Magnetic Domains

1
Magnetic Domains Remanence Acquisition
..how rocks get magnetized
2
Magnetic Remanence
When the magnetization of a body produces an
external field (i.e. it possess a remanence), it
has magnetostatic energy or an energy of self
demagnetisation. Atomic magnetic moments are
dipoles and can most simply be modelled as pairs
of magnetic charges. In a given magnetic
particle the magnetic charges of adjacent atoms
cancel internally within the particle but produce
a magnetic charge distribution at the surface of
the particle. For a uniformly magnetized
spherical particle one hemisphere has a positive
charge and the other a negative charge. This
charge distribution gives rise to an energy known
as the magnetostatic energy.
3
Magnetic Remanence
(From McElhinny McFadden, 2000)
4
Rock Magnetism Magnetostatic Energy
For a uniformly magnetized grain the
magnetostatic energy is proportional to the
square of the magnetization and the magnetostatic
energy becomes extremely high for ferromagnetic
materials with a high magnetization. To reduce
this magnetostatic energy magnetic domains form
within grains, which reduce the size of regions
of uniform charge thereby reducing the surface
magnetization.
5
Rock Magnetism Domains
Subdivision of a ferromagnetic grain into domains.
(After Dunlop Özdemir, 1997)
6
Rock Magnetism Domains
Grains with two or more magnetic domains are
termed multi-domain. Internal to each domain the
magnetization is equal to the saturation
magnetization, but because charges of opposite
sign are adjacent the net magnetization for the
grain is less than the saturation magnetization.
The region separating domains is known as the
domain wall. Domain walls themselves possess a
finite energy that is related to energy exchange
between adjacent atoms and is proportional to the
area of the wall.
(After Butler, 1992)
7
Rock Magnetism Domains
With increasing grain size, and increased surface
area, more magnetic domains are formed to
counteract the increase in magnetostatic energy
due to the increase in the surface area.
Conversely, as grains get smaller the number of
domains decreases until the energy involved in
erecting a domain wall becomes larger than the
decrease in magnetostatic energy resulting from
dividing the grain into two domains. Grains with
only one magnetic domain are termed
single-domain. The grain diameter below which
grains are single-domain is dependent on the
grain shape and the magnetization. Grains with a
low magnetization possess low magnetostatic
energy and hence little incentive to form
magnetic domains.
8
Rock Magnetism Domains
Single-domain, two-domain and multi-domain grain
configurations (top) and the likely number of
domains versus grain diameter for magnetite
(bottom). The black bars represent the range of
grain sizes sizes for which that number of
domains is the lowest energy domain state.
(After Moon Merrill, 1985 Van der Voo, 1990)
9
Rock Magnetism Domains
Domains arise due to a balance of energies within
a grain. The major magnetic energies are the
exchange energy, Eex the magnetostatic or
demagnetising energy, Ed and the anisotropy
energy, Eanis.   The total magnetic energy,
Etot is given by   Etot Eex Ed Eanis
  The Domain State of a magnetic grain is
controlled by minimising these energies and thus
is controlled by grain size, shape and
mineralogy magnetic field, temperature, stress
and crystal defects as well as other more minor
factors. 
10
Rock Magnetism Domains
Exchange energy (Eex) is the energy associated
with coupling through the interaction of the
electrons of adjacent atoms. Eex is minimised by
the parallel (ferromagnetic) or antiparallel
(antiferromagnetic/ferrimagnetic) alignment of
adjacent magnetic moments.   Eex -2JeSiSj
Where Siand Sj are the spin vectors for
adjacent atoms and Je is the exchange integral.
(Where Je gt 0, energy is minimised by spins being
parallel (ferromagnetism). Where Je lt 0, energy
is minimised by spins being antiparallel
(antiferromagnetism, ferrimagnetism).) 
11
Rock Magnetism Domains
Magnetostatic energy (Ed) also called the
internal field energy arises from interaction of
a crystals magnetization with itself. This
energy is dependent on the geometry of the
crystal. It is large for equant grains and small
for elongate grains. An effect of this energy is
shape anisotropy it is easier for magnetisation
to lie along the long axis of an elongate
crystal. Shape anisotropy is thus uniaxial with
two "easy" directions of magnetisation.   Ed ½
?0NVM2 Where N is the demagnetising factor, V is
the volume and M is the magnetisation, and ?0 is
the permeability of free space.  
12
Rock Magnetism Domains
The anisotropy energy (Eanis), the total
anisotropy energy, is the sum of the
magnetocrystalline, magnetostrictive and
magnetoelastic anisotropies. The total
anisotropic energy Eanis is thus given
by   Eanis Ek Estric Eme
13
Rock Magnetism Domains
The magnetocrystalline energy (Ek) arises from
the interaction of the permanent magnetic moment
with the anisotropic crystalline electric field.
This simple means that atomic dipole moments
align more easily along certain crystallographic
axes than others. In magnetite, the 111 axes
are the preferred orientation of magnetisation in
the absence of an external field. This gives a
cubic crystalline anisotropy and therefore 8
"easy" orientations of magnetisation. Shape
anisotropy is a much stronger effect than
crystalline anisotropy and dominates over it for
elongations greater than a few percent.
