Gubbins D., Herrero-Bervera E. Encyclopedia of Geomagnetism and Paleomagnetism

Подождите немного. Документ загружается.

few small magnetite crystals in rock. Note that this method images

domains through deflection of the electron beam by the magnetizations

within domains. Consequently, the TEM method reveals volume

domains, not just their surface manifestations. Similarly, large magne-

tite crystals cut and polished on {100} planes almost invariably exhibit

the closure domains bounded by 71



and 109



walls expected for truly

multidomain magnetite (e.g., Bogdanov and Vlasov, 1966; Özdemir

and Dunlop, 1993, 1997; Özdemir et al., 1995).

To date, domain studies on hematite have been limited to large

(e.g., 100 mm–1 mm) platelets. Even large crystals such as these

contain very few walls and a fairly simple domain structure, owing

to hematite’s weak spontaneous magnetization (about 2 emu cm

–3

)

and low magnetostatic energy (Figure M22) (Halgedahl, 1995, 1998).

Observed number of domains versus grain size

Both Kittel’s original model of domains in a semi-infinite platelet and

calculations for finite grains by (e.g., Moskowitz and Halgedahl, 1987)

lead to the prediction that domain width D / L

1/2

, where L is plate

or particle thickness. These predictions are supported by domain

studies of natural magnetic minerals, which generally yield a power-

law dependence of D on L, although the power may differ somewhat

from 0.5.

In rock magnetism, Soffel (1971) was the first to study the grain-

size dependence of the number of domains in a paleomagnetically

important magnetic mineral. From Bitter patterns on grains of natural,

intermediate (x  0.55) titanomagnetite in a basalt, Soffel determined

that, on average, N (number of domains) / L

1/2

, where L is the aver-

age particle size. This relation translates to D (domain width) / L

1/2

Extrapolation of these data to N ¼ 1 (or, equivalently, to D ¼ L)

yielded a single domain -two domain transition size of 0.6 mm for this

composition. By assuming that Kittel’s model could be applied

to roughly equidimensional grains without serious errors and that

¼ 100 emu cm

–3

for x  0.55, Soffel obtained a wall energy

density of about 1 erg cm

–2

Bitter patterns on natural pyrrhotite in the Bad Berneck diabase

from Bavaria were studied both by Soffel (1977) and by Halgedahl

and Fuller (1983). Halgedahl and Fuller determined the dependence

of domain width on grain size for three states of magnetization:

NRM, after alternating field demagnetization (AFD) in a peak field

of 1000 Oe, and saturation remanence imparted in a field of 15 kOe.

Particles that contained walls in these three different states yielded

similar power-law dependences of D on L: D / L

0.43

(NRM),

D / L

0.40

(AFD), and D / L

0.45

(saturation remanence). The single

domain-two-domain boundary sizes estimated for the three states also

Figure M20 Bitter pattern on a grain of intermediate

titanomagnetite (x  0.6) in oceanic basalt drilled near the

Mid-Atlantic Ridge.

Figure M21 Bitter pattern on a grain of magnetite synthesized

with the glass-ceramic method. In this particular state of

magnetization, the grain contains four walls, whose lengths are

commensurate with the particle’s length. Note that one wall is

pinned very near the particle’s extreme left-hand edge. The small

triangular patterns at the lower edge of the particle represent walls

which enclose small reverse spike domains.

Figure M22 Bitter pattern of a wall on a very large (approximately

150 mm width, 1 mm diameter) platelet of natural hematite from

Elba, Italy. At most this platelet exhibits only 1–2 principal

walls, although small edge domains are often observed.

Apparently, the wall is bowing around a defect near the upper

right-hand edge of the photograph. Only a small part of the crystal

surface is shown.

496 MAGNETIC DOMAINS

were similar, falling between 1.5 and 2 mm. These results were consis-

tent with those of Soffel (1977).

Likewise, Geiß et al. (1996) obtained D / L

0.45

from Bitter patterns

on synthetic magnetite particles grown in a glass-ceramic matrix

(Worm and Markert, 1987). They obtained a single domain-two-

domain transition size for magnetite at approximately 0.25 mm.

In contrast to the results discussed above for titanomagnetite, pyr-

rhotite, and glass-ceramic magnetite, one of Dunlop and Özdemir’s

(1997) data compilations for magnetite samples from several very dif-

ferent provenances yielded D / L

0.25

. The cause of the discrepancy

between this result and those obtained from other samples is not

understood.

Domain wall widths

When studied in the SEM, patterns of dried magnetic colloid afford

high-resolution views of domain walls—or, more precisely, the colloid

accumulations around walls. Moskowitz et al. (1988) applied this

method to polycrystalline pellets of synthetic titanomagnetite substi-

tuted with aluminum and magnesium (Fe

2.2

0.1

0.6

). Hence-

forth, this composition is referred to as “AMTM60.” Dried Bitter

patterns on unpolished surfaces were virtually identical in style to

those common to materials controlled by strong uniaxial anisotropy,

such as barium ferrite. Patterns indicated closely spaced stripe

domains, sinusoidally wavy walls, and elaborate wavy walls, which

alternated with nested arrays of reverse spikes. Direct measurements

from SEM photographs yielded wall widths between 0.170 and

0.400 mm.

In the same study, Moskowitz et al. (1988) also measured the wave-

lengths, amplitudes, and domain widths of the sinusoidally wavy

patterns. Using these parameters and the experimental value of sponta-

neous magnetization for AMTM60, they applied Szymczak’s (1968)

model to estimate the exchange constant and the uniaxial anisotropy

constant, the latter presumably due to residual stress generated, while

the pellet cooled from the sintering temperature.

Very high-resolution images of domains and domain walls have

been obtained with MFM on magnetite. The first images were reported

by Williams et al. (1992) from a {110} surface on a large crystal of

natural magnetite. They recorded a magnetic force profile across a

180



wall. This record indicated that the spins within the wall reversed

their polarity of rotation along the length of the wall, demonstrating

that walls in real materials can be much more complex than those

portrayed by simple models.

In a study of glass-ceramic magnetite particles with MFM, Pokhil

and Moskowitz (1996, 1997) found that, along its length, an individual

wall can be subdivided into several segments of opposite polarity. The

segments are separated by Bloch lines, the transition regions where

polarity changes sense. Rather than being linear, subdivided walls

zigzag across a grain. Analogous to wavy walls, the zigzags help to

reduce a grain’s total magnetostatic energy. The number of Bloch lines

within any specific wall was found to vary with repeated AF demagne-

tization treatments. Thus walls, like particles, can occupy LEM states.

Owing to its high-resolution capabilities, the MFM can provide esti-

mates of wall width. Proksch et al. (1994) obtained MFM profiles

across a 180



wall on a {110} surface of natural magnetite. The

deconvolved signal yielded a half-width, assumed to be commensurate

with wall width, of about 0.21 mm.

Experimental evidence for local energy minimum

domain states

In their study of Bitter patterns on natural pyrrhotite, Halgedahl and

Fuller (1983) noted that grains of virtually identical size could contain

very different numbers of domains, despite these same particles having

undergone the same magnetic treatments. Moreover, they found that an

individual particle could arrive in very different domain states—i.e.,

with different numbers of walls—after different cycles of minor

hysteresis. Clearly, such particles did not always occupy a domain

state of absolute minimum energy.

These observations led Halgedahl and Fuller (1983) to the conclu-

sion that a particle could occupy domain states other than the ground

state. Shortly thereafter, Moon and Merrill (1984, 1985) dubbed these

states as LEM states, on the basis on their one-dimensional micromag-

netic results for magnetite. Subsequent domain observation studies by

Geiß et al. (1996) provided strong evidence for LEM states in magne-

tite as well.

