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

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Recently, Roberts and Weaver (2005) described multiple mechanisms

for CRM involving sedimentary greigite. The resolution of paleomag-

netic time series would be compromised in sediments where CRM

occurs in authigenic magnetic minerals, formed below the remanence

lock-in depths. In light of this analysis t, it is possible that sediments

discussed earlier in this section experienced multiple episodes of

CRM. The first might arise from diagenesis of magnetite and other

iron oxides to iron sulfides during initial burial. A later CRM

might be produced in magnetite due to diagenesis of iron sulfides or,

possibly, in hematite due to dedolomitization in an oxidizing envir-

onment, depending on the sediment composition and prevailing

geochemistry.

Concluding Remarks

This report on CRM is not exhaustive and reflects the interests, biases

and limitations of the author. It is an update of a similar article written

over fifteen years ago (Levi, 1989). In the future, as paleomagnetists

address more difficult tectonic and geomagnetic questions, requiring

data from structurally more complex, metamorphosed, and older for-

mations, it will be increasingly likely that CRM will contribute to the

NRM. Paleomagnetists have become more adept at isolating different

remanence components, using detailed and varied demagnetization pro-

cedures. It is usually assumed that the most resistant remanence,

whether with respect to increasing temperatures, alternating fields, or

a particular leaching agent is also the primary component. However,

CRM stabilities are highly variable, and this assumption is unlikely to

be satisfied universally. During the past fifteen years, there has been pro-

gress in understanding several aspects of CRM, including (a) the recog-

nition that even for some very young subaerial lavas the NRM may

comprise a low-temperature CRM component, and (b) that in some

active sedimentary environments, diagenesis leads to CRM in ferrimag-

netic iron sulfides. A more comprehensive understanding of CRM is

needed to assist paleomagnetists to interpret complex, often multicom-

ponent, NRMs with probable CRM overprints. This goal would be

advanced by conducting controlled field and laboratory CRM experi-

ments to (1) recognize the varied geochemical environments that

produce different magnetic minerals and their associated CRMs;

(2) determine the ranges of magnetic and mineralogical stabilities

with respect to different demagnetization procedures and for isolating

different CRM components; and (3) develop procedures for identifying

the timing and sequencing of multi-component CRMs.

Shaul Levi

Figure M109 Downcore profiles of magnetic intensitie s and solid sulfur for Kasten core W7710-28, Oregon continental slope. The

magnetization intensities were partially AF demagnetized at 15 mT. Solid sulfur concentrations of total (circles) and acid-insoluble

(triangles) fractions on a sulfate-free basis, measured by X-ray fluorescence (modified from Karlin and Levi, 1983).

Figure M110 Downcore profiles of the NRM intensity, partially

AF demagnetized at 20 mT, and the saturation magnetization for

core TT11 from NE Pacific Ocean (modified from Karlin, 1990).

586 MAGNETIZATION, CHEMICAL REMANENT (CRM)

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MAGNETIZATION, CHEMICAL REMANENT (CRM) 587

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MAGNETIZATION, DEPOSITIONAL REMANENT

The magnetization acquisition processes in unconsolidated sediments

have been long studied (e.g., Johnson et al., 1948; King, 1955; Granar,

1958). The early studies showed that magnetic minerals in the sedi-

ments align along the ambient magnetic field during deposition

through the water column. The magnetization resulting from the sedi-

mentation process has been referred as depositional or detrital rema-

nent magnetization (DRM). The magnetization acquisition process is

still not well understood, and the role of the complex interplay of

processes occurring during deposition, water-sediment interface pro-

cesses, burial, and compaction, etc., require further analyses. The

characteristics and stability of the remanent magnetization of unconso-

lidated sediments are determined by the composition, grain size, and

shape of individual grains. During deposition in aqueous media, the

magnetic particles are subject to the aligning force of the ambient

magnetic field, plus the gravitational and dynamic forces. In tranquil

conditions alignment of magnetic grains is relatively effective in

depositional timescales, which are affected by Brownian forces.

Nagata (1961) showed that equilibrium with the ambient magnetic

field is attained in a scale of 1 s. Therefore, saturation magnetization

should be expected in natural depositional systems, with the DRM

intensity independent of the ambient magnetic field intensity. How-

ever, this is not the case, and the magnetization intensity is related to

the intensity of the ambient magnetic field (Johnson et al., 1948).

