i o n and e v e n the n u m b e r of w a l l s a r e not n e a r l y so w e l l known.
A Faraday effect apparatus was used with a photomultiplier tube and a sample-averaging apparatus to find the total area of the circles as a function of time during an applied field pulse. Before each measurement was made, a bubble array was formed by applying a series of pulses of the proper size and width as explained later. The wall mobility can be calculated using the data in the followingways. If a field pulse is applied to a sample containing a circular domainpattern, the domains shrink such that the rate of change of the circle radius is proportional to the excess field Hexcess. The excess field acting on a domain wall is the sum of the applied field Ha, the internal demagnetizing field Hd, the wall field Hw which is a measure of the inward pressure exerted by the wall energy, and finally the coercive force Hc. Vwall
: dr/dt
= -p.(H a - H d - H c + H w)
[1]
w h e r e r is the d o m a i n r a d i u s . The w a l l v e l o c i t y can be e x t r a c t e d f r o m the e x p e r i m e n t a l data and is j u s t p r o p o r t i o n a l to the s q u a r e r o o t of the slope of the d o m a i n a r e a vs t i m e plot. Then, if the v a l u e of the e x c e s s f i e l d can be found, the w a l l m o b i l i t y is known.
EXPERIMENTAL All measurements were made on I - or 2-mil thick single crystal GdIG slabs which were lapped and polished from a I0 rail slice sawed from a large single crystal. J. M. NEMCHIK, formerly of Carnegie-Mellon University, Pittsburgh, Pa., is now with Bell Telephone Laboratories, Whippany, N. J. S.H. CHARAP is with Department of Electrical Engineering, Carnegie-Mellon University. This manuscript is based on a paper presented at the annual conference sponsored by the Electronic Materials Committee of the Institute of Metals Division of the Metallurgical Society of AIME and held August 30-September 2, 1970, in New York City. METALLURGICAL TRANSACTIONS
Fig. 1--Photomi
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