LEM states and thermom agnetic treatments: hysteresis

A particularly unexpected type of LEM state in pyrrhotite and inter-

mediate titanomagnetite is a SD-like state that certain particles can

occupy after being saturated in a strong external field, even though

these same particles readily accommodate walls in other states of mag-

netization. Bitter patterns on intermediate (x  0.6) titanomagnetite in

oceanic basalt and on natural pyrrhotite in diabase were studied during

hysteresis by Halgedahl and Fuller (1980, 1983). An electromagnet

was built around the microscope stage for these experiments, permit-

ting one to track the evolution of walls continuously, while varying

the applied field. In states of saturation remanence, most particles in

a large population contained one or more walls, as expected on the

basis of previous theories. However, a significant percentage—nearly

40%—of the finer (5–15 mm) particles observed appeared saturated

after the maximum field was shut off (Figure M19a and b). Within a

large population of such grains it was found that the number of

domains was described well by a Poisson distribution. Halgedahl and

Fuller (1980, 1983) proposed that grains, which failed to nucleate

walls, could make a substantial contribution to saturation remanence.

Furthermore, such grains might explain much of the known decrease

in the ratio of saturation remanent magnetization to saturation magne-

tization with increasing particle size. This hypothesis was extended to

the case of weak-field TRM.

Particles in SD-like states remained saturated, until nucleation was

accomplished by applying a back-field of sufficient magnitude. In

some cases, the nucleating field was strong enough to sweep a freshly

nucleated wall across the particle and thereby result in a state of satura-

tion (or near-saturation) in the opposite sense. In other cases, the new

wall moved until it was stopped by a pinning site. In the smaller grains

studied (e.g., smaller than 20 mm) the nucleation field dropped off with

increasing grain size L according to a power law in L

1/2

Boyd et al. (1984) reported Bitter patterns on natural magnetite

grains carrying saturation remanence, and these patterns suggested

SD-like states. These results were surprising, in view of magnetite’s

strong tendency to self-demagnetize.

Subsequent domain observations and hysteresis studies of hematite plate-

lets from Elba, Italy demonstrated that, after exposure to strong fields, even

large crystals could arrive in states suggesting near-saturation. Often,

however, small, residual domains clung to the platelet’s surface in these

states. Back-fields were necessary to nucleate principal domains, and

these nucleation fields also followed a power-law in L

1/2

(Halgedahl,

1995, 1998).

Results from titanomagnetite and pyrrhotite were interpreted by

Halgedahl and Fuller (1980, 1983) in light of previous theoretical

and experimental work on high-anisotropy, industrial materials synthe-

sized to produce magnetically hard, permanent magnets. In such mate-

rials, nucleation of walls is an energetically difficult process (Brown,

1963; Becker, 1969, 1971a,b, 1976). According to Brown’s original

theory, the nucleation of a fresh wall requires the following condition

to be fulfilled:

2K=M

< jH

appl

¼ H

Here, 2K/M

is the local anisotropy field at the nucleation site; H

the local demagnetizing field at the site, assumed to be opposite in

sense to M

; and H

appl

is the field applied to the sample. In samples

MAGNETIC DOMAINS 497

where back-fields are necessary to accomplish nucleation, H

appl

opposite to the sample’s original saturation magnetization. Wall

nucleation may occur either at crystal defects where 2K/M

is anoma-

lously low or where the local demagnetizing field H

is anomalously

high, as at shape defects on a crystal’s surface. Note that Brown’s the-

ory of nucleation differs from the kind of “global” nucleation resulting

from micromagnetic models. Brown-type nucleation may depend

on the presence of defects, which fulfill the above condition. By

contrast, micromagnetic models assume that particles are defect-free.

However, SD-like states also can result from submicroscopic walls

being trapped by surface and volume defects (Becker, 1969, 1971a,b,

1976). There are two cases. First, when a saturating field is shut off,

a submicroscopic, virgin wall can nucleate but remain pinned at a local

defect. In the second case, a strong applied field may be insufficient to

completely saturate a particle. When this occurs, preexisting domain

walls may be driven into surface or volume defects and become

trapped. In both cases, the particle appears to be saturated at the top

of a hysteresis loop. Experimentally, the saturation remanent state

appears to be SD-like. A back-field, opposite in sense to the maximum

field, is required to break free these residual walls and the submicro-

scopic domains which they enclose.

These two phenomena can be distinguished by observing both the

position where a reverse nucleus first appears in a grain and the field

required for its appearance. If complete saturation of a grain, followed

by nucleation of a fresh wall, has occurred, then the nucleus will

always appear at the same location and in the same back-field, regard-

less of the maximum field’s polarity. Of course, the submicroscopic

nucleus could have been trapped by a defect just after it was nucleated

initially. If the grain was not saturated completely, then both the loca-

tion where the nucleus appears and the field required to expand this

nucleus and make it visible depend on the direction in which a wall

was driven in the first place and on the back-field’s magnitude—

that is, on the specific trapping site (Becker, 1969, 1971a,b, 1976;

Halgedahl and Fuller, 1983).

The style of domain structure and the range of LEM states that a

particle can occupy can depend on thermomagnetic history. In a study

of Bitter patterns on natural, polycrystalline pyrrhotite, Halgedahl and

Fuller (1981) discovered that crystallites displayed arrays of undulat-

ing walls on their surfaces after acquiring TRM in a weak external

field. By contrast, after AF demagnetization in a strong peak field

the same crystallites exhibited planar walls. Evidently, cooling through

the TRM blocking temperature locked in a high-temperature config-

uration of walls, whose curved shapes promoted lower magnetostatic

energy than did a planar geometry.

As indicated by Moon and Merrill’s theoretical results for magne-

tite, a particular LEM state can be stable across a broad range of grain

size. This prediction is born out by experiments and calculations by

Halgedahl and Ye (2000) and Ye and Halgedahl (2000), who investi-

gated the effects of mechanical thinning on domain states in natural

pyrrhotite particles. In their experiments, several individual pyrrhotite

grains in a diabase were mechanically thinned and their Bitter patterns

observed after each thinning step. Despite some grains being thinned

to about one-fourth of their initial diameter, the widths of surviv-

ing domains and positions of surviving walls remained unaffected

(Figure M23). Neither nucleations nor denucleations were observed,

although calculations indicated that thinning would cause significant

changes in GEM domain states.

Bitter patterns on crystallites of polycrystalline AMTM60 were stu-

died after many replicate TRM acquisition and AF demagnetization

experiments (Halgedahl, 1991). In each particle, the number of

domains varied from one experiment to the next, describing a distri-

bution of TRM states. For states of weak-field TRM, this distribu-

tion could be broad and could include SD-like states (Figure M24).

After replicate AF demagnetizations, however, typical distributions

were narrow and clustered about a most probable state, possibly the

GEM state.

Thermal evolution of magnetic domain structures

observed at elevated temperatures

The manner in which domain structure evolves with temperature car-

ries clear implications for TRM. In very early models of TRM, such

changes were either ignored or were assumed not to occur. Instead,

some models assumed that the number of domains remained constant

from the Curie point to room temperature in a weak external field,

and that the blocking of TRM was controlled solely by the growth

of energy barriers associated with defects which, eventually, locked

walls in place.

Yet changes in the number of domains with temperature could pro-

foundly affect how pseudosingle-domain and multidomain particles

acquire TRM. Temperature-induced nucleations or denucleations of

walls should trigger sudden changes of the internal demagnetizing

field. As a result, preexisting walls, which survive a domain transition,

could be dislodged from imperfections where they were pinned initi-

ally at higher temperatures.

In rock magnetism, domain observation experiments to study the ther-

mal response of domain structure have focused on two magnetic miner-

als: (a) magnetite, owing to its great importance to the paleomagnetic

Figure M23 Bitter patterns on a grain of natural pyrrhotite in a

diabase before and after mechanical thinning. (a) Initial state,

before thinning, (b) after thinning the particle to about one-half of

its original length along a direction parallel to the trends of the Bitter

lines, and (c) final state, after the particle has been thinned to about

one-fourth of its original length.

498 MAGNETIC DOMAINS

signal carried by many rocks, and (b) intermediate titanomagnetite,

owing to its significance to marine magnetic anomalies and to its moder-

ately low-Curie temperature, which renders study of Bitter patterns fea-

sible at moderate temperatures. High-temperature experiments have

yielded highly variable results.