The DRM intensities lower than saturation values have been related

to misalignment effects of Brownian motion of submicron ferrimag-

netic grains (Collinson, 1965; Stacey, 1972). Near the water-sediment

interface, flow conditions may become relatively stable and simple by

having laminar flow (Granar, 1958) but still the deposition process is

complex. The interplay and characteristics of the bottom sediments

result in a variety of fabrics in the deposited sediments.

In general, reorientation of magnetic minerals occurring after deposition

and before consolidation of the sediment is referred as postdepositional

DRM. Perhaps, the most notable distinction between depositional DRM

and postdepositional DRM is the occurre nce of the so-called inclination

error present in depositional DRM (Johnson et al., 1948; King, 1955;

Granar, 1958). If I

is the inclination of the ambient Earth’s mag-

netic field at the time of sediment deposition, then the inclination

of magnetization I

can be expressed in terms of

¼ arctanðf tan I

where f is a factor that is determined experimentally. The inclination

error has been ascribed to deposition of elongated grains with along-

axis magnetizations tending to lie parallel to the sediment interface

and deflecting the magnetization toward the horizontal plane. Labora-

tory experiments have been conducted to evaluate effects of the inten-

sity of the ambient magnetic field, size and shapes of the magnetic

grains, deposition on horizontal, inclined, and irregular surfaces, bottom

currents, etc. (e.g., Johnson et al., 1948; King, 1955; Rees, 1961). The

inclination error has been observed in laboratory experiments, where

the angular difference can be as high as 20



(King, 1955), but it is smal-

ler (5–10



) or absent in natural sediments.

Barton et al. (1980) studied the change with time in the DRM acqui-

sition process of laboratory-deposited sediments and found that in less

than 2 days, there was no appreciable inclination error. In natural con-

ditions, postdepositional DRM presents no significant inclination error.

One of the major differences between laboratory experiments and nat-

ural conditions is the deposition rate. The time taken for realignment

has been estimated in a few years and is apparently related to the water

content of the sediments. Verosub et al. (1979) experimentally reexa-

mined the role of water content in acquisition of postdepositional

DRM and suggested that small-scale shear-induced liquefaction is

the main magnetization process. There are also several additional fac-

tors involved; for instance bottom water currents, changing water

levels, presence of organic matter, biological activity (bioturbation),

particle flocculation, floccule disaggregation, dewatering, etc.

In general, it appears that rapidly deposited sediments show inclina-

tion and bedding inclination errors, similar to those observed in labora-

tory experiments. Slowly deposited or high-porosity sediments show

small or no inclination error. Postdepositional DRM will realign the

magnetization direction; this process may occur in short timescales

of days or months, but may occur in periods of years or decades

following deposition (Tarling, 1983).

In addition to studies of secular variation and magnetostratigraphy

in sedimentary sequences, there has also been much interest in deter-

mining relative paleointensities from sedimentary records (Tauxe,

1993). Long records of relative paleointensities have been derived

from marine and lake sedimentary sequences, and results have been

compared with volcanic records and other records. There have been

also several attempts to examine the effects of depositional factors in

the DRM intensity, including for instance the effects of clay mineral-

ogy, electrical conductivity of sediments, pH and salinity (Lu et al.,

1990; Van Vreumingen, 1993; Katari and Tauxe, 2000). Katari and

Bloxham (2001) examined the effects of sediment aggregate sizes on

the DRM intensities, and proposed that intensity is related to viscous

drag that produces misalignment of magnetic particle aggregates. They

argue that interparticle attractions arising from electrostatic or van der

Waals forces and/or biologically mediate flocculation results in forma-

tion of aggregates (which present a log-normal size distribution) pre-

venting settling of individual smaller grains.

The depositional and postdepositional DRM in laboratory experi-

ments and naturally deposited sediments have been intensively studied;

nevertheless, further work is required to understand the complex inter-

play of processes and then develop magnetization acquisition models

(e.g., Verosub, 1977; Tarling, 1983; Tauxe, 1993; Katari and Bloxham,

2001).

Jaime Urrutia-Fucugauchi

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588 MAGNETIZATION, DEPOSITIONAL REMANENT

Katari, K., and Tauxe, L., 2000. Effects of pH and salinity on the

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Stacey, F., 1972. On the role of Brownian motion in the control of

detrital remanent magnetization of sediments. Pure and Applied

Geophysics, 98: 139–145.

Tarling, D.H., 1983. Palaeomagnetism, Principles and Applications in

Geology, Geophysics and Archaeology. London: Chapman & Hall,

379 pp.

