Chapter 4
Magnetic anisotropy and domains

Rocks often contain assemblages of ferromagnetic minerals dispersed within a matrix of diamagnetic and paramagnetic minerals. In later chapters we will be concerned with the magnetization of these assemblages, but here we continue our investigation of the behavior of individual particles. In Chapter 3 we learned that in some crystals electronic spins work in concert to create a spontaneous magnetization that remains in the absence of an external field. The basis of paleomagnetism is that these ferromagnetic particles carry the record of ancient magnetic fields. What allows the magnetic moments to come into equilibrium with the geomagnetic field and then what fixes that equilibrium magnetization into the rock so that we may measure it millions or even billions of years later? We will begin to answer these questions over the next few chapters.

We will start with the second part of the question: what fixes magnetizations in particular directions? A basic principle is that ferromagnetic particles have various contributions to the magnetic energy which controls their magnetization. No matter how simple or complex the combination of energies may become, the grain will seek the configuration of magnetization which minimizes its total energy. The short answer to our question is that certain directions within magnetic crystals are at lower energy than others. To shift the magnetization from one “easy” direction to another requires energy. If the barrier is high enough, the particle will stay magnetized in the same direction for very long periods of time – say billions of years. In this chapter we will address the causes and some of the consequences of these energy barriers for the magnetization of rocks. Note that in this chapter we will be dealing primarily with energy densities (volume normalized energies), as opposed to energy and will distinguish the two by the convention that energies are given with the symbol E and energy densities with ϵ.

In Chapter 6, we will discuss the behavior of common magnetic minerals, but to develop the general theory, it is easiest to focus on a single mineral. We choose here the most common one, magnetite. It has a simple, cubic structure and has been the subject intensive study. However, we will occasionally introduce concepts appropriate for other magnetic minerals where appropriate.

The simplest permanently magnetized particles are quasi-uniformly magnetized. These so-called single domain (SD) particles have spins that act in concert, staying as parallel (or anti-parallel) as possible. As particles get larger, the external energy can be minimized by allowing neighboring spins to diverge somewhat from strict parallelism; these particles are referred to as pseudo-single domain or PSD. Eventually, the spins organize themselves into regions with quasi-uniform magnetization (magnetic domains) separated by domain walls and are called multi-domain (MD) particles. These more complicated spin structures are very difficult to model and most paleomagnetic theory is based on the single domain approximation. Therefore we begin with a discussion of the energies of uniformly magnetized (single-domain) particles.


Figure 4.1: a) A magnetite octahedron. [Photo of Lou Perloff in The Photo-Atlas of Minerals.] b) Internal crystal structure. Directions of the body diagonal ([111] direction) and orthogonal to the cubic faces ([001] direction) are shown as arrows. Big red dots are the oxygen anions. The blue dots are iron cations in octahedral coordination and the yellow dots are in tetrahedral coordination. Fe3+ sits on the A sites and Fe2+ and Fe3+ sit on the B sites. c) Magnetocrystalline anisotropy energy as a function of direction within a magnetite crystal at room temperature. The easiest direction to magnetize (the direction with the lowest energy – note dimples in energy surface) is along the body diagonal (the [111] direction). [Figure from Williams and Dunlop, 1995.]

 4.1 The magnetic energy of particles
  4.1.1 Exchange energy
  4.1.2 Magnetic moments and external fields
  4.1.3 Magnetocrystalline anisotropy energy
  4.1.4 Magnetostriction - stress anisotropy
  4.1.5 Magnetostatic (shape) anisotropy
  4.1.6 Magnetic energy and magnetic stability
 4.2 Magnetic domains
 4.3 Thermal energy
 4.4 Putting it all together
 4.5 Problems