Reference Work Entry

Encyclopedia of Geomagnetism and Paleomagnetism

pp 535-540

Magnetic Remanence, Anisotropy

  • Ann M. Hirt

It has been known since the early 1950s that rocks and sediments display a magnetic anisotropy when constituent mineral grains have a preferred orientation (Graham, 1954; Hargraves, 1959). Magnetic fabric is usually described by the anisotropy of magnetic susceptibility (AMS), measured in weak applied fields. With this method all minerals in a rock or sediment contribute to the susceptibility. Therefore, the observed anisotropy is the sum of the individual mineral components, their specific susc\eptibility anisotropy and their preferred alignment. Since nonferromagnetic matrix minerals often make up the bulk composition of a rock or sediments, the low‐field susceptibility of these minerals can dominate the measured signal. The anisotropy of magnetic remanence (AMR) is only dependent on the ferromagnetic grains (s.l.) in a rock. Since the number of different ferromagnetic phases is more limited, the source of the AMR is easier to distinguish, and the degree of anisotropy is less sensitive to mineral variation (Jackson, 1991).

In early studies several authors noted that certain rocks that display AMS also have natural remanent magnetizations (NRMs) that are shallowly inclined toward the plane of high susceptibility (Howell et al., 1958; Hargraves, 1959; Fuller, 1960). This observation promoted the first studies examining the anisotropy of remanent magnetization. Since then numerous investigations have used the anisotropy of remanent magnetization to determine if the ferromagnetic minerals are preferentially aligned, which may in turn affect the characteristic remanent magnetization (ChRM) of a rock.

Theoretical background

The physical theory of magnetization and the magnetic behavior of minerals is given elsewhere in this volume. Detailed coverage on the theory of AMS and AMR is available in several textbooks and review papers (Jackson, 1991; Rochette et al., 1992; Tarling and Hrouda, 1993; Borradaile and Henry, 1997; Tauxe, 2002). A cursory description necessary to understand the basis of anisotropy of remanent magnetization follows.

The magnetization M of a material is a vector sum of two components: the induced magnetization M i and remanent magnetization M r,
The induced magnetization can be expressed as

where χ is the susceptibility, a material constant that can be described by a tensor of second order, and H is the inducing field. The remanent magnetization is the magnetization that remains after the material is removed from an applied magnetic field and is carried by ferrimagnetic minerals.

A mathematical description of a weak‐field magnetic remanence is analogous to AMS. This has been described in Stacey and Banerjee (1974) as
where k r is the remanent susceptibility, which is also a material constant that can be described by a tensor of second order for linearly anisotropic magnetizations.

It can be represented geometrically by an ellipsoid with principal axes parallel to the eigenvectors of k r and lengths equal to the corresponding eigenvalues, where k r1k r2k r2. It must be noted that M r should be both linearly dependent on the intensity of the inducing field and reversible.

In a rock or sediments, we are interested in the total contribution of all ferrimagnetic minerals to the observed signal. If a material is isotropic, i.e., the minerals show no preferred orientation, then M i will be along the direction of the applied field and M r will be in the direction of the field that produced the remanence. If, however, the minerals in a rock or sediment have a preferred orientation then the acquired magnetization will lie between the applied field direction and the direction of the easy axis of magnetization. The easy axis of magnetization may be related to the shape of the grain, as is the case for ferrimagnetic spinel. Minerals that display shape anisotropy have a high spontaneous magnetization and a slight departure from equidimensional habit leads to the magnetization being preferentially aligned along the long axis of a grain. Crystallography may also control the direction of magnetization, due to the geometric distribution of atoms within the crystallographic lattice. The ferrimagnetic minerals, hematite and pyrrhotite, are controlled by magnetocrystalline anisotropy. Compared to the value along the c‐axis, the susceptibility in the basal plane is two orders of magnitude higher in hematite and three orders of magnitude higher in pyrrhotite. Stress within a mineral may also lead to an anisotropic acquisition of magnetization, known as magnetostriction. It arises from the strain dependence of the anisotropy constants and has been observed in titanomagnetite.

