Ms where Kx is the first magnetocrystalline anisotropy constant.

2M, where X is the average magnetostrictive coefficient and a is the internal stress amplitude.

It should be noted that the values of Ms for magnetite (480 x 103 Am"1) and hematite (2.2 x 103 Am"1) are widely different and this means that different forms of anisotropy are important in the two cases. For hematite it is obvious that shape anisotropy is of no significance compared with either magnetocrystalline or stress-induced anisotropy. Hematite has high coercivities that are probably due to stress-induced anisotropy. Then X = 8 x 10"6 and for an internal stress of ct= 100 MPa (lkb), B'c = 500 mT. For magnetite the effect of mechanical stress is minor since a uniaxial stress of a = 10 MPa (0.1 kb), which is close to the breaking strength, only gives B'c =2 mT with X = 36 x 10"6. In the case of magnetocrystalline anisotropy, Kx = 1.35 x 104 Jm"3, so this cannot give rise to coercivities in excess of B'c = 60 mT. Shape anisotropy, however, can give rise to coercivities considerably greater than this. The theoretical maximum (for infinitely long needles) is given by B'c = V2 \x0Ms ~ 300 mT).

The magnetic susceptibility %s (initial susceptibility) of a random assemblage of SD grains (Fig. 2.12c) in which shape anisotropy predominates is given by

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