The first domain observations on magnetite above room temperature

in the Earth’s field were made by Heider et al. (1988), using particles

of hydrothermally recrystallized magnetite embedded in an epoxy

matrix. Depending on the particle, Bitter patterns could be followed

to approximately 200



C, above which temperature the patterns

grew too faint to distinguish against a grain’s bright background.

Surprisingly, heating to very moderate temperatures drove certain

walls across much of a particle; in some cases, denucleation occurred.

Upon cooling, walls reassembled in a similar, though not identical,

arrangement to that observed initially at room temperature. In some

cases repeated thermal cycling between room temperature and about

200



C produced different numbers of domains in the same particle.

Ambatiello et al. (1995) used the MOKE to study domain widths

versus temperature in several large (>5 mm) crystals of natural mag-

netite cut and polished on {110} planes. At room temperature, these

planes were dominated by broad (40–90 mm), lamellar domains sepa-

rated by 180



walls, terminating in closure domains at crystal edges.

On {111} planes they found complex, nested arrays of very small clo-

sure domains, which finely subdivided the main closure structure.

Unlike the Bitter technique, the MOKE is applicable to the Curie

point of magnetite (580



C), at least in theory. In practice, the amount

of Kerr rotation in magnetite is very small even at room temperature;

this rotation decreases progressively as M

drops with heating. As

the Curie point is approached, the contrast between adjacent domains

grows exceedingly faint. For this reason, Ambatiello and colleagues

successfully imaged domains to 555



C, but no higher.

According to their observations, domain widths generally increased

with heating, and such changes were thermally reversible. However,

the temperature that triggered changes depended on the provenance

of the sample. In some samples, domain widths remained nearly con-

stant until significant broadening of domains occurred above 400



In other samples, domains began to broaden at far lower temperatures.

To explain the overall character of their results, Ambatiello et al.

(1995) calculated the thermal dependence of domain widths on

the basis of the closed, “Landau-Lifshitz ”-type structure shown in

Figure M16c. Their calculations included the magnetoelastic energy

associated with closure domains, as well as the “m*” correction to

magnetostatic energy, originating from small deviations of spins away

from the easy axis near a crystal surface. There were several discrepan-

cies between experimental and model results. One mechanism which

they put forth to explain these discrepancies was that heating promoted

an even finer subdivision into small domains at the crystal surface.

This would cause a greater collapse of magnetostatic energy than pre-

dicted from their model and thus a more pronounced broadening of

body domains than expected.

Bitter patterns observed at elevated temperatures on natural, inter-

mediate titanomagnetites have been reported by Soffel (1977), Metcalf

and Fuller (1987a,b, 1988), and Halgedahl (1987). Because the mag-

netic force gradients around a wall weaken rapidly with heating, walls

attract increasingly less magnetic colloid as the Curie point is

approached. Consequently, these authors could follow patterns from

room temperature to about 10



to 20



below their samples’ Curie

points (Soffel, 1977: T

¼ 105



C; Metcalf and Fuller, 1987a,b,

1988, Halgedahl, 1987: T

approximately 150



C). During heating, pat-

terns gradually faded to obscurity, with few significant changes in

domain structure.

Remarkably, some titanomagnetite particles studied by Metcalf and

Fuller (1987a,b, 1988) displayed no Bitter lines after cooling from the

Curie point in the Earth’s field. This observation provided supporting

evidence for Halgedahl and Fuller’s (1983) proposal that weak-field

TRM acquired by populations of pseudosingle-domain grains could,

in part, be attributable to particles which failed to nucleate walls

during cooling.

The possible importance of LEM states to TRM acquisition was

raised by work on synthetic, polycrystalline AMTM60 (Halgedahl,

1991). Observations focused on grains that displayed simple “Kittel-

like” patterns suggesting lamellar domains (Figure M14). The sample

was cycled repeatedly between room temperature and the Curie point

of 75



C in the Earth’s field, although patterns lost definition near



C. Bitter patterns were observed continuously throughout heatings

and coolings.

As discussed above and shown in Figure M24, replicate TRM

experiments often produced different numbers of domains in the same

particle. Some of these domain states suggested that the particle was

entirely saturated, with no visible Bitter lines, or nearly saturated, with

only small spike domains at grain boundaries.

During heating, few changes in domain patterns were observed,

except for the usual fading as the Curie temperature was approached.

SD-like states were quite thermally stable, exhibiting no changes dur-

ing thermal cycling until the sample was heated nearly to, or above,

the Curie point. As a result of heating above a certain critical tempera-

ture, followed by cooling, a SD-like state could be transformed to a

LEM state with several domain walls.

Continuous observation of Bitter patterns on AMTM60 during cool-

ing revealed that denucleation was the mechanism by which a particle

arrived in a final LEM state. Walls which initially nucleated just below

grew visible after the sample cooled slightly through just a few

degrees. With further cooling, however, the number of domains often

Figure M24 Bitter patterns on a crystallite of titanomagnetite

(“AMTM60”: see text) after each of eight replicate TRM

acquisition runs in the Earth’s field.

MAGNETIC DOMAINS 499

decreased either through contraction of large, preexisting spike

domains, or by straight walls moving together and coalescing into

spikes. In both cases, the spikes often would collapse altogether.

Nucleations were never observed during cooling, once Bitter patterns

grew visible. In some cases, denucleation left behind large volumes

which, apparently, contained no walls, although walls were present

elsewhere in the grain. In other cases, denucleation left behind a

grain that appeared nearly saturated, but for small edge domains. In

both cases denucleation appeared to produce anomalously large

moments in particles that contained several walls after other TRM runs

(Halgedahl, 1991).

Results of the experiments described above on AMTM60 lend

further support to the hypothesis that particles in metastable SD states

can make significant contributions to stable TRM acquired in weak

fields. Furthermore, particles which do contain domain walls can carry

anomalously large TRM moments, if denucleation leaves behind large

volumes in which walls are absent.

These experimental results are at odds with theoretical results by

Dunlop et al. (1994) for LEM-LEM transitions in magnetite at high

temperatures. At present this disagreement has not been explained

fully. However, it is important to note that the model of Dunlop

et al. (1994) assumes that (1) such transitions are driven by thermal

fluctuations, and that (2) occupation frequencies of LEM states follow

Boltzmann statistics for thermal equilibrium, before domains are

blocked in. It is reasonable to expect that thermally activated jumps

among LEM states occur very rapidly and discontinuously during

times on the order of 1 s or less; rapid transitions such as these are

impossible to track under a microscope. By contrast, many of the

denucleations observed by Halgedahl (1991) occurred via continuous

wall motions easily tracked over laboratory time scales of several sec-

onds. It is questionable, therefore, whether the changes exhibited by

AMTM60 were driven by the thermal fluctuation mechanism modeled

by Dunlop et al. (1994). Perhaps the denucleations observed are not

stochastic processes. Additional analyses and experiments are needed

to determine the controlling mechanisms.

Observed temperature dependence of magnetic domain

structure: low temperatures

Magnetite undergoes two types of transitions at low temperatures,

which can profoundly affect domain structure and remanence (e.g.,

see detailed discussions in Stacey and Banerjee, 1974; Dunlop and

Özdemir, 1997). First, at the isotropic point (approximately 130 K)

the first magnetocrystalline anisotropy constant, K

, passes through

zero as it changes sign from negative at temperatures above the transi-

tion to positive below it. Second, at the Verwey transition, T

(approxi-

mately 120 K), magnetite undergoes a crystallographic transition from

cubic to monoclinic.

At the isotropic point domain walls should broaden dramatically,

because wall width is proportional to K

1/2

, K being the crystalline

anisotropy constant. It follows that, by cooling through the isotropic

point, walls may break free of narrow defects, which pinned them at

higher temperatures. At the Verwey transition the easy axis of magne-

tization changes direction. In multidomain and pseudosingle-domain

magnetite, this thermal passage should cause domain structure and

domain magnetizations to reorganize completely, so that much of an

initial remanence acquired at room temperature would be demagne-

tized by cooling below T

. Low-temperature demagnetization has

proved useful in removing certain spurious components of NRM,

which are surprisingly resistant to thermal demagnetization above

room temperature. Thus, it is important to determine how these transi-

tions affect domain structure.