Types of remanent magnetization

A rock or sediment can acquire different types of remanent magnetizations. Some types of remanence are acquired by natural processes, whereas other types are imparted under laboratory conditions. When rocks form from molten lava or sediments are deposited, the magnetic moments of ferromagnetic minerals align statistically with the prevailing Earth's magnetic field and receive a remanent magnetization, known as the NRM.

The NRM that is found in rocks that are formed from molten lava is called a thermal remanent magnetization (TRM). When individual ferrimagnetic minerals cool through their Curie temperature or Néel temperature, the ferrimagnetic grains take on the magnetization of the ambient magnetic field. TRM is very stable over time. Sediments acquire their remanent magnetization as they are deposited. The ferrimagnetic grains align statistically in the ambient field as they settle and the acquired magnetization is called a detrital remanent magnetization (DRM). As the grains are cemented in the matrix of the sediment, the resulting magnetization is a postdetrital remanent magnetization (pDRM).

It is also possible to give a material a TRM in the laboratory by heating the material above the Curie or Néel temperature of the constituent ferrimagnetic phases and cooling it in a field of known direction and intensity. Other laboratory‐acquired remanent magnetizations include anhysteretic remanent magnetization (ARM) and isothermal remanent magnetization (IRM). An ARM is acquired when an alternating field (H AC) is superimposed on a weak DC bias field, which serves to impart a magnetization in a known direction. All ferrimagnetic minerals with a coercivity less than or equal to H AC will be remagnetized. Anhysteretic remanence shows grain‐size dependence in magnetite (Figure M56a), such that single‐domain grains (0.03–0.05 μm) have a higher remanence than larger multidomain grains. Grains of superparamagnetic size effectively carry no remanent magnetization at temperatures where they are superparamagnetic.
Figure M56

(a) Variation in the intensity of anhysteretic remanent susceptibility (k a, intensity of ARM normalized for the applied DC field) as a function of grain size in magnetite. (b) Variation in intensity of saturation IRM in different magnetic minerals as a function of grain size (after Jackson, 1991).

An IRM is acquired in a strong DC field (H IRM, generally >10 mT) of known intensity and direction. All ferrimagnetic grains with a coercivity less than or equal to H IRM will be remagnetized. Since IRM is a strong‐field remanence the imparted magnetization is not linearly related to H IRM. If the applied field is below saturation and if only the first‐order terms are considered, a symmetric matrix can be assumed for constant H IRM (Cox and Doell, 1967; Stephenson et al., 1986; Jackson, 1991). Saturation IRM also shows a grain‐size dependence for (titano‐)magnetite, hematite, and pyrrhotite (Figure M56b).

Measurement of the anisotropy of magnetic remanence

All methods that measure the AMR require a laboratory magnetization to be imparted along a set of known directions. The most commonly applied laboratory magnetization is an ARM, although several studies have used other types of magnetization, such as IRM and TRM. Since the remanent anisotropy is a symmetric tensor of second rank, at least six independent measurements must be made to define the tensor. Many measurement schemes for the AMS have been proposed over the years (see Borradaile and Henry, 1997), based on early suggestions of Nye (1957), who suggested 13 positions (Figure M57, excluding position 5 and 9), and Girdler (1961), who suggested nine positions (positions 1–4, 6–8, 10, 11). Cox and Doell (1967) first described a method to measure the anisotropy of IRM (AIRM), using 15 independent positions (1–11, with positions 1, 3, 5, and 7 measured twice). McCabe et al. (1985) proposed using ARM to define the remanent anisotropy; they used the same positions as used by Girdler (1961) to measure AMS.
Figure M57

Lower hemisphere, equal area plot that shows the directions of magnetic field used to investigate the acquisition of anisotropic remanent magnetization.

Independent of the type of remanence that is applied and the number of positions that are used, a general procedure is followed. First a sample is demagnetized and its remanent magnetization is measured as a basis for the “demagnetized” or natural remanent state. A laboratory magnetization is then applied along the first axis, the imparted remanent magnetization is measured, and the component due to the imparted magnetization is found by vector subtraction of the natural remanence. The sample is again demagnetized to remove the imparted magnetization and the demagnetized state is measured as a control. This procedure is repeated along all the selected field positions, and the measurements are used to define the matrix k r. Differences between the best‐fit ellipsoid and the individual measurements give the residuals, and these can be minimized by using a least‐squares computation. Jackson (1991) proposed that a goodness‐of‐fit (GoF) can be determined from

where RMS is the root mean squared residuals normalized to k mean. The expression is an estimate of how well the anisotropy ellipsoid is resolved. The ellipsoid can be considered well resolved for GoF values under 10%; typically values are on the order of a few percent.