Tauxe, L., 1993. Sedimentary records of relative paleointensity of the

geomagnetic field: theory and practice. Reviews of Geophysics, 31:

319–354.

Van Vreumingen, M., 1993. The influence of salinity and flocculation

upon the acquisition of remanent magnetization in some artificial

sediments. Geophysical Journal International , 114: 607–614.

Verosub, K.L., 1977. Depositional and postdepositional processes in

the magnetization of sediments. Reviews of Geophysics and Space

Physics, 15: 129–143.

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Letters, 6: 226–228.

MAGNETIZATION, ISOTHERMAL REMANENT

Introduction

As indicated by the name, isothermal remanent magnetization (IRM) is

a remanent magnetization (RM) acquired without the aid of changes in

temperature. There are actually many processes that can produce RMs

isothermally (see, e.g., CRM, VRM, DRM, and ARM ), but by conven-

tion we restrict the use of the term IRM to denote a remanence result-

ing from the application and subsequent removal of an applied DC

field. IRMs are thus intimately related to hysteresis. Conventional

nomenclature uses M

for the IRM determined by measurement of a

hysteresis loop (and M

if the cycle reaches saturation), whereas

IRM and SIRM are typically used for remanence measurements made

with a zero-field magnetometer after magnetization on a separate

instrument (electromagnet, pulse magnetizer, etc.).

Weak fields, such as the geomagnetic field, are generally very inef-

fective in producing IRMs, and therefore IRMs are rarely significant

components of NRM. (A notable exception is found in rocks struck

by lightning, as discussed below.) IRMs are therefore primarily of

interest as laboratory-produced remanences, and are used in sample

characterization, in studying the mechanisms affecting stable rema-

nence, and as a normalizing parameter for estimation of relative

paleointensity. The attributes of principal interest are: the intensity

(dipole moment per unit mass or volume); the coercivity (range of

fields over which significant acquisition occurs) or stability (resistance

to demagnetization by thermal, alternating-field, and/or low-temperature

methods); and the anisotropy (dependence on orientation of the applied

field).

Grain-scale processes and remanent states of

individual particles

In a sufficiently strong applied field, the magnetic structure inside a

ferromagnetic particle is simple: uniform magnetization parallel to

the field, i.e., saturation magnetization (M

). With decreasing applied

field intensity, interesting complexities develop in response to the

internal demagnetizing field, magnetocrystalline anisotropy and stress:

magnetization may rotate away from the applied field direction toward

an easy axis determined by grain shape, crystal orientation or stress;

the magnetization may become nonuniform, with spins arranged in

“flower” or “vortex” structures; domains may nucleate and grow, with

magnetizations oriented at high angles to those of neighboring domains.

Upon complete removal of the saturating applied field, the particle

reaches its saturated remanent state, with a net intensity M

 M

oriented in general with a positive component parallel to the applied

field direction, i.e., M

RS//

> 0 (although self-reversal of IRM has been

reported in rare cases, e.g., Zapletal, 1992). The ratio M

for an

individual particle thus ranges from 0 to 1, depending on the saturated

remanent domain state, and M

RS//

depends additionally on easy-axis

orientation(s) with respect to the applied field direction.

For an ideal single-domain (uniformly magnetized) particle, M

equal in magnitude to M

, and the ratio M

RS//

is thus determined by

the particle anisotropy (number and symmetry of easy axes) and orien-

tation (Gans, 1932; Wohlfarth and Tonge, 1957). For an ideal SD

particle with uniaxial (e.g., shape) anisotropy, oriented at an arbitrary

angle f to the applied field, M

RS//

¼ cos(f) and M

RS⊥

sin(f); M

RS//

thus ranges from 0 for an applied field perpendicular

to the easy axis (i.e., the moment rotates 90



as the field is removed)

to 1 for the parallel case. Magnetocrystalline anisotropy often involves

multiple symmetrically equivalent easy axes (e.g., the cubic body

diagonals in magnetite, and the cube edges in Ti-rich titanomagne-

tites). For a multiaxial SD particle, the maximum angle (f

max

) that

may separate the applied field from the nearest easy axis is reduced

(Figure M111), and the minimum ratio M

R//

is accordingly increased.