Using an MFM specially adapted to operate at low temperature,

Moloni et al. (1996) were the first to image domains in magnetite at

temperatures near the two transitions. Their sample was a synthetic

magnetite crystal cut and polished on a {110} surface. At room

temperature, the crystal displayed 180



,71



, and 109



walls on

{110}, as expected for multidomain magnetite. At 77 K—that is,

below the Verwey transition—they observed both straight, 180



walls

separating broad, lamellar domains, and wavy walls accompanied by

reverse spikes. Both types of domain structure were consistent with a

uniaxial anisotropy arising from monoclinic crystal structure and for

which 2pM

/K < 1. They interpreted the broad, “body” domains as

being magnetized along <100> easy axes within {110} planes. The

wavy walls were interpreted to indicate domains with magnetizations

directed along an easy axis that lay out-of-plane. This mixture of

domain styles was thought to reflect lateral variations in the easy axis,

due to c-axis twinning below T

. As the crystal was warmed to a few

degrees below T

the domain structure disappeared entirely below the

instrument’s noise level, evidently undergoing a complete reorganiza-

tion near the crystallographic transition.

Ultrahigh-resolution imaging of micromagnetic

structures

Very recently, off-axis electron holography in the TEM has been used

to image magnetic microstructures in submicron magnetite intergrown

with ulvospinel (Harrison et al., 2002). This method enables one to

image the magnetization vectors within very small, single particles,

at a resolution approaching nanometers. Harrison et al. (2002) discov-

ered that clusters of magnetically interacting blocks of magnetite could

assume both vortex and multidomain-like states. This promising

method should prove highly fruitful in future experimental tests of

micromagnetic models.

Susan L. Halgedahl

Bibliography

Amar, H., 1858. Magnetization mechanism and domain structure of

multidomain particles. Physical Review, 111: 149–153.

Ambatiello, A., Fabian, K., and Hoffmann, V., 1999. Magnetic domain

structure of multidomain magnetite as a function of temperature:

observation by Kerr microscopy. Physics of the Earth and Plane-

tary Interiors, 112:55–80.

Appel, E., and Soffel, H.C., 1984. Model for the domain state of

Ti-rich titanomagnetites. Geophysical Research Letters, 11:

189–192.

Appel, E., and Soffel, H.C., 1985. Domain state of Ti-rich titanomag-

netites deduced from domain structure observations and suscept-

ibility measurements. Journal of Geophysics, 56: 121– 132.

Becker, J.J., 1969. Observations of magnetization reversal in cobalt-

rare-earth particles. IEEE Transactions on Magnetics, MAG-5:

211–214.

Becker, J.J., 1971a. Magnetization discontinuities in cobalt-rare-earth

particles. Journal of Applied Physics , 42: 1537–1538.

Becker, J.J., 1971b. Interpretation of hysteresis loops of cobalt-

rare-earths. IEEE Transactions on Magnetics, MAG-7: 644–647.

Becker, J.J., 1976. Reversal mechanism in copper-modified cobalt-

rare-earths. IEEE Transactions on Magnetics, MAG-12: 965–967.

Bogdanov, A.K., and Ya. Vlasov, A., 1965. Domain structure in a sin-

gle crystal of magnetite. (English trans.). Izvestiya Akademii Nauk,

SSSR, Earth Physics, series no. 1., 28–32.

Bogdanov, A.A., and Ya Vlasov, A., 1966. The domain structure of

magnetite particles. (English trans.), Izvestiya Akademii Nauk,

SSSR, Physics, Solid Earth, 9: 577–581.

Boyd, J.R., Fuller, M., and Halgedahl, S., 1984. Domain wall nuclea-

tion as a controlling factor in the behaviour of fine magnetic parti-

cles in rocks. Geophysical Research Letters, 11: 193–196.

Brown, W.F., 1963. Micromagnetics. New York: John Wiley, 143 pp.

Chikazumi, S., 1964. Physics of Magnetism. New York: John Wiley,

664 pp.

500 MAGNETIC DOMAINS

Cullity, B.D., 1972. Introduction to Magnetic Materials. Addison-

Wesley, Reading, MA, 666 pp.

Dunlop, D.J., and Özdemir, O., 1997. Rock Magnetism: Fundamentals

and Frontiers. Cambridge: Cambridge University Press, UK,

573 pp.

Dunlop, D.J., Newell, A.J., and Enkin, R.J., 1994. Transdomain ther-

moremanent magnetization. Journal of Geophysical Research, 99:

19,741–19,755.

Fabian, K., Kirchner, A.,Williams, W., Heider, F., and Leibl, T., Three-

dimensional micromagnetic calculations for magnetite using FFT.

Geophysical Journal International, 124:89–104.

Foss, S., Moskowitz, B., and Walsh, B., 1996. Localized micromag-

netic perturbation of domain walls in magnetite using a magnetic

force microscope. Applied Physics Letters, 69: 3426–3428.

Foss, S., Moskowitz, B.M., Proksch, R., and Dahlberg, E.D., Domain

wall structures in single-crystal magnetite investigated by magnetic

force microscopy. Journal of Geophysical Research, 103:

30,551–30,560.

Frandson, C., Stipp, S.L.S., McEnroe, S.A., Madsen, M.B., and Knud-

sen, J.M., 2004. Magnetic domain structures and stray fields of

individual elongated magnetite grains revealed by magnetic force

microscopy (MFM). Physics of the Earth and Planetary Interiors,

141: 121–129.

Fukuma, K., and Dunlop, D.J., Grain-size dependence of two-

dimensional micromagnetic structures for pseudo-single-domain

magnetite (0.2–2.5 mm). Geophysical Journal International, 134:

843–848.

Geiß, C.E., Heider, F., and Soffel, H.C., Magnetic domain observa-

tions on magnetite and titanomaghemite grains (0.5–10 mm). Geo-

physical Journal International, 124:75–88.

Halgedahl, S.L., 1987. Domain pattern observations in rock magnet-

ism: progress and problems. Physics of the Earth and Planetary

Interiors, 46: 127–163.

Halgedahl, S.L., 1991. Magnetic domain patterns observed on syn-

thetic Ti-rich titanomagnetite as a function of temperature and in

states of thermoremanent magnetization. Journal of Geophysical

Research, 96: 3943–3972.

Halgedahl, S.L., 1995. Bitter patterns versus hysteresis behavior in

small single particles of hematite. Journal of Geophysical

Research

, 100: 353–364.

Halgedahl, S.L., 1998. Barkhausen jumps in larger versus small plate-

lets of natural hematite. Journal of Geophysical Research, 103:

30,575–30,589.

Halgedahl, S., and Fuller, M., 1980. Magnetic domain observations of

nucleation processes in fine particles of intermediate titanomagne-

tite. Nature, 288:70–72.

Halgedahl, S.L., and Fuller, M., 1981. The dependence of

magnetic domain structure upon magnetization state in polycrystal-

line pyrrhotite. Physics of the Earth and Planetary Interiors, 26:

93–97.

Halgedahl, S., and Fuller, M., 1983. The dependence of magnetic

domain structure upon magnetization state with emphasis upon

nucleation as a mechanism for pseudo-single domain behavior.

Journal of Geophysical Research, 88: 6505–6522.

Halgedahl, S.L., and Ye, J., 2000. Observed effects of mechanical

grain-size reduction on the domain structure of pyrrhotite. Earth

and Planetary Science Letters, 176(3): 457–467.

Harrison, T.J., Dunin-Borkowski, R.E., and Putnis, A., 2002. Direct

imaging of nanoscale magnetic interactions in minerals. Proceed-

ings of the National Academic Sciences, 99: 16,556–16,561.

Heider, F., 1990. Temperature dependence of domain structure in nat-

ural magnetite and its significance for multi-domain TRM models.

Physics of the Earth and Planetary Interiors, 65:54–61.

Heider, F., and Hoffmann, V., 1992. Magneto-optical Kerr effect on

magnetite crystals with externally applied fields. Earth and Plane-

tary Science Letters, 108: 131–138.

Heider, F., Halgedahl, S.L., and Dunlop, D.J., 1988. Temperature

dependence of magnetic domains in magnetite crystals. Geophysi-

cal Research Letters, 15: 499–502.