Stephenson et al. (1986) suggested an alternative method to obtain the ellipsoid of anisotropy of remanence. They measured the individual diagonal and off‐diagonal matrix elements directly. Here a laboratory remanent magnetization is applied along the sample x‐axis and the three components of the magnetization are measured. The sample is demagnetized and the same field is next applied along the sample y‐axis and all the three components of the magnetization are measured. After demagnetization the field is now applied along the sample z‐axis and the magnetization is measured. This yields nine values that overdefine the tensor and yield a measure of the precision of fit. This method is probably reliable for IRM, since the imparted remanence is relatively large, allowing for accurate determination of the magnetization components oriented normal to the applied field direction. It is less reliable for ARM and TRM where imparted remanences are relatively weak.

Anisotropy of anhysteretic remanent magnetization (AARM)

The anisotropy of ARM has also been called the anisotropy of anhysteretic susceptibility (AAS), since normalizing the magnetization by the field strength converts it to a pseudosusceptibility. An ARM is acquired from the DC bias field, often on the order of 0.05–0.1 mT, superimposed on the AC field. The strength of the bias field is on the order of one to two times that of the Earth's magnetic field. The intensity of the AC field can be chosen as desired, but is generally less than 300 mT, due to limits of commercially available AF demagnetizing units. This limitation means that an ARM can only be imparted to minerals with low coercivity, such as (titano‐)magnetite or pyrrhotite. A detailed description of the measurement procedure is outlined above and has been given in McCabe et al. (1985).

Since the coercivity of ferromagnetic minerals, particularly magnetite and titanomagnetite, is dependent on grain size, it is possible to impart an ARM to a particular grain‐size fraction during demagnetization in the DC bias field. This is accomplished by switching on the DC bias field in a specific AC field range or coercivity window during demagnetization. The imparted magnetization is known as a partial ARM (pARM). Jackson et al. (1988) demonstrated that the method can be used to distinguish if a specific grain‐size fraction is responsible for the observed AARM. For example, a high coercivity window (e.g., 80–150 mT) will only magnetize single‐domain magnetite, whereas a low coercivity window (e.g., 0–30 mT) would magnetize larger multidomain grains (see “Geological Applications” sections for a practical example).

Anisotropy of isothermal remanent magnetization (AIRM)

The advantage of AIRM is that a relatively strong DC field is applied to the sample, such that higher coercivity phases may also be magnetized. As stated above, IRM is not linearly related to the applied field; however, a symmetric matrix can be assumed if only the first‐order terms are considered. Jelinek (1996) proposed a nonlinear AIRM model that more precisely describes the magnetization phenomena, in which the anisotropy is also described by a symmetric second‐order tensor. The typical strength of the applied field is between 5 and 60 mT (Tarling and Hrouda, 1993). Cox and Doell (1967), who proposed the method originally, used an applied field of 700 mT, which is above the saturation of the ferromagnetic phases. The measurement procedure is the same as outlined above. The main difficulty with their method is the complete demagnetization between each imparted magnetization step. If lower fields are used, it should be possible to demagnetize with alternating field (AF) demagnetization. Cox and Doell (1967) rotated their samples in the 700 mT field of an electromagnet to randomize the magnetization, since complete randomization of magnetic domains is reversible.

As with AARM, Cox and Doell (1967) suggested that it is possible to examine a partial IRM. In their case, they proceeded as follows. After measuring the sample magnetized in a 700 mT field, the sample can be subjected to AF demagnetization in a significantly smaller field, e.g., 100 mT. The remaining magnetization is then remeasured. The sample can then be further demagnetized in a stronger field, e.g., 200 mT, and then remeasured. In this manner a set of deviation vectors is produced,

where J r is the measured remanent magnetization, which is produced in the field H, and J m is the mean amplitude of a set of J r vectors averaged over all the results from the different directions of the applied field. This gives a set of D(H′) for each value of the alternating field demagnetization (H′).