For an individual cubic SD magnetite grain, f

max

¼ 54.7



and thus 0.577

 M

RS//

Above a threshold grain size, uniformly magnetized remanent states

become energetically unfavorable, and vortex (Williams and Wright,

1998) or multidomain structures consequently develop, lowering the

total energy by reducing the net remanence of the particle. In a

two-domain particle with antiparallel domain magnetizations, the net

remanence is primarily due to domain imbalance; in asymmetrically

shaped grains the minimum-energy state may yield a significant net

(imbalance) moment (Fabian and Hubert, 1999). Even when domain

moments exactly cancel in two-domain grains, the domain-wall

moment (“psark,” Dunlop, 1977) provides a small but stable net parti-

cle moment. Increasing domain multiplicity generally results in more

perfect mutual cancellation of both the domain moments and the wall

moments (which have been observed to alternate in polarity across

magnetite grains with several domains, Pokhil and Moskowitz,

1997), and there is consequently a strong reduction in M

RS//

with

increasing particle size.

Remanent states: ensembles of particles

Except in very coarse-grained rocks, even a centimeter-sized cubic or

cylindrical specimen contains a very large number of ferrimagnetic

particles. The net IRM of a population of grains is simply the vector

sum of the individual grain remanent moments, and thus its magnitude

depends on the number of remanence-carrying particles, their size

(domain-multiplicity) distribution, particle-level anisotropy, and orien-

tation distribution (i.e., population-level anisotropy) relative to the

applied-field direction. In interacting assemblages, each particle is

influenced not only by the externally applied field but also by the

fields of neighboring particles, so the spatial distribution of grains is

an additional important factor (Muxworthy et al., 2003).

MAGNETIZATION, ISOTHERMAL REMANENT 589

Orientation distribution and bulk anisotropy

The simplest case to consider is that of a perfectly aligned population

of identical single-domain particles, for which the ratio M

RS//

of the

assemblage equals that of each individual particle: M

RS//

¼ cos(f),

where f is the angle between the applied field and the nearest

easy-axis direction in the aligned assemblage. Note that in this case,

as for an individual particle, the net IRM generally has both parallel

and transverse components.

A perfectly aligned population represents an extreme not often

approached in natural materials, most of which are considerably closer

to the opposite limiting case: isotropic (random or quasiuniform)

orientation distribution (OD). For an ensemble of SD particles with

an isotropic OD, M

RS//

is determined entirely by the particle-level

anisotropy (Gans, 1932; Stoner and Wohlfarth, 1948; Wohlfarth and

Tonge, 1957), and the net transverse component is effectively zero.

For uniaxial anisotropy, grain moments rotate on average 60



to the

nearest easy axis when the applied field is removed, yielding M

RS//

¼ M

¼ cos(60



) ¼ 0.5. (This result is obtained by integrat-

ing parallel components over the assemblage, equivalent to integrating

cos(f) over the hemisphere surrounding the applied field orientation,

within which the proximal easy axes are distributed.) With multiaxial

anisotropies the average rotation angle is significantly reduced and

is concomitantly increased. For an ensemble of cubic SSD

particles with <100> easy axes (e.g., TM60) and a uniform OD, the

expected M

RS//

ratio is calculated by integrating cos(f) over the

“capture area” surrounding a cube edge orientation (Figure M111),

yielding M

RS//

¼ M

¼ 0. 832. For <111> easy axes

(e.g., magnetite), integration over the region surrounding a body diag-

onal orientation yields M

RS//

¼ M

¼ 0.866 (Gans, 1932;

Stoner and Wohlfarth, 1948).

For the imperfect antiferromagnets hematite and goethite, as well as

the hard ferrimagnet pyrrhotite, the applied fields typically used in

rock magnetism (1 T produced by electromagnets; 5 T produced

by typical superconducting magnets) are insufficient to achieve satura-

tion. When these minerals occur with fine-grain sizes and/or impure

compositions, applied fields exceeding 60 T may be required to satu-

rate the remanence (Mathé et al., 2005). A hard magnetocrystalline

anisotropy largely confines the remanence to the basal planes of

hematite and pyrrhotite, and to the c-axis for goethite. Hematite’s

basal-plane anisotropy has both a weak triaxial magnetocrystalline

component and a uniaxial magnetoelastic component (Banerjee,

1963; Dunlop, 1971). When the uniaxial anisotropy dominates M

¼ 0.637. In the absence of strong uniaxial anisotropy, the hexago-

nal symmetry results in much higher ratios, up to 0.955 (Wohlfarth and

Tonge, 1957; Dunlop, 1971).