Heisenberg, W., 1928. Zur Theorie des Ferromagnetismus. Zeitschrift

fuer Physik, 49: 619–636.

Hoffmann, V., Schafer, R., Appel, E., Hubert, A., and Soffel, H., 1987.

First domain observations with the magneto-optical Kerr effect on

Ti-ferrites in rocks and their synthetic equivalents. Journal of Mag-

netism and Magnetic Materials, 71:90–

94.

Kittel, C., 1949. Physical theory of ferromagnetic domains. Reviews of

Modern Physics, 21: 541–583.

Metcalf, M., and Fuller, M., 1987a. Magnetic remanence measure-

ments of single particles and the nature of domain patterns in tita-

nomagnetites. Geophysical Research Letters, 14: 1207–1210.

Metcalf, M., and Fuller, M., 1987b. Domain observations of titano-

magnetites during hysteresis at elevated temperatures and

thermal cycling. Physics of the Earth and Planetary Interiors, 46:

120–126.

Metcalf, M., and Fuller, M., 1988. A synthetic TRM induction curve

for fine particles generated from domain observations. Geophysical

Research Letters, 15: 503–506.

Moloni, K., Moskowitz, B.M., and Dahlberg, E.D., 1996. Domain

structures in single crystal magnetite below the Verwey transition

as observed with a low-temperature magnetic force microscope.

Geophysical Research Letters, 23: 2851–2854.

Moon, T., and Merrill, R.T., 1984. The magnetic moments of non-

uniformly magnetized grains. Physics of the Earth and Planetary

Interiors, 34: 186–194.

Moon, T.S., and Merrill, R.T., 1985. Nucleation theory and domain

states in multidomain magnetic material. Physics of the Earth

and Planetary Interiors, 37: 214–222.

Moskowitz, B.M., and Banerjee, S.K., 1979. Grain size limits for

pseudosingle domain behavior in magnetite: implications for paleo-

magnetism. IEEE Transactions on Magnetics , MAG-15:

1241–1246.

Moskowitz, B.M., and Halgedahl, S.L., Theoretical temperature and

grain-size dependence of domain state in x ¼ 0.6 titanomagnetite.

Journal of Geophysical Research, 92: 10,667–10,682.

Moskowitz, B.M., Halgedahl, S.L., and Lawson, C.A., 1988. Mag-

netic domains on unpolished and polished surfaces of titanium-

rich titanomagnetite. Journal of Geophysical Research, 93:

3372–3386.

Muxworthy, A.R., and Williams, W., Micromagnetic calculations of

hysteresis as a function of temperature in pseudo-single domain

magnetite. Geophysical Research Letters, 26: 1065–

1068.

Newell, A.J., Dunlop, D.J., and Williams, W., 1993. A two-dimen-

sional micromagnetic model of magnetization and fields in magne-

tite. Journal of Geophysical Research, 98: 9533–9549.

Özdemir, O., and Dunlop, D.J., 1993. Magnetic domain structures on a

natural single crystal of magnetite. Geophysical Research Letters,

20: 1835–1838.

Özdemir, O., and Dunlop, D.J., 1997. Effect of crystal defects and

internal stress on the domain structure and magnetic properties

of magnetite. Journal of Geophysical Research, 102: 20, 211–20,224.

Özdemir, O., Xu, S., and Dunlop, D.J., 1995. Closure domains in mag-

netite. Journal of Geophysical Research, 100: 2193–2209.

Pokhil, T.G., and Moskowitz, B.M., 1996. Magnetic force microscope

study of domain wall structures in magnetite. Journal of Applied

Physics, 79: 6064–6066.

Pokhil, T.G., and Moskowitz, B.M., 1997. Magnetic domains and

domain walls in pseudo-single-domain magnetite studied with

magnetic force microscopy. Journal of Geophysical Research,

102: 22,681–22,694.

Proksch, R.B., Foss, S., and Dahlberg, E.D., 1994. High resolution

magnetic force microscopy of domain wall fine structures. IEEE

Transactions on Magnetics, 30: 4467–4472.

MAGNETIC DOMAINS 501

Rhodes, P., and Rowlands, G., 1954. Demagnetizing energies of

uniformly magnetised rectangular blocks. Proceedings of the

Leeds Philosophical and Literary Society, Science Section, 6:

191–210.

Smith, P.P.K., 1980. The application of Lorentz electron microscopy

to the study of rock magnetism. Institute of Physics Conference

Series, 52: 125–128.

Soffel, H., 1971. The single-domain-multidomain transition in natural

intermediate titanomagnetites. Zeitschrift fuer Geophysik, 37:

451–470.

Soffel, H.C., 1977. Domain structure of titanomagnetites and its varia-

tion with temperature. Journal of Geomagnetism and Geoelectri-

city, 29: 277–284.

Soffel, H., 1977. Pseudo-single-domain effects and single-domain

multidomain transition in natural pyrrhotite deduced from domain

structure observations. Journal of Geophysics, 42: 351–359.

Soffel, H.C., Aumuller, C., Hoffmann, V., and Appel, E., 1990. Three-

dimensional domain observations of magnetite and titanomagne-

tites using the dried colloid SEM method. Physics of the Earth

and Planetary Interiors, 65:43–53.

Stacey, F.D., and Banerjee, S.K., 1974. The Physical Principles of

Rock Magnetism. Amsterdam: Elsevier, 195 pp.

Szymczak, R., 1968. The magnetic structure of ferromagnetic materi-

als of uniaxial structure. Electronics Technology, 1:5–43.

Weiss, P., 1907. L’hypothèse du champ moléculaire et la propriété fer-

romagnétique. Journal of Physique, 6: 661–690.

Williams, W., and Dunlop, D.J., 1989. Three-dimensional micromag-

netic modelling of ferromagnetic domain structure. Nature, 337:

634–637.

Williams, W., and Dunlop, D.J., 1990. Some effects of grain shape and

varying external magnetic fields on the magnetic structure of small

grains of magnetite. Physics of the Earth and Planetary Interiors,

65:1–14.

Williams, W., and Dunlop, D.J., 1995. Simulation of magnetic hyster-

esis in pseudo-single-domain grains of magnetite. Journal of Geo-

physical Research, 100

: 3859–3871.

Williams, W., and Wright, T.M., 1998. High-resolution micromagnetic

models of fine grains of magnetite. Journal of Geophysical

Research, 103: 30,537–30,550.

Williams, W., Hoffmann, V., Heider, F., Goddenhenreich, T., and

Heiden, C., 1992. Magnetic force microscopy imaging of domain

walls in magnetite. Geophysical Journal International, 111:

417–423.

Worm, H.-U., and Markert, H., 1987. The preparation of dispersed tita-

nomagnetite particles by the glass-ceramic method. Physics of the

Earth and Planetary Interiors, 46: 263–270.

Worm, H.-U., Ryan, P.J., and Banerjee, S.K., 1991. Domain size, clo-

sure domains, and the importance of magnetostriction in magnetite.

Earth and Planetary Science Letters, 102:71–78.

Xu, S., Dunlop, D.J., and Newell, A.J., 1994. Micromagnetic model-

ling of two-dimensional domain structures in magnetite. Journal

of Geophysical Research, 99: 9035–9044.

Ye, J., and Halgedahl, S.L., 2000. Theoretical effects of mechanical

grain-size reduction on GEM domain states in pyrrhotite. Earth

and Planetary Science Letters, 178:73–85.

Ye, J., and Merrill, R.T., 1995. The use of renormalization group the-

ory to explain the large variation of domain states observed in tita-

nomagnetites and implications for paleomagnetism. Journal of

Geophysical Research, 100: 17,899–17,907.

Cross-references

Magnetic Properties, Low-Temperature

Magnetization, Isothermal Remanent (IRM)

Magnetization, Thermal Remanent (TRM)

Paleomagnetism

MAGNETIC FIELD OF MARS

Introduction

Strong magnetic anomalies have been detected over the south hemi-

sphere of Mars. The Mars missions prior to Mars Global Surveyor

(MGS) detected no appreciable magnetic field around the planet,

which led to the conclusion that the Martian core field is weaker than

Earth’s by more than an order of magnitude. However, orbiting at ele-

vations as low as 100–200 km during the science phase and aerobreak-

ing phase, MGS detected a very strong crustal magnetic field, as

strong as 200 nT, over the ancient southern highlands (Acuna et al.,

1999), indicating that the Martian crust is more magnetic than Earth’s

by more than an order of magnitude.

