In order for ferromagnetic minerals to be useful in paleomagnetic studies, their magnetizations must be able to align with the geomagnetic field, and then preserve this remanence for millions of years without further realignment. The main factors influencing the fidelity of a ferromagnetic grain as a paleomagnetic recorder are its magnetic anisotropy and domain structure, which are controlled by grain size and shape as well as mineral structure.
Table 3.1: Geologically common ferromagnetic minerals, and their magnetic properties. Modified from Moskowitz (1991) and Tauxe (1998).
Mineral Composition Spin alignment Curie/N´eel Temp. Coercivity Magnetite Fe3O4 Ferrimagnetic 580◦C 10’s of mT
Ulvospinel Fe2TiO2 Antiferromagnetic -153◦C
Hematite αFe2O3 Canted
antiferromagnetic
675◦C highly variable, can
be 10’s of T Ilmenite FeTiO2 Antiferromagnetic -233◦C
Maghemite γFe2O3 Ferrimagnetic 590–675◦C
Greigite Fe3S4 Ferrimagnetic >330◦C 60–>100 mT
Pyrrhotite Fe7S8 Ferrimagnetic 320◦C highly variable, can
be 100’s of mT Goethite αFeOOH Antiferromagnetic, but
small net moment
120◦C 10s of T
Magnetic anisotropy
The magnetic energy of a ferromagnetic grain is minimised by aligning its mag- netic moment in the direction of the ambient magnetic field; in the absence of other controls on the orientation of their magnetization, ferromagnetic grains would al- ways align with the geomagnetic field and no older remanence would be preserved. However, the energy required to magnetize a grain is usually not constant in all orientations; there are ‘easy’ directions of magnetization in which the associated energy is lower. There are three principal sources of magnetic anisotropy.
• Magnetocrystalline anisotropy. The exchange energy between coupled spins is minimized when spins are aligned along particular crystallographic axes.
• Shape anisotropy. If atomic magnetic moments are modelled as pairs of mag- netic charges, a magnetized grain will have a surface distribution of these charges (Fig. 3.4a), which not only produces an external (dipole) field but also an internal demagnetizing fieldHD which opposes the overall magneti- zation (Fig. 3.4b). Because the strength of this field depends on the surface charge distribution, an elongated grain has a smallerHD along its long axis, resulting in an easy axis of magnetization, because a smaller percentage of the surface is covered by magnetic charges (Fig. 3.4c, d).
• Magnetostrictive anisotropy. Spin realignment exerts stresses on the mag- netic crystal, changing its shape. Conversely, therefore, applied stresses, which further alter the shape of the crystal, can affect the spin alignment and give rise to magnetostrictive anisotropy.
+ - + + - + + + - + - + - + - + - + - + - - + - - - + + + + + + - - - - - - + + - + - + - + - + - + - - + - (a) (b) (c) (d) m HD m m
Figure 3.4: (a) Surface magnetic charge distribution for a uniformly mag-
netized spherical grain, and (b) the resultant internal demagnetizing field. (c, d) Charge distribution in an elongated grain with (c) a moment aligned along the long axis of the grain, and (d) a moment oriented perpendicular to the long axis. After Butler (1992).
The existence of magnetic anisotropy in ferromagnetic grains means that energy is required to shift the direction of their magnetic moment m from one ‘easy’ direction to another. Only a magnetic field greater than the switching or coercive field, hc, can generate enough magnetostatic energy to overcome this anisotropy energy, forcingmthrough the intervening ‘hard’ directions. Ifhc is large, details of an ancient magnetizing field can potentially be recorded for long periods of time. Even at a constant temperature, however, thermal energy can eventually move
macross these energy barriers into a new orientation, a phenomenon referred to as magnetic viscosity. From an initial magnetizationM0, the remanent magnetization
of a population of ferromagnetic grains will decay exponentially:
M(t) = M0e −t τ ,
where t is the elapsed time and τ is the characteristic relaxation time (the time for the remanence to decay to M0/e). Technically, this equation is only valid for
single domain grains (see Section 3.1.3) and only holds as a first approximation for multidomain systems. The probability that m will spontaneously change ori- entation is dependent on the ratio of magnetic anisotropy and thermal energies, hence:
τ = C1 evhcm 2kT
,
where C = frequency factor (≈108 s−1), v = grain volume, k = Boltzmann con-
stant, and T = temperature. Relaxation time is therefore proportional to grain volume and the coercive field, and inversely proportional to temperature. The exponential relationship means that a small increase in grain size will increase τ
by many orders of magnitude, from seconds to>1 Ga; above a particular ‘blocking volume’, τ becomes large enough that a remanent magnetization can be preserved over millions, or even billions of years.
In reality, thermal relaxation in a magnetized rock occurs in the presence of the geomagnetic field, which will cause particles with low hc to align with the present day field direction. This viscous remanent magnetization (VRM) must be removed before any ancient components of magnetization can be measured.
Magnetic domains
Increasing grain size also increases the magnetostatic energy associated with the surface distribution of magnetic charges (Fig. 3.4). Above a certain size, it be- comes energetically favourable for the grain to split into a number of uniformly magnetized domains, oriented along different easy directions of magnetization, which reduces the overall magnetization. The number of domains that form is determined by the balance between the resulting reduction in magnetostatic en- ergy, and the energy required to form domain walls, the regions between adjacent domains across which spins must rotate from one easy direction to another. Three main types of domain structure are recognised:
• Single domain (SD). Below a critical grain size, the energy required to create a domain wall exceeds the reduction in magnetostatic energy achieved in forming one. An SD grain therefore has a uniform magnetization that can only be changed by rotation of its magnetic moment; when SD grains are relatively large and thermally stable, it is energetically difficult to change the direction of magnetization, resulting in high coercivities and magnetic stability (Fig. 3.5). Coercivity is reduced at smaller grain sizes, due to the randomising effect of thermal energy; eventually hc is reduced to the point that the remanent magnetization rapidly decays to zero in the absence of an applied field (τ <100 s); these superparamagnetic (SP) grains are not stable enough to record paleomagnetic information (Fig. 3.5).
• Multi-domain (MD). The division of larger ferromagnetic grains into domains with differently aligned magnetizations leads to a low overall remanence. Additionally, rather than causing the realignment of magnetic moments, applying a field to a MD grain promotes preferential growth of domains with a magnetization parallel to the field. The movement of domain walls is a low energy process that can be accomplished in relatively low fields; thus MD grains also have low coercivities (Fig. 3.5), and are unstable over geological timescales.
• Pseudo-single domain (PSD). The transition from SD-like to MD-like behav- iour is not abrupt (Fig. 3.5). For reasons that are still not fully understood, small MD particles, containing just a few domains, can still have SD-like
properties (large remanent magnetizations and, more crucially, high coerciv- ities) and are capable of preserving a stable paleomagnetic signal.
The size of ferromagnetic grains is therefore of crucial importance in determining their magnetic stability; grains useful for paleomagnetic purposes are in the stable SD (τ >107–109 years) to PSD size range (Fig. 3.5).
PSD stable SD
SP MD
grain size hc
most likely to be stable over geological timescales
Figure 3.5: Variation in domain state and coercivity with increasing grain size.
Stable SD grains, and PSD grains just above the critical SD grain size are the most likely to be stable over geological timescales. From Moskowitz (1991).