Multidimensional Polynomial Algebra for Bubble Circuits

M a g n e t i c domains exist freely in t h i n platelets of orthoferrite crystals obtained by slicing t h e m so t h a t their crystalline axis is perpendicular to t h e surface of t h e platelets. Such domains are also present in very t h i n epitaxial garnet films (Fig. l a ) 011 suitable substrates. W h e n t h e platelets or films are subjected to bias fields, these domains assume cylindrical s h a p e and their d i a m e t e r shrinks to microscopic sizes (Fig. l b ) . Such domains (also called " b u b b l e s " ) are stable under an a p p r o p r i a t e bias field condition a n d t h e y m a y be m a n i p u l a t e d to perform 1 ' 2 storage, gating, looping and also certain elementary logic functions. 3 T h e domains are generally p r o p a g a t e d f r o m one location in t h e circuit to t h e next by subjecting t h e m to the local bias field gradient. Basically 1535 1536 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1972 t h e r e are two m e t h o d s of providing such a field gradient to p r o p a g a t e t h e bubbles. In t h e "field access p r o p a g a t i o n , " 4 an a l t e r n a t i n g m a g n e t ization is imposed in a p a t t e r n e d soft magnetic overlay by an in-plane r o t a t i n g magnetic field generated by a pair of coils carrying an altern a t i n g current. T h e coils completely s u r r o u n d t h e platelet with their axis in its plane. T w o of t h e most commonly used overlay p a t t e r n s are shown in Figs. 2a a n d b. D u r i n g one cycle of t h e a l t e r n a t i n g current in t h e coils, t h e domains in t h e platelet move f r o m one point in a p a t t e r n to t h e corresponding point in the adjoining p a t t e r n .