Several cautionary notes should be made concerning the method and the magnetization process in AIRM. The first caution is with regard to the accuracy with which a field strength can be applied. A field strength between 5 and 60 mT is in a range where the magnetization of a sample is quickly acquired for (titano‐)magnetite and iron sulfides (Figure M58). Slight variations in field strength may lead to apparent anisotropy that is not related to the preferred orientation of ferromagnetic grains. Figure M58 shows a typical IRM acquisition curve for a pelagic limestone. In this example a variation in IRM intensity on the order of 2%, comparable to the required resolution in the study of AMR, would occur if the field strength varied by only ±2 mT.
Figure M58

Example of an IRM acquisition curve for a magnetite‐bearing, pelagic limestone.

Caution must also be exercised when measuring the AIRM in pyrrhotite‐bearing rocks. A study by de Wall and Worm (1993) demonstrated that the shape of the ellipsoid and degree of anisotropy are dependent on the applied field in rocks containing pyrrhotite. Although the orientations of the principal axes are not affected, they showed that the degree of anisotropy in a sample of isometric pyrrhotite ore varied between 3.8 and 1.05 for applied field strengths between 1.5 and 100 mT, respectively. The authors attributed this effect to the control of the observed anisotropy by magnetocrystalline anisotropy in low applied fields, and by magnetostatic anisotropy, which arises from the cylindrical sample shape, in strong fields. Jackson and Borradaile (1991) reported a similar dependence of AIRM and field strength in hematite‐bearing slates, but attributed the effect to different coercivity fractions in the rocks.

It has been noted by Tauxe et al. (1990) that following repeated application of an IRM, the coercivity of the specimen increased after exposure to the first high field, so that in spite of demagnetization to remove the previous magnetization, some grains affected by the first field application were no longer affected by subsequent field applications. The authors attributed this effect to hematite grains with metastable domains, which change domain state during the AIRM experiment.

Anisotropy of thermal remanent magnetization (ATRM)

Heating a sample above the Curie or Néel temperature of its ferromagnetic phases and cooling it in an applied field will produce a TRM. As outlined in the general procedure, the sample must be first demagnetized. This can be achieved either with AF demagnetization or by heating the rock above its Curie temperature (T C) or Néel temperature (T N), and cooling in zero field. The rock is then magnetized in the first field direction by reheating above T C or T N and cooling in a field of fixed intensity and rate of cooling. It is important that the field intensity and rate of cooling is the same in all heating runs. After measurement of the imparted TRM, the sample is again demagnetized. At least six independent heating steps are necessary to define the tensor, 12 if the sample cannot be demagnetized in alternating fields and must be reheated above the blocking temperature. It is important to control that no chemical alteration has occurred, which could produce new ferromagnetic minerals and affect the acquired TRM. Often a thermomagnetic curve is made on a small piece of the sample to check that the ferromagnetic mineralogy is thermally stable.

As for a pARM, a partial TRM (pTRM) can be acquired if the field applied during cooling is turned on only when cooling through a particular temperature range. This requires accurate monitoring of the temperature during cooling.

Geological applications

Several examples are presented below to illustrate how AMR can differ from AMS and the type of geologic information that can be obtained from remanent fabrics. The most common method used in examining AMR is AARM. The experimental method is relatively simple and this magnetization method avoids many problems that have been found in applying IRM or TRM. The method is suitable for magnetite‐ and possibly pyrrhotite‐bearing rocks, but not for high coercivity phases, such as hematite. In this case, AIRM and ATRM are more suitable methods. An example is given for AMR in hematite‐bearing rocks. In the examples below, the magnitudes of the principal axes of the anisotropy ellipsoids are defined as k 1k 2k 3.


If the same processes leading to grain orientation affect the ferromagnetic and paramagnetic minerals in a rock, one would expect that the magnetic fabric of both components should be similar. The orientation of the AARM ellipsoid is close to the AMS ellipsoid, and the main difference between the two fabrics is found in terms of the degree of anisotropy, lineation, and foliation. If the two mineral components formed at separate times in the history of the rock or if deformation mechanisms acting on the different mineral components varied, then it is possible that the susceptibility and remanence magnetic fabrics could be different.

