Chapter 1. General Theory

Transcription

1 Chapter 1. General Theory There are now a number of excellent books on rock magnetism, palaeomagnetism and geomagnetism. Recommended texts on palaeomagnetism are Tarling (1983), Butler (1992) and Tauxe (1999). These books also give a basic introduction to rock magnetism and geomagnetism. A comprehensive book on rock magnetism is by Dunlop & Özdemir (1997) and Merrill et al. (1996) covers geomagnetism. These books have been used (in conjunction with Thomas, 1992 and Eyre, 1994) to give a brief introduction to the general theory relevant to the research undertaken for this thesis. The chapter starts with the fundamentals of magnetism including the mechanisms that allow a magnetic remanence to be held. The second section describes the magnetic minerals commonly found in basalt. The final section discusses features of the geomagnetic field with particular emphasis on the intensity of the magnetic field through time Fundamentals of Magnetism Magnetism is a phenomenon that is exhibited by all material. The magnetic dipole moment of an atom consists of two parts: an orbital dipole moment resulting from the movement of an electron about the nucleus, and a spin moment that is intrinsic to the electron. Dependent on whether the material has permanent dipole moments or not, determines whether the material is paramagnetic or diamagnetic. A third type of magnetism, ferromagnetism, is classified when paramagnetic moments interact in a collective way to produce long range magnetic order. This results in spontaneous magnetism and is of fundamental importance for palaeomagnetism. The magnetisation vector would be free to follow the applied field were it not for magnetic anisotropy, which results in a preferred orientation for the magnetisation and the occurrence of a stable remanence. The three types of magnetism are described in general terms in the following sub sections. The different forms of anisotropy and the formation of magnetic domains are then discussed before the different forms of remanence held by lava are described. For a more thorough introduction to the theory of 6

2 magnetism Hook & Hall (1994) and Dunlop & Özdemir (1997) are recommended Diamagnetism Materials are diamagnetic when they exhibit a weak induced magnetisation in the opposite direction to an applied magnetic field. Atoms or ions with no unpaired electrons have no permanent magnetic moment. However, when an external magnetic field is applied, the electrons assume a precessional mode about the nucleus (equivalent to a small electric current) resulting in a magnetic moment that opposes the field. The magnetisation is independent of temperature, unlike paramagnetism and ferromagnetism. Diamagnetism is a property of all material but is weak compared to the other magnetic phenomena. Most non iron bearing minerals are purely diamagnetic e.g. quartz, calcite and feldspar Paramagnetism Atoms or ions containing unpaired electrons can possess a permanent magnetic moment. In the absence of an applied magnetic field or in the absence of any ordering influence of neighbouring moments (exchange interaction) the moments are essentially randomly oriented. Thermal energy vibrates the crystal lattice causing the atomic magnetic moments to oscillate randomly resulting in no net magnetisation. When a magnetic field is applied it acts to align the moments, creating a net magnetisation. Paramagnetism is this partial alignment of permanent atomic magnetic moments in the direction of the applied magnetic field. There is competition between the thermal energy (kt where k is the Boltzmann constant and T is the temperature) and the magnetic energy E m (also called the Zeeman energy). E m is from the torque of B on each atomic magnetic moment m where, E m = m B Electrons have spin (s) as well as orbital angular momentum (l) and thus an orbital and spin magnetic moment. However, the transition metals and their compounds behave as though the total angular momentum J, is equal to S (vector 7

3 sum of individual s) not L±S (L is vector sum of l). This is as the orbital contribution to the magnetic moment is quenched, so to a first approximation, the magnetic moment is due to electron spin only. Thus unpaired electron spins behave as magnetic dipoles. The magnetic moment m is given by m = g µ J = gµ B where g is the gyromagnetic ratio ( 2) and µ B is the Bohr magneton which is the elementary unit or quantum of magnetic moment. B S µ B eh = 2m e = Am 2 where e and m e are the charge and mass of an electron respectively, and h is h/2π where h is Planck s constant. Atomic magnetic moments are space quantised, taking up certain orientations (states) in an applied field. There are 2J + 1 states with energies E = m gµ m where the quantum number m J takes on values J,, J. The magnetisation is a macroscopic consequence of the net statistical population of these energy states. Although at ordinary temperatures the degree of alignment of moments is small, it is sufficient to outweigh diamagnetism. The transition elements contain the most unpaired spins of all the elements and are responsible for the majority of paramagnetic behaviour seen in rocks. All material with unpaired electrons, at some temperature, exhibit paramagnetism. J B B Ferromagnetism Ferromagnetism is used here as a general term to cover all forms of material that exhibit spontaneous magnetisation. Spontaneous magnetisation is caused by strong interactions (exchange energy) between neighbouring spins that occur in certain crystals. Overlapping electron orbitals may couple the orientation of neighbouring magnetic moments leading to long range order. This is known as exchange interaction and can produce strong macroscopic magnetisation. For magnetic oxides the exchange between neighbouring cations is via an intermediate oxygen ion. This is known as super exchange interaction. In a solid there is simultaneous exchange coupling between spins in all neighbouring atoms. The situation is analogous to the coupling in which lattice 8