When particle moments are diminished by the development of non-

uniform remanent states, the ratio M

of the population decreases

proportionally. For magnetite there is a more or less continuous

decrease in the remanence ratio with increasing grain size. Data com-

piled by Dunlop (1995) for the size range 40 nm  d  400 mm show

that M

varies in proportion to d

–n

(0.5  n  0.65), with two

separate size-dependent trends: stress-free hydrothermally grown

grains have significantly lower remanence ratios than similarly sized

crushed grains or grains grown by the glass ceramic method.

Bulk IRM anisotropy is controlled both by particle-level anisotropy

and by the orientation distribution of the population. Like other bulk mag-

netic anisotropies, the anisotropy of IRM (AIRM) has been used to char-

acterize rock fabric for geological applications and for evaluating

directional fidelity of NRM (Fuller, 1963; Cox and Doell, 1967; Daly

and Zinsser, 1973; Stephenson et al., 1986; Jackson, 1991; Kodama,

1995). IRM differs from weak-field induced and remanent magne-

tizations (e.g., susceptibility, ARM, and TRM) in that it is generally a

nonlinear function of applied field, and consequently the tensor mathe-

matics used to describe linear anisotropic magnetizations are not valid

for AIRM, except when very weak magnetizing fields ( a few millite-

sla) are used. Nevertheless it is a relatively rapid and very sensitive

method of characterizing magnetic fabric (Potter, 2004).

“Partial IRMs” and coercivity spectrum analysis

Partial TRMs (pTRMs) and partial ARMs (pARMs) are generated when

a weak but steady bias field is applied during some part, but not all, of

the cooling or AF decay. Clearly no direct analog can exist for IRM, but

“pIRM” equivalents can be produced physically (by partial demagneti-

zation of an IRM), or calculated mathematically (by subtraction of IRMs

acquired in different fields). Partial IRMs and their ratios are very

widely used for sediment characterization in environmental magnetism

(Thompson and Oldfield, 1986; King and Channell, 1991; Oldfield,

1991; Verosub and Roberts, 1995; Dekkers, 1997; Maher and Thompson,

1999). For example the hard fraction, HIRM, is determined by subtracting

the IRM acquired in 300 mT (IRM

300

) from SIRM, to estimate the contri-

bution of antiferromagnetic minerals (e.g., hematite and goethite) to the

saturation remanence. HIRM, as conventionally defined, is an absolute,

concentration-dependent parameter. The soft fraction is more often

quantified in relative terms through the so-called S-ratios, calculated from

measurements of SIRMand of the IRM subsequently acquired in an oppo-

sitely directed field of 100 mT (IRM

–100

)or300mT(IRM

300

): S

100

IRM

–100

/SIRM, and S

300

¼IRM

–300

/SIRM. These ratios range from

1 (for samples containing only hard antiferromagnets) to þ1(for

samples dominated by soft ferrimagnets).

A more thorough method of deconstructing an SIRM uses application

of two successive orthogonal applied fields of decreasing strength to

reset the remanence of the intermediate- and low-coercivity fractions;

Figure M111 Cube edge <100> directions (diamonds) are the

magnetocrystalline easy axes for high-Ti titanomagnetites. Due to

the cubic symmetry, an applied field can be oriented no more

than y

max

¼ 54.7



from the nearest easy axis of an individual

grain. For a randomly oriented assemblage of ideal SD grains with

<100> easy axes, M

¼ 0.832 (Gans, 1932). This is most

easily calculated in the particle coordinate system, by noting that

an IRM parallel to the polar easy axis results from application of a

sufficiently strong field oriented anywhere within the “capture

area” comprised of the eight adjacent congruent spherical

triangles (outlined in bold). For each particle, M

R//

¼ cos(f),

and for the assemblage M

is obtained by integrating cos(f)

over the “capture area.” Body diagonal <111> directions

(triangles) are the magnetocrystalline easy axes for magnetite at

temperatures above the 130 K isotropic point; the “capture area”

for these consists of six congruent spherical triangles, and

integration of cos(f) over this area yields M

¼ 0.866 for a

randomly oriented assemblage of ideal SD grains with <111>

easy axes.