The first example illustrates how rock rheology can lead to two different magnetic fabrics. The Lower Paleozoic stratigraphic sequence from the Central Appalachian Fold and Thrust Belt includes the Lower Ordovician Coburn limestone, which is overlain by the Reedsville/Martinsburg shale in central Pennsylvania, USA. Both lithologies underwent the same deformation during the Alleghenian orogeny. The AMS was measured with an Agico KLY‐2 susceptibility bridge, and the susceptibility fabric in the limestones can be characterized by a prolate ellipsoid with k 1 subparallel to pencil structure in the overlying shales, which is also the structural trend of the major fold structures, and k 2 and k 3 distributed in a girdle normal to the k 1 axes (Figure M59). The prolate fabric is the result of a horizontal tectonic compaction superimposed on the vertical bedding compaction. The shales, on the other hand, have oblate AMS ellipsoids with k 3 subparallel to the pole to bedding and k 1 aligned within the bedding plane, subparallel to the pencil structure or fold axis. The bedding compaction controls the susceptibility fabric in the shales.
Figure M59

Lower hemisphere, equal area plot showing the orientation of the principal axes of the AMS (upper plots) and AARM (lower plots) for the Coburn limestone (left) and Reedsville/Martinsburg shale (right). The principal axes k 1 are squares, k 2 are triangles, and k 3 are circles in this and subsequent figures. Bedding plane in shales is shown with the dashed line.

Magnetite is the major ferromagnetic phase in both lithologies. Anisotropy of ARM was investigated using a 0.1 mT DC bias field with a 150 mT alternating field, and the measurement procedure of McCabe et al. (1985). The AARM of the limestones is similar to the AMS fabric both in the orientation of the principal axes and the shape of the ellipsoid (Figure M59). This suggests that the susceptibility and remanent fabrics in the limestone are both controlled by magnetite. The AARM in the shales, however, is characterized by prolate ellipsoids, in which k 1 is well‐grouped and subparallel to the pencil directions and k 2 and k 3 are distributed in a girdle in a plane with k 1 as its pole (Figure M59). This remanent fabric shows that the magnetite grains have been more strongly affected by the horizontal compaction. The difference between the AMS and AARM fabrics can be explained by the fact that paramagnetic clays and phyllosilicates dominate the AMS fabric, which is largely controlled by bedding compaction. The magnetite grains acted as rigid particles in a passive matrix during deformation, and were therefore quicker to respond to the horizontal compression.

In the second example the AARM was determined in the Ordovician Martinsburg Formation from Lehigh Gap in eastern Pennsylvania using ARMs applied in two different coercivity ranges. Samples were taken from the part of the outcrop in which pencil structures are well developed and a bedding and incipient cleavage can be identified. Magnetite and pyrrhotite are the main ferromagnetic phases in the rocks, as determined from IRM acquisition and thermal demagnetization of a multiple component IRM. The AARM was first determined using a 0.035 mT DC bias field with an alternating field of 30 mT, and then using a 0.1 mT DC bias field with an alternating field of 100 mT, in which the DC bias field was turned on between 60 and 100 mT. The first application would only affect coarser ferromagnetic grains, whereas the higher coercivity range would selectively magnetize finer grain sizes (Figure M56a). Figure M60a shows that the low coercivity AARM fabric is not well defined, but the anisotropy is loosely related to tectonic compaction. This suggests that the coarser grain were less efficient in orienting in the strain field. The high coercivity fabric is well‐defined and characterized by a triaxial ellipsoid, in which the k 3 axes are subparallel to the pole to cleavage, and k 1 axes mirror the pencil lineation.
Figure M60

Lower hemisphere, equal area plots of the AARM for (a) low-coercivity range (0.035 mT bias field, 0–30 mT AF), and (b) high-coercivity range (0.1 mT bias field, 60–100 mT AF). The bedding plane is shown with the dotted line and the cleavage plane with the dashed line.