There is evidence from the Martian meteorites that a magnetic field

as strong as 3000 nT has existed on the surface of Mars. The oldest

Martian meteorite (ALH84001) formed before 4 Ga (e.g., Collinson,

1997; Kirschvink et al., 1997; Weiss, et al., 2002; Antretter et al.,

2003) and the young Martian meteorites that have crystallization ages

ranging from 0.16 to 1.3 Ga (Nyquist et al., 2001) are magnetized in a

weak field of less than 3000 nT (e.g., Cisowski, 1986; Collinson,

1997; McSween and Treiman, 1998). Whether the meteorites were

magnetized by a weak core field or by the local crustal field is still

debated. There is good evidence that the strong anomalies of the crust

have existed for the last 4 Ga (Arkani-Hamed, 2004a).

The magnetometer on board of MGS has provided immense amount

of magnetic data since it resumed its mapping phase when its highly

elliptical orbit was reduced to an almost circular polar orbit at a mean ele-

vation of 400 km. Besides the magnetometer, MGS carried an electron

reflectometer, which has also indirectly provided data on the magnetic

field of Mars (e.g., Mitchell et al., 2001). This article is concerned with

the magnetometer data. The first section presents a spherical harmonic

model of the magnetic field of Mars that is derived from the mapping-

phase magnetic data. The second section is concerned with the first-

order interpretation of the anomalies. The final section summarizes the

major points of the article.

The spheri cal harmonic model of the magnetic field

The first magnetic anomaly map of Mars was derived by Acuna et al.

(1999) from the low-altitude MGS data acquired at 100–200 km eleva-

tions during the science phase and aerobreaking phase. It was presented

without altitude corrections. Subsequently, Purucker et al. (2000) reduced

the radial component anomalies to a constant elevation of 200 km, and

Arkani-Hamed (2001a) derived a 50



spherical harmonic model of the

magnetic potential at 120 km altitude using all three vector components

of the magnetic field. The later magnetic field models of Mars by

Arkani-Hamed (2002), Cain et al. (2003), and Langlais et al. (2004) were

obtained using all three components of the magnetic field acquired at the

low- and high-altitude phases.

A highly repeatable and reliable magnetic anomaly map of Mars is

essential for the investigation of the relationship between the tectonic

features and the magnetization of the Martian crust. MGS has pro-

vided a huge amount of high-altitude magnetic data acquired within

360–420 km altitudes. Although the high altitude of the spacecraft

limits the resolution of the data (e.g., Connerney et al., 2001; Arkani-

Hamed, 2002), the huge amount of the data provides an opportunity to

derive a highly repeatable and accurate magnetic anomaly map at that

altitude. For this purpose Arkani-Hamed (2004b) used the nighttime

radial component of the high-altitude data, which is least contaminated

by noncrustal sources, and selected the most common features on the

basis of covariance analysis. The vast amount of the data allowed him

to divide the entire data into two almost equal sets, acquired during

two different periods separated by more than a year, and to derive two

separate spherical harmonics models of the magnetic field. The spherical

harmonic model of the radial component of the magnetic field R is

expressed as

502 MAGNETIC FIELD OF MARS

Rð r ; q ; j Þ¼

n ¼1

ð n þ 1 Þða =r Þ

n þ2

m¼ 0

ð C

cos mj þ S

sin mj Þ P

ðcos y Þ

where a is the mean radius of Mars (3393 km); r, y , and j are distance

from the center, colatitude, and east longitude (the coordinate system

is centered at the center of mass of Mars); P

ðcos y Þ is the Schmidt-

normalized associated Legendre function of degree n and order m;

and S

are the Gauss coefficients; and N denotes the highest

degree harmonics retained in the model. The covariance analysis of

the two models showed that the covarying coefficients of the models

are almost identical over harmonics of degree up to 50, with correla-

tion coefficients greater than 0.95. These harmonics are highly repea-

table and hence reliable. Figure M25/Plate 13a shows the radial

component of the magnetic field of Mars at 100 km altitude, derived

by averaging the covarying harmonic coefficients of the two models

up to degree 50 and downward continuing from 400 to 100 km alti-

tude. The color bar is saturated to better illustrate the weak anomalies.

Interpretation of the magnetic anomalies

Figure M25/Plate 13a shows strong magnetic anomalies arising from

the remanent magnetization of the crust. This section provides first-

order interpretation of the anomalies.

The magnetic anomalies in the northern lowlands are very weak

compared to those in the south. Many buried impact craters in the low-

lands suggest similar ages for the crust in the north and south (Frey

et al., 2001). There is no striking evidence that the composition of

the Martian crust had a distinct north-south dichotomy before the

formation of the lowlands that would have prevented the formation

of strong magnetic bodies in the north. The weak anomalies in the

lowlands are most likely the relicts of stronger ones that existed before

the formation of the lowlands. Zuber et al. (2000) disputed the impact

origin of the lowlands and suggested crustal thinning due to a giant

mantle plume. According to this hypothesis, the magnetic source

bodies must have been partially demagnetized by the thermal effects

of the plume, and to a lesser extent by near-surface low-temperature

hydration (e.g., Arkani-Hamed, 2004a).

Figure M25/Plate 13a shows that the giant impact basins Hellas

(41



S, 70



E), Argyre (50



S, 316



E), and Isidis (13



N, 88



E) are

almost devoid of magnetic anomalies. These basins were formed by

large impacts 4 Ga, which resulted in strong shock pressures and

high temperatures, capable of demagnetizing the crust beneath

the basins (Hood et al., 2003; Mohit and Arkani-Hamed, 2004;

Kletetschka et al., 2004). The crust beneath these basins is completely

demagnetized to a distance of 0.8 basin radius, where the shock pres-

sure exceeded 3 GPa, and partially demagnetized to 1.4 radius

where the pressure exceeded 2 GPa. This observation together with

the fact that many intermediate-size impacts that created craters of

200–500 km diameter have little demagnetization effect led Mohit

and Arkani-Hamed (2004) to suggest that the magnetic carriers of

Martian crust have high coercivity. The resulting demagnetization

depends on the coercivity of the magnetic minerals, magnetite, hema-

tite, and pyrrhotite, suggested for the Martian crust (e.g., Kletetschka

et al., 2000, 2004; Hargraves et al., 2001). Cisowski and Fuller

(1978) found that remanence with a coercivity of 70 mT was 20%

demagnetized after a shock of 1 GPa and 70% after a shock of

4 GPa. Under a shock of 1 GPa, the remanence of the multidomain

hematite and magnetite are reduced by 20% and 68%, respectively

(Kletetschka et al., 2002, 2004). Shock experiments on high coercivity

(300 mT) single-domain pyrrhotite samples showed that a shock of

1 GPa removed 50% of the magnetization at room temperature, and

they were completely demagnetized by shocks exceeding 2.75 GPa,

undergoing a transition to a paramagnetic phase (Rochette et al.,

2003). The high-pressure magnetic measurements in a diamond anvil

cell showed that magnetite behaved as single domain with high coerciv-

ity at high pressures (Gilder et al., 2002). The survival of the magnetic

anomalies beneath intermediate-size craters can be partly due to the

increase of the coercivity of already high-coercive magnetic carriers of

the Martian crust during the passage of the shock wave.

The magnetic anomalies over Tharsis bulge are much weaker than

those in the south. The bulge formed through major volcanic activities

in Noachian and Early Hesperian, although minor volcanism likely

continued to the recent past (e.g., Hartmann and Neukum, 2001).

Figure M25/Plate 13a The radial component magnetic map of Mars at 100 km altitude derived from the high-altitude MGS data using

the spherical harmonic of degree up to 50. The color bar is saturated to better illustrate the weak anomalies. Units are in nanotesla.