4 vibrations transmit elastic waves through a crystal. Standing waves in the lattice (phonons) are analogous to quantised spin waves (magnons). Magnons are normal modes, which are the fundamental thermal excitations of a ferromagnetic system. They also have particle properties and can be excited, for example, during neutron bombardment of a magnetic crystal. Spin waves (Fig. 1.1) are the long range manifestation of the short range 9

5 so that a strong spontaneous magnetisation results along the spin axis. Magnetite is an example of a ferrimagnetic mineral. Net spontaneous magnetisation Ferromagnetism Antiferromagnetism Ferrimagnetism Canted Antiferromagnetism Figure 1.2 Different possible exchange coupled spin structures and the net spontaneous magnetisation of each (after Dunlop & Özdemir, 1997). Above a critical temperature T c (Curie temperature) in ferro/ferrimagnetic materials and T N (Néel temperature) in antiferromagnetic material, long range order is lost due to thermal fluctuations and paramagnetic behaviour is observed Anisotropy As well as the ability to possess spontaneous magnetisation, ferromagnetic material can acquire a remanence. This arises where there is anisotropy energy so that the minimisation of energy results in a preferred orientation of the magnetisation vector. Uniaxial anisotropy energy E anis is given by 2 E anis = K sin θ where K is the anisotropy constant and θ is the angle between the easy direction and the magnetisation. When the shape of a grain is other than spherical it is easier for the grain to be magnetised parallel to its long axis (the easy axis). This is known as shape or magnetostatic anisotropy and is important for strongly magnetic material such 10

6 as magnetite. The anisotropy is in the demagnetising field H D, of the grain, so that the preferred orientation is one where H D is minimised as this minimises the self energy, E self. The self energy of a grain of volume V and magnetisation M due to surface magnetic poles is given by E V self = H 1 2 µ M D = 2 µ M NV where N is the demagnetising factor and µ 0 is the permittivity of free space (4π x 10-7 H/m). Magnetocrystalline anisotropy is when crystal symmetry results in certain orientations of the magnetisation vector being energetically preferred. This occurs because the electrostatic environment in the region of the magnetic ion imposes a preferential alignment on the electron orbital. These in turn influence the orientation of the electron spins through spin orbit coupling. This anisotropy is important in minerals with low spontaneous magnetisation such as haematite. The interaction between atoms within a grain produces a strain, giving rise to barriers against change in magnetisation. This leads to magnetoelastic anisotropy (magnetostriction) Magnetic Domains Exchange energy and anisotropy energy are minimised by having coherent spin systems, whereas self energy favours an incoherent spins system (as this minimises surface magnetic flux). In large grains the development of domains separated by domain walls is a compromise between the two competing mechanisms for energy minimisation. Domains are regions where spins are oriented parallel to each other whereas domain (Bloch) walls are regions where the spin axes rotate sequentially from the spin orientation of one domain to the other. These grains are termed multi domain, MD. It is easier to move domain walls than rotate an entire moment of a single domain SD grain. Magnetic grains with few domains behave much like single domain grains in terms of their magnetic stability and saturation remanence and are termed pseudo single domain, PSD. If the thermal energy of a single domain grain is sufficient to prevent it from retaining a permanent alignment then it is described as superparamagnetic, SP, as it behaves similarly to a paramagnet but with a much stronger magnetisation. 11