590 MAGNETIZATION, ISOTHERMAL REMANENT

the resultant “triaxial” IRM is then thermally demagnetized to deter-

mine the unblocking temperature distribution associated with each

coercivity fraction (Lowrie, 1990). The threshold fields are selected

for isolation of different mineralogical and grain-size fractions; Lowrie

(1990) used 5 T for the initial SIRM (sufficient to magnetize hematite

and goethite at least partially); 0.4 T for the first orthogonal overprint

(to reorient the remanence of the ferrimagnets magnetite and pyrrho-

tite); and 0.12 T for the second overprint (to realign the remanence

of soft MD carriers).

For many geological applications, recognition and quantification of

a few discrete IRM-carrying fractions is adequate, but finer subdivi-

sion of SIRM into a quasicontinuous coercivity distribution can be

made by differentiation of the IRM acquisition curve (Dunlop,

1972). Starting from a demagnetized state, application of successively

stronger fields results in growth of IRM as domain structures change

and single-domain moments are reoriented, each at a critical field

determined by particle anisotropy and orientation. The resulting coer-

civity spectrum can be analytically decomposed if it assumed that the

distributions each follow some prescribed form, typically lognormal

(Figure M112 ) (Robertson and France, 1994; Stockhausen, 1998;

Heslop et al., 2002; Egli, 2003, 2004 a,b).

Starting from the SIRM state, application of successively larger oppo-

site-polarity “backfields” causes the net remanence first to decrease and

then to grow in the reverse direction, eventually reaching the negative

SIRM state; this process is often termed “DC demagnetization” but it

is perhaps more useful to think of it as a part of the isothermal rema-

nent hysteresis cycle. The remanent coercivity H

is defined as the

field-axis intercept of the remanent hysteresis loop, exactly as the bulk

coercivity H

is defined for the in-field loop.

Interaction effects

In the absence of interparticle interactions, the IRM acquisition curve

for SD ensembles has a simple and direct relationship to the “DC

demagnetization” curve (Wohlfarth, 1958). In each case, a particular

applied field activates the same set of particles; in the former case ran-

domly oriented moments (in the demagnetized ensemble) are replaced

with a net IRM, whereas in the backfield case a net IRM is replaced with

its opposite-polarity equivalent. The change in the latter case is exactly

twice that in the former, and thus the relationship between the initial

acquisition curve M

IRA

(H ) and the backfield curve M

IRB

(H )is:

IRB

(H ) ¼ SIRM2M

IRA

(H ). For AF demagnetization, each peak

AF erases the remanence imprinted by the corresponding DC applied

field, so M

(

H) ¼ SIRMM

IRA

), i.e., there is a mirror symmetry

of the IRM acquisition and AF demagnetization curves for noninteracting

SD populations.

There are two commonly used graphical illustrations of these rela-

tionships. The Henkel plot graphs M

IRB

(H ) as a function of M

IRA

(H )

(Henkel, 1964). For noninteracting SD ensembles, the relationship is

linear, with a slope of 2(Figure M113a ). The Cisowski plot

(Cisowski, 1981) or crossover plot (Symons and Cioppa, 2000) simul-

taneously graphs the acquisition curve M

IRA

) together with the

AF-demagnetization curve M

(

H ) and/or the appropriately rescaled

DC-backfield curve M

IRB

(H ) ¼ 0.5(SIRM þ M

IRB

(H )), as functions

of the AC and DC fields (Figure M113b). On this plot, noninteracting

SD populations are indicated by mirror symmetry, with an intersection

at the point whose field coordinate is equal to both the median destruc-

tive field (MDF; also referred to as

1=2

, Dankers, 1981) and the median

acquisition field (MAF; also referred to as H

(Dankers, 1981)), and

whose magnetization coordinate is equal to 0.5*SIRM.

A crossover ratio R < 0.5 (equivalent to a trajectory on the Henkel plot

that “sags” below the line of slope 2) indicates that MAF > MDF,

in other words that the ensemble is harder to magnetize than to demag-

netize. Such behavior is a hallmark of either a negatively interacting

SD population or MD carriers (for which self-demagnetization pro-

duces the equivalent effect); these two possibilities often cannot be

definitively distinguished on the basis of IRM data alone (Dunlop

and Özdemir, 1997). Crossover ratios R > 0.5 are virtually never

observed, in part due to the extreme rarity of MD-free magnetic assem-

blages in natural materials, but further suggesting that interactions in

SD assemblages, when they occur, are primarily negative.