MAGNETIC FIELD OF MARS 503

There are many lines of evidence that the volcanic layers of Tharsis are

not significantly magnetized, they are formed either in the absenc e of a

core dynamo or in the waning period of the dynamo (Arkani-Hamed,

2004b). Many places of Tharsis have been punctured by tectonic

processes, which could have created detectable magnetic anomalies

if the Tharsis plains were appreciably magnetized. Here two major

features, Valles Marineris and shield volcanoes, are discussed in

some detail.

Figure M25/Plate 13a shows no distinct magnetic edge effects asso-

ciated with Valles Marineris, a canyon of over 5 km mean depth, 100–

400 km width, and 3500 km length. The models proposed for the

formation of this giant canyon (e.g., Schultz, 1997; Tanaka, 1997;

Wilkins and Schultz, 2003) indicate a vast amount of mass wasting.

Many of the proposed models imply that upper strata of the canyon

floor are porous. The porous floor and possible long-existing water make

the rocks more susceptible to demagnetization by low-temperature

hydration. The magnetization of mid-ocean ridge basalt on Earth

declines from  20 to 5Am

–1

in the first 30 Ma, likely a result of

low-temperature hydration by circulating pore water (e.g., Bliel and

Petersen, 1983). Also a positive Bouguer anomaly of 150 mGal is

associated with the central part of the canyon, implying crustal thinning

and mantle uplift of  15 km. If the Tharsis crust were strongly magne-

tized before the formation of the canyon, it is to be expected that the crust

in the canyon would be partly demagnetized, giving rise to detectable

magnetic edge effects. The absence of the expected edge effects indi-

cates that the preexisting Tharsis plains were not significantly magne-

tized. Figure M25/Plate 13a shows that the formation of the canyon

has ruptured the magnetic anomalies in the eastern part of the canyon

between 290



E and 320



E. The anomalies must have existed before

the formation of Valles Marineris that occurred during Late Noachian

to Early Hesperian (e.g., Anderson et al., 2001). Figure M25/Plate 13a

also shows no magnetic signature associated with the shield volcanoes

Olympus, Arsia, Pavonis, and Ascreaus, suggesting that the underlying

preexisting Tharsis plains had not been appreciably magnetized. Other-

wise, the thermal effects of the shield volcanoes could have demagne-

tized part of them and created low-magnetic patches in the magnetized

plains, giving rise to detecta ble magnetic anomalies.

There was no active core dynamo during the formation of the shield

volcanoes, from Early Hesperian to Late Amazonian. Hood and Hartde-

gen (1997) estimated the magnetic anomaly that would have been pro-

duced by the entire volcanic structure if were magnetized by a core field

an order of magnitude weaker than the Earth ’ s core field. The lack of

such a magnetic anomaly indicates that no core dynamo existed during

the formation of shield volcanoes to magnetize the volcanic flows.

Many lines of evidence suggest that the core dynamo decayed dur-

ing Early Noachian. The lack of magnetic anomalies associated with

giant impact basins, the absence of magnetic edge effect of Valles

Marineris, and the fact that the huge amount of volcanic flows of Syria

Planum, occurred from Noachian to Early Amazonian (e.g., Anderson

et al., 2001) and those of Olympus and Tharsis mounts, occurred from

Early Hesperian to Late Amazonian, show no magnetic signatures

strongly argue against an active core dynamo since Early Noachian

(Arkani-Hamed, 2004b).

Attempts have been made to estimate the paleomagnetic pole posi-

tion of Mars. Arkani-Hamed (2001b) modeled 10 widely distributed

relatively isolated small magnetic anomalies. Assuming that the source

bodies were magnetized by a dipol e core field, he found that most of the

pole positions were clustered within a 30



circle centered at 25



230



E. Moreover, both north and south magnetic poles were found

in the cluster, suggest ing reversal of the core field polarity. Using the

two weak magnetic anomalies near the geographic north pole, Hood

and Zacha rian (2001) found paleomagnetic poles in general agreement

with Arkani-Hamed (2001b). Arkani-Hamed and Boutin (2004) used

magnetic profiles from the low- and high-altitude data to model

nine anomalies. The magnetic pole positions determined from their

models showed clustering of the poles at the same general region, but

not as tightly as those of Arkani-Hamed (2001b).

The magnetic field of Mars provides information about the rota-

tional dynamics of the planet. None of the paleomagnetic poles are

close to the present rotation pole. If the axis of dipole core field were

close to the axis of rotation at the time the magnetic sources acquired

magnetization, which is the case for the terrestrial planets at present,

the paleomagnetic pole positions suggest appreciable, 20



–60



, polar

wander since the magnetic bodies were magnetized. Polar wander of



to 120



were proposed on the basis of geological features (Murray

and Malin, 1973; Schultz and Lutz-Garihan, 1982; Schultz and Lutz-

Garihan, 1988). Approximating the topographic mass of Tharsis bulge

by a surface mass, Melosh (1980) predicted polar wander of up to 25



from the effects of the bulge on the moment of inertia of the planet .

Willeman (1984) suggested that compensation of Tharsis bulge would

limit the amount of polar wander to less than 10



. The theoretical

studies of polar wander by Spada et al. (1996) showed that Mars could

have undergone polar wander by as much as 70



, in response to

surface loads such as Olympus and Tharsis mounts.

Summary

Figure M25/Plate 13a presents the most recent and highly accurate

spherical harmonic model of the radial component of the magnetic

field of Mars derived from the high-altitude mapping-phase magnetic

data from MGS, using harmonics of degree up to 50. It shows that

the northern lowland formation and the large impacts that created the

giant basins Hellas, Isidis, and Argyre have significantly demagnetized

the crust and there was no active core dynamo to remagnetize the

crust. The absence of magnetic edge effects associated with Valles

Marineris, and the lack of magnetic signatures of the large shield vol-

canoes Olympus and Tharsis mounts imply that core dynamo did not

exist from Late Noachian to Late Amazonian, and likely to the present.

The fact that intermediate-size craters, with diameters 200–500 km,

show no sign of demagnetization of the underlying crust indicates that

the magnetic carriers of the Martian crust have high coercivity. The

clustering of the paleomagnetic poles far from the present rotation axis

implies polar wander of Mars by about 20



–50



since the magnetic

source bodies were magnetized. Finally, the presence of both north

and south paleomagnetic poles in the cluster suggests that the core

field of Mars had polarity reversals.

Acknowledgment

This research was supported by the Natural Sciences and Engineering

Research Council (NSERC) of Canada.

Jafar Arkani-Hamed

Bibliography

Acuna, M.H. et al., 1999. Global distribution of crustal magnetization

discovered by the Mars Global Surveyor MAG/ER experiment.

Science, 284: 790–793.

Anderson, R.C. et al., Primary centers and secondary concentrations of

tectonic activity through time in the western hemisphere of Mars.

Journal of Geophysical Research, 106 : 20,563–20,585.

Antretter, M., Fuller, M., Scott, E., Jackson, M., Moskowitz, B., and

Soleid, P., 2003. Paleomagnetic record of Martian meteorite

ALH84001. Journal of Geophysical Research, 108(E6): 5049,

doi:10, 1029/2002JE001979.

Arkani-Hamed J., 2001a. A 50 degree spherical harmonic model of the

magnetic field of Mars. Journal of Geophysical Research, 106:

23,197–23,208.

Arkani-Hamed, J., 2001b. Paleomagnetic pole positions and poles

reversals of Mars. Geophysical Research Letters, 28: 3409–3412.

Arkani-Hamed, J., 2002. An improved 50-degree spherical harmonic

model of the magnetic field of Mars, derived from both high-

altitude and low-altitude observations. Journal of Geophysical

Research, 107: 10.1029/2001JE001835.

504 MAGNETIC FIELD OF MARS

Arkani-Hamed, J., 2004a. Timing of the Martian core dynamo. Jour-

nal of Geophysical Research, 109(E3): E03006, doi:10.1029/

2003JE002195.

Arkani-Hamed J., 2004b. A coherent model of the crustal magnetic

field of Mars. Journal Of Geophysical Research, 109: E09005,

doi:10.1029/2004JE002265.

