By William F.Jr. Brown

The sleek concept of ferromagnetic magnetization tactics has from the start well-known the significance of magnetoelastic inter­ activities. many of the magnetoelastic calculations, besides the fact that, were basecl at the thought built by means of R. BECKER and others within the early 1930's. That concept has a number of defects; find out how to therapy them is the topic of this monograph. I first turned conscious of the shortcomings of the conventional idea via a severe research of electrical and magnetic forces, which I undcrtook as a member of the COULOMB'S legislation Committee of the yank Asso­ ciation of Physics academics. My conclusions have been released in 1951 within the American 10Z/rnal of Physics; an software of them to an issue in magnetostriction was once released in 1953 in experiences oflvlodern Physics. With the advance, in 1956, of the "nucleation box" thought of micromagnetics, the necessity for a scientific and self-consistent concept of magnetoelastic interactions grew to become extra urgent. the conventional thought expected that the nucleation box may still fluctuate negligibly from that of a inflexible physique; yet my 1953 magnetostriction calculation prompt that phrases passed over in that concept will be vital. within the educational 12 months 1963/64, 1 used to be eventually capable - because of a sabbatical furlough - to discover the time wanted for systematic improvement of a uncomplicated idea of magnetoelastic interactions in a ferromagnet.

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The torque concept can be used directly if one wishes to extcnd the theory to dynamic processes. Calculations based on these equations have been summarized elsewhere (BROWN [11], SHTRIKMAN and TREVES [1]). Part of our present problem is to modify them so as to include magnetoelastic interactions. 3. 1. The analysis of stress. The classical analysis of stress has been presented fairly consistently, except for notation, in a number of treatises on elasticity; see, for example, LOVE [1] and SOKOLNIKOFF [1].

The symbol C for their IX l' was first used in my 1940 paper on the approach to saturation (BROWN [3]). The symbol A for trxP (= te). used in a 1949 review by KITTEL [lJ. Eq. 11). mv2 (its equation of motion then becomes F = 2ka). Sometimes A is described as "the" exchange constant. with a reference to LAN DAU and LIFSHITZ [lJ; actually they never used that particular constant, and the reader who seeks a definition of it in their papers will seek in vain. 2, Eq. 12)]. 3. 62) For cu bie crystals (b ij = C (jii)' the first terms in these two equations become.

2 5) and eABC is 1 if A, B, C are an even permutation of 1,2,3, -1 if they are an odd permutation, and O otherwise. 'L dX (1)dX(2). â(XA , X B ) A (3. 26) B' in the last expression, A and B are stiU summed over, but p, q, r are an even permutation of 1,2,3:q=P+1 (mod 3) and r=p+2 (mod 3). The next steps enable us to express the right member of Eg. 10), Xp,pXp,q=lJpq . It, for given q, these three eguations (P=1, 2, 3) are solved for the three guantities X1,q' X 2 ,q' and X 3 ,q, the result is (3·27) where both p, q, r and P, Q, Rare even permutations of 1,2,3.

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