Tan and Kodama (2002) investigated paleomagnetic directions in the Mississippian Mauch Chunk Formation in eastern Pennsylvania. They found that the inclination of the ChRM was shallower than the expected direction and used AMR to see if the ferromagnetic grains showed preferential flattening in the bedding plane. Hematite is the sole ferromagnetic carrier in the red beds, and the ChRM was isolated in thermal demagnetization above 670 °C. IRM acquisition curves indicate that 85%–90% of the saturation IRM is activated in an applied field of 1.2 T. The AMS in the rocks has a degree of foliation on the order of 1.01 to 1.04, which would not result in a significant inclination flattening. An IRM was applied along nine directions following the method of McCabe et al. (1985) using a 1.2 T impulse field, and the tensor solution was found using a method outlined in Tauxe (2002). Samples were heated to 670 °C and cooled in zero field, so that only the ChRM‐bearing hematite retains an IRM. In this manner the magnetic fabric due to the grains that are responsible for the ChRM can be isolated. The AIRM shows that the k 3 axes are well‐grouped along the pole to bedding in both the undemagnetized and thermally demagnetized samples (Figure M61). The k 1 and k 2 axes lie in the bedding plane and are slightly better grouped in the undemagnetized samples. Both sets of data show the same degree of lineation, but the demagnetized samples show a slightly higher degree of foliation (Figure M61). In both AIRM cases the degree of flattening is almost an order of magnitude higher than in the AMS. Tan and Kodama (2002) used the AIRM and AMS data to obtain an individual particle anisotropy factor, which was then used to correct the paleomagnetic inclination. They could show that, after correction, the expected inclination was in good agreement with a European igneous paleopole of the same age.
Figure M61

Lower hemisphere, equal area plots of the AIRM for undemagnetized samples (upper left) and thermally demagnetized samples (upper right) from red beds of the Mauch Chunk Formation. Principal axes ratios (lower plot) for the undemagnetized (solid circles) and demagnetized (open circles) samples (after Tan and Kodama, 2002).


Selkin et al. (2000) made a combined study of AMS, ATRM, and AARM in an anorthositic layer from the Upper Banded Series of the Precambrian Stillwater complex. The susceptibility fabric, which was measured with a KLY‐2 susceptibility bridge, is compatible with the preferred orientation of plagioclase crystals in the samples, where k 3 is normal to the foliation plane of the rock and k 1 is close to the c‐axis orientation of plagioclase (Figure M62a). Thermal demagnetization data indicates that titanium‐poor magnetite is the main ferromagnetic phase in the samples. The AARM was measured in a 0.05 mT DC bias field and 180 mT alternating field using six different positions. The ATRM was determined by heating the samples to 600 °C and cooling in a 25 μT field in air; six positions were used to define the tensor. The two different remanent fabrics are similar, but distinctly different from the susceptibility fabric (Figure M62b,c). The AARM and ATRM ellipsoids are prolate with k 1 well‐grouped, coinciding with the pole to the foliation plane defined by the plagioclase crystals and k 3 constrained in the direction of the plagioclase c‐axes. The authors interpret these results as showing that single‐domain magnetite grains are responsible for the remanent anisotropy. Needles of single‐domain magnetite have been identified by TEM in plagioclase in various intrusions, including the Stillwater complex, and often the needles are perpendicular to the plagioclase c‐axes. Further support for this interpretation was obtained from hysteresis loops made along the direction of the principal axes of the remanence ellipsoids. Single‐domain magnetite could also be responsible for an inverted magnetic fabric in susceptibility anisotropy. However, the same fabric would be obtained if paramagnetic minerals are responsible for the AMS. The AMR was used to correct estimates of paleointensity, which were affected by the preferential alignment of the magnetite grains.
Figure M62

Lower hemisphere, equal area plot for the magnetic fabric of an anorthosite sample, measured by (a) AMS, (b) ATRM, and (c) AARM. Large black symbols show the principal axes of the plagioclase fabric, and small black symbols are the site mean averages of the individual sample measurements (open symbols). P is the degree of anisotropy (k 1/k 3), L is the degree of lineation (k 1/k 2), and F is the degree of foliation (k 2/k 3) (after Selkin et al., 2000).


Magnetic Susceptibility, Anisotropy Magnetization, Anhysteretic Remanent (ARM) Magnetization, Isothermal Remanent (IRM) Magnetization, Natural Remanent (NRM) Magnetization, Thermoremanent (TRM)

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