Theoretical treatment of interactions in multidomain assemblages

has been hindered by the analytical and numerical intractability of

modeling interacting nonuniformly magnetized grains. However,

recent results obtained at the resolution limit of micromagnetic model-

ing (Muxworthy et al., 2003) shows that in general, interaction begins

Figure M112 Coercivity spectrum analysis (methods of Heslop et al., 2002), modeling the measured IRM acquisition (solid circles)

as the sum of log-Gaussian distributions, in this case with three components (open symbols). Integrating and summing yields the

model IRM curve (solid black). The individual components can be interpreted as different mineral and/or grain-size populations.

MAGNETIZATION, ISOTHERMAL REMANENT 591

to have significant effects for SD and PSD grains (30–250 nm) when

the separation between particles is less than or equal to twice the par-

ticle diameter; this is comparable to the threshold for susceptibility

interaction effects (Hargraves et al., 1991; Stephenson, 1994; Cañon-

Tapia, 1996). Interestingly, the model results show that IRM interac-

tions are primarily negative (decreasing M

) for single-domain

ensembles, but positive (increasing M

) for grains >100 nm.

Kinetic effects : time-dependent IRM (TDIRM)

Néel (1949a,b, 1955) theory provides the basis for understanding phe-

nomena such as magnetic viscosity, thermoremanence,andfrequency-

dependent susceptibility, by specifying how magnetization kinetics

depend on factors including temperature, applied field, and particle size.

At room temperature, and for typical experimental timescales of millise-

conds to hours, thermal fluctuations are most significant for nanometric

particles; for magnetite the transition from superparamagnetic to stable

SD behavior occurs under these conditions at approximately 20–30 nm.

A highly sensitive method of probing the SP-SSD threshold uses

IRM acquisition with varying exposure times (Worm, 1999).

At any fixed absolute temperature T, the initial magnetization M

an assemblage of single-domain grains grows or decays in time (t),

approaching an equilibrium value in a constant applied field H:

MðtÞ¼M

t=t

þ M

ð1  e

t=t

Þ (Eq. 1)

where the equilibrium magnetization M

is:

ðT; HÞ¼M

tanh



(Eq. 2)

and the relaxation time t is:

tðT; HÞ¼t

exp

ðTÞH

ðTÞð1  H=H

ðTÞÞ

2kT

(Eq. 3)

In these equations V is grain volume, H

is microscopic coercivity, k is

Boltzmann’s constant (1.38  10

–23

–1

), m

is the permeability of

free space (4 p  10

–7

–1

), and t

is approximately 10

–9

s. Very

fine (small V ) and/or very soft (low H

) grains have shorter relaxation

times, and equilibrate more quickly, than do larger and/or magnetically

harder SD grains.

Note that relaxation time drops very sharply as the applied field H

approaches H

. IRM is thus acquired quickly, and then becomes stabi-

lized (t increasing sharply) when the applied field is removed. Time-

dependent IRM is significant in populations of SD particles with

narrow distributions of V and H

, i.e., with a narrow distribution of

relaxation times in the applied field H. Exposure times less than

the mean relaxation time are too short for significant acquisition of

remanence, but exposure times one or two orders of magnitude larger

may allow substantial equilibration with the applied field. The time-

dependence of IRM in such assemblages is much stronger than the

frequency-dependence of susceptibility (w

). For example, ash-flow

tuffs from Yucca Mountain Nevada have a w

of up to 35% per dec-

ade, the highest known for any geological material; in contrast their

IRM intensities increase by as much as 800% with a tenfold increas e

in exposure time (Worm, 1999). The time-dependence is effectively

amplified for IRM by the strong asymmetry between acquisition and

decay rates.

Lightning strikes and IRM in nature

Lightning has long been recognized as a significant mechanism for

overprinting natural remanence (Matsuzaki et al., 1954; Cox, 1961;

Graham, 1961), due primarily to the strong magnetic fields locally

generated by the intense currents involved in lightning strikes. These

currents, typically 10

–10

A, are dominantly upward-directed (i.e.,

electrons flow down from the cloud to the ground along the ionized

flow path), and most lightning flashes include three or four separate

upward current pulses (“return strokes”), spaced about 50 ms apart (e.

g., Krider and Roble, 1986).

The magnetic field B generated by a straight filamentary current I of

effectively infinite length, at a point located at a perpendicular distance

r, has a magnitude m

I/(2pr). For example, a 30 kA current produces a

field of 60 mT at r ¼ 10 cm, sufficient to impart a significant IRM in

most materials. The orientation of the field is perpendicular to both I

and r, i.e., the field lines are circles, centered on and perpendicular

to the filamentary current. Both of these characteristics, concentric

directional geometry and 1/r field dependence, have been observed

by Verrier and Rochette (2002) in IRM overprints in samples collected

around known lightning strikes (Figure M114).

