. The Bell System technical journal . l be spread over a region aconsiderable number of atoms wide. Calculation indicates that lessenergy is required if the electron spins change direction gradually fromatom to atom as indicated in Fig. 17. The spreading of the transitionregion over many atoms instead of over one, is analogous to theseparation of similar electric charges; the mutual forces tend to spreadthem over a region as large as possible and they are held together 18 R. M. Bozorth and J. F. Dillinger, Phys. Rev., 35, 733-752 (1930). 30 BELL SYSTEM TECHNICAL JOURNAL only by some other forc
. The Bell System technical journal . l be spread over a region aconsiderable number of atoms wide. Calculation indicates that lessenergy is required if the electron spins change direction gradually fromatom to atom as indicated in Fig. 17. The spreading of the transitionregion over many atoms instead of over one, is analogous to theseparation of similar electric charges; the mutual forces tend to spreadthem over a region as large as possible and they are held together 18 R. M. Bozorth and J. F. Dillinger, Phys. Rev., 35, 733-752 (1930). 30 BELL SYSTEM TECHNICAL JOURNAL only by some other forces such as those imposed by an electric field. The expression for the energy of interaction in a boundary layer has been derived by Bloch,^^ and found to be inversely proportional to the thickness of the layer, kd 1 a 0 per unit area of boundary. Here k is Boltzmanns constant, 6 theCurie temperature, a the distance between atoms and 5 the thicknessof the layer; since the layer has no sharp limit, 5 is measured between , 1 ■>8S f. Fig. 17- -The nature of the domain boundary. The transition region between twodomains is believed to be about 1000 atom diameters thick. points at which the spins are inclined at a certain small angle (a almost0° or 180° as shown) to the spins in the middle of the domains. The forces of interaction are opposed by forces ( of crystalanisotropy or strain) which correspond to fixed values of energy perunit volume. This opposing energy is thus directly proportional to thethickness of the boundary, 7i = Cb. The minimum energy occurs when dh ^^° + ^^) = 0 i» F. Bloch, Physik, 74, 295-335 (1932). See also the more recent article byH. Kersten in Probleme der Technischen Magnetizurungskurve (R. Becker, ed.)42-72, Springer, BerHn (1938). THE PHYSICAL BASIS OF FERROMAGNETISM 31 or 5 = yikdIiaC) = 5o In iron and similar materials free from any considerable strain thevalue of C is determined by the crystal anisotropy and is about10^ ergs/cm.^ 6 «
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