Arkani-Hamed, J., and Boutin, D., 2004. Paleomagnetic poles of Mars:

Revisited. Journal of Geophysical Research, 109: doi:10.1029/

2003JE0029.

Bliel, U., and Petersen, N., 1983. Variations in magnetization intensity

and low-temperature titano-magnetite oxidation of ocean floor

basalts. Nature, 301: 384–388.

Cain, J.C., Ferguson, B., and Mozzoni, D., 2003. An n ¼ 90 model of

the Martian magnetic field. Journal of Geophysical Research, 108:

10.1029/2000JE001487.

Cisowski, S.M., 1986. Magnetic studies on Shergotty and other SNC

meteorites. Geochemica Cosmochemica Acta, 50: 1043–1048.

Cisowski, S., and Fuller, M., 1978. The effect of shock on the magnet-

ism of terrestrial rocks. Journal of Geophysical Research, 83:

3441–3458.

Collinson, D.W., 1997. Magnetic properties of Martian meteorites:

implications for an ancient Martian magnetic field. Planetary

Science, 32: 803–811.

Connerney, J.E.P., Acuna, M.H., Wasilewski, P.J., Kletetschka, G.,

Ness, N.F., Remes, H., Lin, R.P., and Mitchell, D.L., 2001. The

global magnetic field of Mars and implications for crustal evolu-

tion. Geophysical Research Letters, 28 : 4015 –4018.

Frey, H., Shockey, K.M., Frey, E.L., Roark, J. H., and Sakimoto, S.E.H.,

2001. A very large population of likely buried impact basins in the

northern lowlands of Mars revealed by MOLA data. Lunar and Pla-

netary Science Conference XXXII, Abstr. 1680.

Gilder, S.A., Le Goff, M., Peyronneau, J., and Chervin, J., 2002.

Novel high pressure magnetic measurements with application

to magnetite. Geophysical Research Letters, 29: 10,1029/

2001GL014227, 2002.

Hargraves, R.B., Knudsen, J.M., Madsen, M.B., and Bertelsen, P.,

2001. Finding the right rocks on Mars. EOS: Transactions, Amer-

ican Geophysical Union, 82: 292–293.

Hartmann, W.K., and. Neukum, G., 2001. Cratering chronology and

the evolution of Mars.

Space Science Reviews, 96: 165–194.

Hood, L.L., and Hartdegen, K., 1997. A crustal magnetization model

for the magnetic field of Mars: a preliminary study of the Tharsis

region. Geophysical Research Letters, 24: 727–730.

Hood, L.L., and Zacharian, A., 2001. Mapping and modeling of mag-

netic anomalies in the northern polar region of Mars. Journal of

Geophysical Research, 106: 14601–14619.

Hood, L.L., Richmond, N.C., Pierazzo, E., and Rochette, P., Distribu-

tion of crustal magnetic fields on Mars: Shock effects of basin-

forming impacts. Geophysical Research Letters, 30(6): 1281,

doi:10.1029/2002GL016657.

Kletetschka, G., Wasilewski, P.J., and Taylor, P.T., 2000. Mineralogy

of the sources for magnetic anomalies on Mars. Meteoritics and

Planetary Science, 35: 895–899.

Kletetschka, G., Wasilewski, P.J., and Taylor, P.T., 2002. The role of

hematite-ilmenite solid solution in the production of magnetic

anomalies in ground- and satellite-based data. Tectonophysics,

347: 167–177.

Kletetschka, G., Connerney, J.E.P., Ness, N.F., and Acuna, M.H.,

2004. Pressure effects on Martian crustal magnetization near

large impact basins. Meteoritics and Planetary Science, 39:

1839–1848.

Kirschvink, J.L., Maine, A.T., and Vali, H., 1997. Paleomagnetic evi-

dence of a low-temperature origin of carbonate in the Martian

meteorite ALH84001. Science, 275: 1629–1633.

Langlais, B., Purucker, M.E., and Mandea, M., 2004. Crustal magnetic

field of Mars. Journal of Geophysical Research, 109: E002008,

doi:10.1029/2003JE002048.

McSween, H.Y., and Treiman, A.H., 1998. Martian meteorites, Chap-

ter 6 in Planetary materials. Reviews in Mineralogy, 36: 53.

Melosh, H.J., 1980. Tectonic patterns on a reoriented planet: Mars.

Icarus, 44: 745–751.

Mitchell, D.L. et al., 2001. Probing Mars’ crustal magnetic field and

ionosphere with the MGS electron reflectometer. Journal of Geo-

physical Research, 106: 23,419–23,427.

Mohit, P.S., and Arkani-Hamed, J., 2004. Impact demagnetization of

the Martian crust. Icarus, 168: 305–317.

Murray, B.C., and Malin, M.C., 1973. Polar wandering on Mars.

Science, 179: 997–1000.

Nyquist, L.E. 2001. Ages and geological history of Martian meteor-

ites. In Kallenbach, R., Geiss, J., and Hartmann, W.K. (eds.),

Chronology and Evolution of Mars. Dordrecht, the Netherlands:

Kluwer Academic Publishers.

Purucker, M., Ravat, D., Frey, H., Voorhies, C., Sabaka, T., and

Acuna, M., 2000. An altitude-normalized magnetic map of Mars

and its interpretation. Geophysical Research Letters, 27:2449–2452.

Rochette, P., Fillion, G., Ballou, R., Brunet, F., Ouladdiaf, B., and

Hood, L., 2003. High pressure magnetic transition in pyrrhotite and

impact demagnetization on Mars. Geophysical Research Letters,

30(13): 1683, doi:10.1029/2003GL017359.

Schultz, P.H., and Lutz-Garihan, A.B., 1982. Grazing impacts on

Mars: a record of lost satellites. Journal Geophysical Research,

87: A84–A96.

Schultz, P.H., and Lutz-Garihan, A.B., 1988. Polar wandering of Mars.

Icarus, 73:91–141.

Schultz, R.A., 1997. Dual-process genesis for Valles Marineris and

troughs on Mars, presented at the XXVIII Lunar and Planetary

Science Conference, Houston, Texas.

Spada, G. 1996. Long-term rotation and mantle dynamics of the

Earth, Mars and Venus. Journal of Geophysical Research, 101:

2253–2266.

Tanaka, K.L., 1997. Origin of Valles Marineris and Noctis Labyr-

inthus, Mars, by structurally controlled collapses and erosion of

crustal materials, presented at the XXXVIII Lunar and Planetary

Science Conference, Houston, Texas.

Weiss, B.P., Vali, H., Baudenbacher, F.J., Kirschvink, J.L., Stewart,

S.T., and Schuster, D.L., 2002. Records of an ancient Martian field

in ALH84001. Earth and Planetary Science Letters, 201: 449–463.

Wilkins, S.J., and Schultz, R.A., 2003. Cross faults in extensional set-

tings: stress triggering, displacement localization, and implications

for the origin of blunt troughs at Valles Marineris, Mars. Journal of

Geophysical Research, 108: E6, 5056, doi:1029/2002JE001968.

Willeman, R.J., 1984. Reorientation of planets with elastic litho-

spheres. Icarus, 60: 701–709.

Zuber, M.T. 2000. Internal structure and early thermal evolution of

Mars from Mars Global Surveyor topography and gravity. Science,

287: 1788–1793.

MAGNETIC FIELD OF SUN

The Sun has been observed to exhibit a breathtaking variety of mag-

netic phenomena on a vast range of spatial and temporal scales. These

vary in spatial scale from the solar radius down to the limit of present

resolution of the most powerful satellite instrumentation, and with

durations varying from minutes to hundreds of years, encompassing

the famous 11-year sunspot cycle. This dynamic and active field,

which is visible in extreme ultraviolet wavelengths as shown in Figure

M26/Plate 14a, is responsible for all solar magnetic phenomena, such

as sunspots, solar flares, coronal mass ejections and the solar wind,

and also heats the solar corona to extremely high temperatures. These

have important terrestrial consequences, causing severe magnetic storms

and major disruption to satellites, as well as having a possible impact on

MAGNETIC FIELD OF SUN 505