However in most cases the patterns are not so clear. Although the

current in a lightning bolt flows along an effectively infinite (typically

Figure M113 Top: Henkel (1964) plot for a sample with ideal

noninteracting SD behavior. Bottom: Cisowski (1981) plot of the

same data (backfield data rescaled and reflected). After Worm and

Jackson (1999), with permission of the authors and publisher.

592 MAGNETIZATION, ISOTHERMAL REMANENT

5 km) and relatively straight vertical path between cloud and ground,

the path along and below the ground surface is much shorter and more

irregular, as shown by the geometry of fulgurites, which are formed

when rocks or sediments are melted by lightning. (Temperatures in

the ionized channel typically reach 30000 K, five times the tempera-

ture of the sun’s surface). This irregularity may be expected to disrupt

the simple cylindrical symmetry of the induced magnetic field. In the

absence of simple directional symmetry, the diagnostic feature for

identification of lightning-produced IRM is a combination of high

NRM intensity (or more specifically, high NRM/SIRM ratios) and

moderate-to-low resistance to AF demagnetization (Cox, 1961; Graham,

1961); thermal demagnetization is generally much less effective at

separating lightning overprints (e.g., Tauxe et al., 2003).

Quantitative estimates of lightning currents (Wasilewski and

Kletetschka, 1999; Verrier and Rochette, 2002; Tauxe et al., 2003)

require both a paleointensity determination and an estimate of the

separation between sample location and lightning strike. Wasilewski

and Kletetschka (1999) and Tauxe et al. (2003) estimate lightning field

intensities by finding the lab field that produces an IRM of the same

intensity as the lightning overprint. Because lightning remanences

may decay with time, this approach yields a minimum estimate of

the magnetizing field associated with a strike. Verrier and Rochette

(2002) use an alternative approach based not on the overprint intensity

but on the AF amplitude required to erase it.

Mike Jackson

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Cross-references

Magnetic Anisotropy, Sedimentary Rocks and Strain Alteration

Magnetic Domain

Magnetization, Anhysteretic Remanent (ARM)

Magnetization, Chemical Remanent (CRM)

Magnetization, Depositional Remanent (DRM)

Magnetization, Natural Remanent (NRM)

Magnetization, Thermoremanent (TRM)

Magnetization, Viscous Remanent (VRM)

MAGNETIZATION, NATURAL

REMANENT (NRM)

Natural remanent magnetization (NRM) is remanent magnetization

that has been acquired naturally (i.e., not artificially acquired in a

laboratory). It is the remanent magnetization of a sample (such as rock

or baked archaeological material) that is present before any laboratory

experiments are carried out. Magnetization is usually measured nor-

malized to either the sample volume (units of A m

1

) or sample mass

(units of A m

1

). NRM can consist of one or more types of mag-

netization depending on the history of the sample. Rock samples that

have been exposed to the Earth’s magnetic field for many millions of

years may have experienced several different processes of magnetization

during that time, producing multiple components of magnetization.

Components acquired at the time of rock formation are termed primary

594 MAGNETIZATION, NATURAL REMANENT (NRM)

and later components are termed secondary. The NRM is then the vector

sum of all the naturally acquired components of magnetization:

NRM ¼ Primarycomponent þ

Secondarycomponents

i ¼ 0, 1, 2, ... , n, where n is the number of secondary components.

Both primary and secondary components in a rock can record geological

events (for example, the time of formation, metamorphism, or an

impact event) and are of interest in unraveling the geological history

of the rock. Generally, however, it is the primary remanence acquired

on formation that is of most interest to the paleomagnetist. Depending

on the intensity and duration of the events responsible for secondary

magnetizations (also known as overprints), the latter may partially or

completely replace the primary magnetization.

Figure M115 Example of thermal and AF demagnetization. Solid (open) symbols on the orthogonal vector plot (OVP) represent vertical

(horizontal) components of magnetization. (a) Thermal demagnetization of Australian Tertiary basalt. There is a viscous secondary

component that is removed by 200



C to leave the primary component of remanence. (b) AF demagnetization of recent Turkish basalt.

There is a small viscous secondary component that is removed by 20 mT to leave the primary component of remanence.

MAGNETIZATION, NATURAL REMANENT (NRM) 595