7 Remanence Acquisition Rocks remain magnetised in a certain direction through the competing roles of exchange energy, anisotropy energy and thermal energy. There are a number of mechanisms by which magnetic remanence can be acquired. Those mechanisms relevant to lava are described in the following sections Magnetic Viscosity and Relaxation Time Magnetic viscosity is the change of magnetisation over time at constant temperature. Occasionally a particle will have sufficient thermal energy to overcome the anisotropy energy barrier and the moment will switch its direction along its easy axis. Over time, in the absence of an applied field, the moments of an assemblage of particles will tend to become randomly oriented. The initial magnetisation M 0 will decay over time such that M t τ ( t) = exp M 0 where t is time, and τ is the relaxation time (the time for the remanence to decay to 1/e of its initial value). The value of τ is a measure of the probability that a grain will have sufficient thermal energy to overcome the anisotropy energy therefore = 1 C exp where C is a frequency factor ( τ Kv kt s -1 ). Relaxation time therefore changes rapidly with small changes in volume, v and temperature, T. SP grains have t s and are unstable on a laboratory time scale Viscous Remanent Magnetisation The magnetisation that is acquired through viscous processes is called viscous remanent magnetisation, VRM. With time, more and more grains will gain sufficient energy to overcome anisotropy energy barriers so that they are more in alignment with an applied field. If a sample with no initial remanence is placed in a magnetic field then the magnetisation M(t) will grow over time to the equilibrium magnetisation M eq such that 12

8 M t ( t) = M eq 1 exp Thermal Remanent Magnetisation Néel (1949; 1955) produced the theory of thermal remanent (thermoremanence) magnetisation TRM, for SD grains. According to the theory there is a sharply defined range of temperatures over which τ increases from geologically short to geologically long time scales. The temperature at which τ is about s is defined as the blocking temperature, T b. At or above T b, but below the Curie temperature, magnetic grains will be superparamagnetic. As the grains cool, τ increases further so that the magnetisation becomes effectively blocked in and the rock acquires a geologically significant TRM. A rock can acquire a natural TRM in two different ways: as it cools after extrusion, or as it cools from a later heating event. As a rock cools from above its Curie temperature thermal energy decreases until magnetic anisotropy energy becomes important enough to freeze in the magnetic moment. The remanence of an assemblage of randomly oriented grains, acquired by cooling through their blocking temperature, in the presence of a magnetic field should be parallel to the magnetic field and the intensity of the remanence should be linearly related to the intensity of the field (for weak fields such as the Earth s). The whole spectrum of grain sizes and shapes in a rock leads to a distribution of blocking temperatures but each individual grain has one and only one value of T b. On cooling between two particular temperatures only a portion of the grains will be blocked, so that the rock contains a partial thermoremanence, ptrm. Néel theory predicts that each ptrm is independent of all others and that a ptrm acquired by cooling through two particular temperatures can be removed by exposure to the same temperature in zero field. This is the case for SD grains but not for MD grains (e.g. Dunlop & Özdemir, 1997 and Section 2.3.2) Chemical Remanent Magnetisation A chemical remanent magnetisation, CRM, is acquired as a result of chemical processes occurring in the presence of a magnetic field at temperatures below the Curie temperature. Relaxation time is a strong function of volume as τ 13

9 well as temperature. A CRM can be acquired as new minerals are formed, or when existing magnetic minerals are altered. As newly formed minerals grow CRM is acquired as a result of passing through a critical volume (as opposed to a critical temperature for TRM). CRM can also form when existing magnetic minerals alter to other magnetic minerals, for example by low temperature oxidation (Section 1.2.1). In this case the CRM is a secondary magnetisation that contaminates the primary TRM acquired during cooling. The behaviour of CRM (in particular alteration CRM) is complicated and does not necessarily accurately record the magnetising field direction or intensity (e.g. Dunlop & Özdemir, 1997 and Section 2.3.4) Isothermal Remanent Magnetisation Magnetic material may acquire a remanence from exposure to a strong magnetic field, without any heating. The magnetic field reduces the height of anisotropy energy barriers in the direction of the field and increases the barriers antiparallel to the field. For a sufficiently strong field this energy is dominant and small thermal fluctuations are sufficient to displace the moments of SD grains to the direction of the field. For MD grains, domain walls will move in such a way as to increase those domains parallel to the field and decrease those that are antiparallel. The removal of the strong magnetic field allows some moments in both SD and MD grains to return to their original orientations but many remain in their new orientation, giving rise to an isothermal remanent magnetisation, IRM. Rocks may naturally acquire an IRM by lightning strike. The laboratory application of IRM is used as a rock magnetic technique (Section 2.1.4) Natural Remanent Magnetisation The magnetic remanence contained in a rock, collected from a geological formation, is called the natural remanent magnetisation, NRM. The NRM may have been acquired by a number of different mechanisms so that the NRM is often a combination of a number of different components, each with its own history. For lava, the component of interest is usually the TRM formed at the time of extrusion. 14

