I ■ ■v> ■ LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN 510.84 IZ6T no. 131 -140 cop. 3 The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft/ mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. To renew call Telephone Center, 333-8400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN hov o i m S^ 1 Q 1 "R5 L161— O-1096 Digitized by the Internet Archive in 2013 http://archive.org/details/modelofpartialsw135rays *<>f. 3 DIGITAL COMPUTER LABORATORY UNIVERSITY OF ILLINOIS URBANA, ILLINOIS REPORT NO. 135 MODEL OF PARTIAL SWITCHING IN POLYCRYSTALLINE FERROMAGNETICS by S. R. Ray March 19, 1963 The method of partial switching of ferrite memory cores in digital computer memories has come into extensive use since the advantages of greater 1-3 speed and lower energy consumption were pointed out. No theoretical or conceptual explanation of the process of partial switching has been presented, however . In this paper, some generally known properties of domain wall motion and polycrystalline materials are brought together to provide a heuristic explanation of the microscopic partial switching process. For- mulation of these concepts results in a, simple, accurate macroscopic model. The results are striking in view of the microscopic complexity of partial switching phenomena. BACKGROUND The ba.sic mechanisms of domain nucleation and wall growth in polycrystalline ferromagnetics have been elucidated by Goodenough and by Menyuk and Goodenough. It was found that domain walls are nucleated at a. set of centers when the applied field intensity, H, exceeds a certain value, H , the nucleation field. The domain walls are then driven outward with a n' velocity proportional to (H-H )/S where H is the "threshold field intensity" and S is the "switching constant." -1- A viscous damping force opposes the expanding walls until collision and mutual annihilation occurs. The magnetization is reversed in the wake of the moving walls which are usually assumed to be 180 walls. If a, driving field of sufficient amplitude and proper direction is applied to an initially saturated specimen, then the specimen undergoes "full switching" which may be truncated after a time leaving the specimen in an intermediate flux state. Figure 1 illustrates an idealized cross -section of the magnetic material at some instant during switching from an initial saturated state. If the driving field is truncated at that instant, it has been demonstrated that the domain structure is stable and, therefore, remains substantially unchanged after cessation of the driving field. If a. driving field is then applied in the opposite polarity to the original drive, a, flux reversal occurs which exhibits voltage -time curves with faster switching and greater peak amplitude, per unit drive amplitude, than the full switching curves . These are the partial switching curves which appear typically as illustrated in Figure 2. DEVELOPMENT OF THE MODEL Ba.sic Assumptions Consider a magnetic specimen in a, saturated state, - $ . Lf a rectangular driving field, H , is applied for time, T , then a certain mean ' w w' radius of domains, < R >, would "be established for those domains whose walls ha,ve not "been annihilated prior to T . w Then, < R > = K T (l) w w where K = (H - H )/S, the domain wall velocity in seconds and |H > |H w w o" ' ' w 1 ' c but sufficiently small that rotational switching is negligible. (Here and hereafter, the subscripts "w" and "r" denote "write" and "read" by cor- respondence with the operations of a partial switching core memory.) If a, driving field, H = -H is then applied to the specimen, the r w wall in existence at time T ("established wall") will move ba.ck toward the w x nucleation center from which it originated. It is assumed that a new wall is nucleated and moves outward ("renucleated wall"). The two counter -moving walls, traveling at equal velocity, are mutually annihilated when they collide at time < T /2 > and radius < R/2 > as indicated in Figure 3« w 7 ' Therefore, during the application of H , the flux reversal is attributed to two components, namely, '->' UNIVERSITY OF . US LIBRARY (l) the renucleated walls which move outward and repeat the flux reversal (except for sign) which occurred during application of H and w (2) the established walls which retrace, in reverse order, the mean configurations taken during application of H . w These two components of flux reversal are modified by collision of the renucleated and established