Effect of magnetocrystalline anisotropy in single-domain polycrystalline cobalt islands

This paper on small uniaxial stress changing the remanent magnetization of rock is a companion to my previous paper on stress changing susceptibility, both phenomena being of current interest in attempts at earthquake forecasting.Theoretical expressions are derived (using rigorous energy-minimization but ignoring thermal activation) for reversible change in remanence 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. Thermal (or chemical), anhysteretic, and saturation remanence are discussed.For remanence change perpendicular to the stress axis, one expects −1/2 the above expressions for change parallel to the stress axis, which is easily proven for thermal remanence.The expressions predict that for magnetite-bearing rock the decrease in thermal remanence along a 100 bar (1 × 104 kPa) compression axis should be 0.76% for spherical single-domain grains, 0.27% for 1.4 to 1 elongation along [Formula: see text], and 0.09% for great elongation along [Formula: see text]. The decrease for equidimensional multidomain grains with strongly-pinned walls should be ~0.38%. These are all much smaller than the corresponding estimates for susceptibility, but both remanence and susceptibility decreases should become larger and more comparable as titanium content increases.

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Application of Micromagnetic Models for Barium Ferrite Magnets

Materials Science Forum ◽

10.4028/www.scientific.net/msf.820.199 ◽

2015 ◽

Vol 820 ◽

pp. 199-204 ◽

Cited By ~ 2

Author(s):

Marcos Flavio de Campos ◽

Fernanda A. Sampaio da Silva

Keyword(s):

Particle Size ◽

Grain Size ◽

Coercive Force ◽

Total Energy ◽

Barium Ferrite ◽

Magnetocrystalline Anisotropy ◽

Single Domain ◽

Square Root ◽

Single Domain Particle ◽

Magnetostatic Energy

The applicability of micromagnetics for phases with high magnetocrystalline anisotropy as barium ferrite Ba2Fe12O19and Nd2Fe14B is discussed. The Stoner-Wohlfarth model is very suitable for such phases, and also for PtFe and PtCo. It was discussed how to take into account the total energy of the system for grain size above the single domain particle size. For this situation of large grain size, the net magnetostatic energy of the system cannot be neglected. From energy considerations, it follows that the coercive force should decrease with the inverse of the square root of the grain size.

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

Canadian Journal of Earth Sciences ◽

10.1139/e76-120 ◽

1976 ◽

Vol 13 (9) ◽

pp. 1186-1200 ◽

Cited By ~ 6

Author(s):

J. P. Hodych

Keyword(s):

Magnetic Susceptibility ◽

Coercive Force ◽

Thermal Activation ◽

Magnetocrystalline Anisotropy ◽

Uniaxial Stress ◽

Single Domain ◽

Stress Axis ◽

Compression Axis ◽

Initial Magnetic Susceptibility ◽

Approximate Expressions

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.

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Polarity Determination in Sphalerite and Wurtzite Structures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100136106 ◽

1990 ◽

Vol 48 (2) ◽

pp. 500-501

Author(s):

Stuart McKernan ◽

C. Barry Carter

Keyword(s):

Opposite Polarity ◽

Single Domain ◽

Polar Material ◽

Electron Microscopic ◽

Dynamical Interaction ◽

X Ray ◽

Polarity Determination ◽

The Absolute ◽

Microscopic Techniques

The determination of the absolute polarity of a polar material is often crucial to the understanding of the defects which occur in such materials. Several methods exist by which this determination may be performed. In bulk, single-domain specimens, macroscopic techniques may be used, such as the different etching behavior, using the appropriate etchant, of surfaces with opposite polarity. X-ray measurements under conditions where Friedel’s law (which means that the intensity of reflections from planes of opposite polarity are indistinguishable) breaks down can also be used to determine the absolute polarity of bulk, single-domain specimens. On the microscopic scale, and particularly where antiphase boundaries (APBs), which separate regions of opposite polarity exist, electron microscopic techniques must be employed. Two techniques are commonly practised; the first [1], involves the dynamical interaction of hoLz lines which interfere constructively or destructively with the zero order reflection, depending on the crystal polarity. The crystal polarity can therefore be directly deduced from the relative intensity of these interactions.

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