10 1.2. Magnetic Minerals Dunlop & Özdemir (1997) give a comprehensive description of magnetic minerals. Below is a brief summary of the magnetic minerals found in lava and the two types of oxidation that often occur. The oxides of iron and titanium are the most important terrestrial magnetic minerals. Their compositions can be seen on a Ti 4+ -Fe 2+ -Fe 3+ ternary diagram (Fig. 1.3). Two solid solution series are particularly important in palaeomagnetism, the titanomagnetite Fe 3-x Ti x O 4 series and the haemoilmenite Fe 2-y Ti y O 3 series. Going left and up along the two series on Fig. 1.3, represents increasing Ti substitution into the crystal lattice of magnetite and haematite. The amount of Ti substitution in titanomagnetites is denoted by x, and for haemoilmenites is y. Values for x and y range from 0 (magnetite or haematite) to 1 (ulvöspinel or ilmenite). Titanomagnetites are cubic minerals with an inverse spinel structure and haemoilmenites (also known as titanohaemites) are characterised by rhombohedral symmetry. Rutile TiO (Ti4+ 2 ) Imeno-Rutile 1/3 FeTi 2 O 5 Imenite 1/3 FeTiO 3 Ulvospinel 1/3 Fe 2 TiO 4 Titanohaematites Pseudobrookite 1/3 Fe 2 TiO 5 Titanomagnetites Titanomaghaemites Wurstite FeO (Fe2+ ) Magnetite γ = spinel = Maghaemite 1/3 Fe 3 O 4 α = corundum = Haematite 1/2 Fe 2 O (Fe3+ 3 ) Figure 1.3 Ternary diagram for iron-titanium oxides, showing the titanomagnetite and titanohaematite solid-solution lines and the titanomaghaemite field. Low temperature oxidation of the titanomagnetites causes their composition to move in the direction of the arrows (after Tarling, 1983). 15

11 Oxidation of Titanomagnetite The most common primary magnetic minerals in basaltic rocks are titanomagnetites. However, there is usually enough oxygen in the melt to oxidise the titanomagnetites via the process of high temperature (deuteric) oxidation. In addition there is low temperature oxidation or maghaemitisation, which is the conversion of titanomagnetite to titanomaghaemite and is usually a result of secondary weathering at ordinary temperatures. During both of these processes the bulk compositions of the titanomagnetite grains follow the same oxidation lines but the resulting phase assemblages are different. Low temperature oxidation converts a single phase spinel to another single phase spinel with a different lattice parameter. High temperature oxidation results in intergrown spinel (near magnetite) and rhombohedral (near ilmenite) phases. These intergrowths mimic the exsolution texture of intergrown phases of the same crystal structure and the process is often called oxyexsolution. This is an example of a topotactic transformation where one phase converts to another while preserving some of the original crystalline planes and directions. The nonmagnetic ilmenite lamellae effectively subdivide larger grains in to a number of smaller magnetically independent regions. Petersen (1976) gives a rough estimate of the temperatures at which these two forms of oxidation occur, high temperature oxidation at temperatures above about 500 C, low temperature oxidation at temperatures below about 300 C and between these values a mixture of both processes may occur. It is probable that the majority of high temperature oxidation occurs above the Curie temperature of magnetite resulting in a highly stable thermochemical remanence TCRM acquired during, or shortly after initial cooling. Low temperature oxidation may occur a long time after the rock has formed. The end product maghaemite has the same composition as haematite but has a spinel structure. Maghaemite is metastable and converts over time to haematite The Earth s Magnetic Field Complex motions in the electrically conducting fluid outer core generate the Earth s magnetic field, via some form of dynamo action (Merrill et al., 1996). 16