walls . It is well known that physical imperfections and magnetostrictive 7 effects hinder wall movement,, Wall velocity variations and even wall o segmentation have been directly observed in thin film measurements. On this basis a dispersion of walls is assumed which causes the wall length to be annihilated non-deterministically during collision of the counter - moving walls. In the absence of direct data, it is assumed that the colli- sion is governed collectively, if not for individual domains, by Gaussian statistics . Formulation of the Model Assume that a full switching curve is given by V"(t,K ) and that the w switching is truncated at t = T . Then the partial switching curve for the w same magnitude of drive field, |H = I H I , is : 7 1 r ' ' w 1 ■k- V (t r ,K r ) = |v(t r ,K r ) + V[(T w -t r ),K r ]| • [l-G(t r ,T w /2, a )] (2) where G(t ,T 1 2. n) is a Gaussian distribution in the variable t , with rw r mean value T 1 2 and standard deviation, a . w' ' u The first term on the right side of equation (2) corresponds to the two components described in the preceding section. The second term specifies the statistics of collision of the counter -moving walls. A family of experimental and model-predicted curves are displayed for comparison in Figure k. The value of a is empirically assigned as = 0.2t where t is the peaking time of the full switching curve, V(t,K ). This value is known to w hold uniformly over the range 0-100$ switching and for drives up to ^H in two standard varieties of Mg-Mn memory cores. The graphical construction technique equivalent to Eq. (2) is demonstrated in Figure 5 ■ CONCLUSIONS A model of partial switching has been developed which has the following properties: -5- 1. It depends only upon knowledge of the full switching voltage - time waveform for determining the partial switching family (0-100$ switching). 2. It is independent of the origin of the full switching waveform, i.e., whether theoretical or experimental, and need not depend upon knowledge of the parameters H or S. 3. The corresponding graphical technique for generating the partial switching waveforms is extremely simple. k. The model is ba.sed upon well known concepts of domain wall motion and the histology of polycrystalline technical materials. The accuracy of prediction of the partial switching waveforms is commensurate with experimental accuracy in all ca.ses which have been tested, • INITIAL MAGNETIZATION DIRECTION + REVERSED MAGNETIZATION DIRECTION * NUCLEATION CENTER Figure 1 - Idealized Domain Cross-Section During Full Switching -7- o o e° CO o . \ ? ■ ,8 \6 \7 . / / / rV S.2 \ 3 ■ 7**" ^ \ -^<— \5 -H — i — i — 50 100 300 350 150 200 250 t(nano sec.) ACTUAL CONDITIONS: Tw = 200 ns. Fr = 515 ma. - turns (read mmf.) CURVE Fw ( write mmf. in ma. -turns)) (D 430 465 - 538 • 615 - 704 - 772 ■ 858 1610 s FULL SWITCHING 400 ® ® Figure 2 - Typical Family of Partial Switching Curves -8- RADIUS AT t 'ESTABLISHED WALL" NUCLEATED WALL" = Tw Figure 5 - Idealized Counter-Moving Walls During Partial Switching 091 02T 08 Ofr (AW) A •n -P «J H O H cd O a 3 tic S •H ■3 O P •H •H P P £ •H fin -10- O CD £ > O J-i •H 2 -P o V 3 bO f-i C p> -H W ,3 C o o P O -H h ra co ° d p. p J, CO & ^ ! LO. CD u p W ■H &4 -11- REFERENCES 1. A One -Word Model of a. Word-Arrangement Memory, R. W. McKay, H. N. Yu, and C. Pottle. Univ. of Illinois, Digital Computer Laboratory, Report No. 79, May, 1957- 2. A High-Speed Ferrite Storage System, C. J. Quartly. Electronic Engineering , vol. 31, December, 1959; PP- 756-758. 3. Studies in Partial Switching of Ferrite Cores, Roger H. Tancrell and Robert E. McMahon. J. Appl. Phys ., vol. 31, May, i960, pp. 762-771- k. A Theory of Domain Creation and Coercive Force in Polycrystalline Ferromagnetics, J. B. Goodenough. Phys . Rev . , vol. 95, Aug., 195^-, pp. 917-932. 5- Magnetic Materials for Digital Computer Components. I. A Theory of Flux Reversal in Polycrystalline Ferromagnetics, N. Menyuk and J. B. Goodenough. J. Appl. Phys ., vol. 26, January, 1955, PP • 8-l8. 6. Engineering Model of a Partial Switching Effect in Ferrite Cores, S. R. Ray. Ph.D. Thesis, Univ. of Illinois, Urbana, Illinois, I96I. (Also Univ. of Illinois, Digital Computer Laboratory, Report No. Ill, September, 1961.) 7- Ferrites (book), J. Smit and H. P. J. Wijn. John Wiley and Sons, New York, N. Y., 1959, PP- 6O-77. 8. Research in Ferromagnetics, Laboratory for Electronics, Inc., Boston, Mass. Annual Report No. 570-A3, Sept., 1962 . ■12- 1/