Single-domain theory for the reversible effect of small uniaxial stress upon the initial magnetic susceptibility of rock

Abstract

The phenomenon of small uniaxial stress changing the magnetic susceptibility of rock is of current interest as a possible aid in earthquake forecasting.In this paper, theoretical expressions are derived (using rigorous energy-minimization, but ignoring thermal activation) for reversible susceptibility change parallel to the stress axis for samples containing single-domain grains of a ferromagnet with cubic magnetocrystalline anisotropy (K1, positive or negative) and anisotropic magnetostriction. The grains are assumed to be non-interacting and randomly oriented spheres or ellipsoids of revolution elongated along [Formula: see text], [Formula: see text] or [Formula: see text]. Also, approximate expressions are given for samples containing multidomain grains with very strongly pinned walls.For susceptibility change perpendicular to the stress axis, one expects −½ the above expressions, which is proven for spherical single-domain grains with isotropic magnetostriction using a magnetometer analogy.The expressions predict that for magnetite-bearing rock the decrease in susceptibility along a 100 bar compression axis should be 4.7% for spherical single-domain grains (coercive force ~100 Oe), 1.6% for 1.4 to 1 elongation along [Formula: see text] (coercive force ~500 Oe), and 0.6% for great elongation along [Formula: see text]. The decrease for equidimensional multidomain grains with strongly pinned walls (coercive force ~100 Oe) should be ~1.2%—less at smaller coercive force according to some theoreticians, possibly more according to my experiments.