12 A better understanding of the processes that generate the magnetic field can be obtained by studying the magnetic characteristics found at the Earth s surface. More than 90% of the present magnetic field, as measured at the Earth s surface can be ascribed to a geocentric axial dipole (GAD) inclined at a small angle to the axis of rotation. The remainder of the field is the non-dipole field, which gives rise to patterns of complex anomalies causing deviations from the simple dipole configuration. The magnetic field vector at the surface of the Earth is usually defined by the intensity H, and the angles of declination D and inclination I as shown in Fig The present day configuration is defined as having normal polarity where inclination is positive (negative) in the northern (southern) hemisphere. D Geographic North x I Magnetic North East y H = (x 2 + y 2 + z 2 ) 1/2 D = tan -1 (y / x) I = sin -1 (z / H) Horizontal Total Vector Vertical z Figure 1.3 Components of the geomagnetic field vector. It is well known that the magnetic field direction and intensity change with time. This is known as secular variation and is an interesting research topic in itself (e.g. Merrill et al., 1996). It is also well known that field reversals have occurred through time with several hundred reversals having occurred over the last 160 Ma (Merrill et al. 1996). However, the geomagnetic field is dipolar to first order, so over sufficient time, the average geomagnetic field can be modelled as a geocentric axial dipole. This assumption is central to palaeomagnetism and is 17

13 known as the geocentric axial dipole hypothesis. For a GAD inclination I, and the geographic latitude λ, are related by the dipole equation tan I = 2 tan λ and D = 0 everywhere. To compare palaeomagnetic results for the ancient field from different localities a palaeomagnetic pole is calculated. The virtual geomagnetic pole, VGP, is the pole of an imaginary geocentric dipole corresponding to the observed geomagnetic directions at a particular latitude and longitude. Similarly, a virtual dipole moment can be calculated to express the field intensity (Smith, 1967). A VDM is independent of latitude and hence palaeointensity data from different localities can be compared. The VDM is given by, VDM 4πR µ 3 2 = H a (1 + 3cos θ m 0 where R is the radius of the Earth, H a is the ancient field intensity and θ m is the magnetic co latitude. The present day axial dipole moment is 7.8 x Am 2 (1995 IGRF, Barton et al., 1996). This is similar to the value often quoted for the last 5 Ma, 8 x Am 2 (e.g. McFadden & McElhinny, 1982). However, it has recently been suggested (Juarez & Tauxe, 2000) that the present field is anomalously high and that the average dipole field for the time period Ma is 5.49 ± 2.36 x Am 2. This is comparable to the average palaeofield for the time period Ma of 4.2 ± 2.3 x Am 2 given by Juarez et al. (1998). The time average values are evaluated from compilations of palaeointensity data. The most up to date palaeointensity compilation is the IAGA pint97 database (Perrin et al., 1998) that contains all published palaeointensity data up to 1997 (Fig 1.4). Different palaeomagnetists use different acceptance criteria of palaeointensity results and therefore accept and reject different amounts of data from the database. This significantly changes the time average results because of the general lack of palaeointensity data. ) 1/ 2 18

14 all data in pint97 database VDM x Am Age Ma Figure 1.4 All data contained in the pint97 palaeointensity database (1692 data points), including expanded scale for Ma (1401 data points). No errors are shown. Despite the general lack of palaeointensity data Perrin & Shcherbakov (1997) were able to show that for the last 400 Ma the main field has been dipolar, including during an interval of weak field known as the Mesozoic dipole low, MDL (Prévot et al., 1990). In addition, Perrin & Shcherbakov (1997) showed that insufficient sampling of a Neogene type field could not have produced the MDL, indicating that the MDL is a real feature in the palaeointensity record. The extent of the MDL is not currently known due to the lack of palaeointensity data. Recent studies however, indicate that it may be representative of a generally weak pre- Cenozoic field (Thomas et al., 1998) and that the weak field may also have lasted for a large part of the Cenozoic (e.g. Juarez et al., 1998). Another aspect in which the sparse amount of palaeointensity data limits our geomagnetic knowledge is that at present it is not possible to tell conclusively 19

15 if the processes that control reversal frequency and field strength are coupled. It has been predicted that the average dipole moment is both weaker (e.g. Loper & McCartney, 1986) and stronger (e.g. Larson & Olson, 1991; Larson & Kincaid, 1996; McFadden & Merrill, 1997) during superchrons. Palaeointensity data at present however, supports the suggestion that the processes that control reversal frequency and field strength are in fact decoupled (e.g. McFadden & Merrill, 1986; Prévot et al., 1990). 20