14
Rock Magnetism Domains
Magnetization of a single crystal of magnetite
along different crystallographic axes. 111 is
the magnetocrystalline easy axis, while 100 is
the magnetocrystalline hard axis.
(After Nagata, 1961)
15
Rock Magnetism Domains
The magnetostrictive energy (Estric) arises from
the fact that when a crystal is magnetised it
changes shape. This introduces the possibility of
magnetically induced mechanical stress in grains
where the whole volume is not magnetised in the
same direction.
16
Rock Magnetism Domains
The magnetoelastic energy (Eme) results from the
effects of stress on a crystal, which alters the
direction of spontaneous magnetisation. The
origins of stress may be external (macrostress)
or internal, (microstress), due to crystal
imperfections e.g. dislocations, inclusions etc.
Microstress is important when considering
intra-crystal magnetic processes and remanence.
17
Rock Magnetism Domains
The total anisotropic energy Eanis is thus given
by   Eanis Ek Estric Eme   For
magnetically uniaxial grains Eanis KVsin2?
Where K is the anisotropy constant, V is the
grain volume and ? is the angle between the
direction of magnetization and the easy axis. 
18
Rock Magnetism Domains
Whether a grains will subdivide into two or more
magnetic domains is strongly influenced by the
size of the grain and at the critical size the
energy of a single domain grain will be the same
as the energy of the 2 domain state the energy
required to erect a domain wall between the two
domains. ESD E2D EW   ESD ½ ?0NVM2 For a
sphere N is 4?/3 and the volume ?d3/6 where d
is the diameter.
19
Rock Magnetism Domains
The energy of the wall (EW) ?wLW where ?w is
the wall energy per unit area, L is the length of
the wall and W is the width of the
wall.   Combining the above equations gives a
critical diameter d such that   D 4?w/?0NSDM2
If we substitute values for magnetite the
critical diameter comes out to be about 0.04?m.
This is actually less than the wall width for the
domain walls in magnetite (about 0.2?m).
20
Rock Magnetism Single domain grains
The theory of the magnetization of an assemblage
of single-domain particles is essentially due to
the work of Néel (1955). The grain-size below
which particles are single-domain is termed the
single-domain threshold grain size (d0). This
size is dependent on the grain shape and
saturation magnetization. For haematite, which
has a low saturation magnetization, this grain
diameter is circa. 15mm, so a large proportion of
haematite encountered in rocks is single-domain.
Magnetite has a much higher saturation
magnetization, and for cubic magnetite the
critical diameter for single domain behaviour is
approximately 0.05mm. Elongate magnetite
particles may still be single-domain up to 1mm.
Single-domain particles can be very efficient
carriers of remanent magnetization.
21
Rock Magnetism Single domain grains
Magnetite at 290K
(After Butler Banerjee, 1975)
22
Rock Magnetism Single domain grains
During demagnetization the net magnetic moment of
a single-domain grain cannot be reduced by
internal cancellation of domain movements through
domain wall movement. Instead, magnetic moments
can only be made to change direction or rotated
toward the applied field. However, there are
resistances to the rotation of the magnetization,
the dominant ones being shape anisotropy and
magnetocrystalline anisotropy.
23
Rock Magnetism Single domain grains
Shape anisotropy is related, as the name
suggests, to the shape of the grains. Highly
elongate grains have a much lower magnetostatic
energy when magnetized along their length rather
than perpendicular to their length. This is
because the percentage of surface area covered by
magnetic charges is small when the magnetization
lies along the long axis. Magnetization
perpendicular to the long axis produces a
substantial surface charge. The magnetic charge
distribution produces a field internal to the
grain, called the internal demagnetizing field,
which opposes the magnetization of the grain.
Therefore the internal demagnetizing field
perpendicular to the long axis will be greater
than that along the long axis.
24
Rock Magnetism Single domain grains
The difference in magnetization along and
perpendicular to the long axis gives rise to a
difference in magnetostatic energy, which
represents a barrier to rotation of the
magnetization through the perpendicular
direction. To force the magnetization to rotate
through this barrier an external magnetizing
field is required, which is known as the
microscopic coercive force. For needle-shaped
single-domain magnetite, at room temperature,
this field reaches a maximum of approximately
300mT, though in naturally occurring magnetite
this extreme shape anisotropy is rarely
encountered. More usually coercivities of
magnetite lie within the range 30-70mT. The
coercivity of haematite is at least 0.1T and
usually higher.
25
Physics of Magnetism Hysteresis
When a ferromagnet is subjected to a cyclic
change in the external field the magnetisation is
not directly proportional to the applied field by
there is a lag in the magnetisation, which is
known as hysteresis. H is the applied field, J is
the induced magnetization. Js is the saturation
magnetization, Jr is the saturation remanence and
Hc is the coercivity. The various hysteresis
properties are not solely intrinsic properties
but are dependent on grain size, domain state,
stresses and temperature. Because hysteresis
parameters are dependent on grain size, they are
useful for magnetic grain sizing of natural
samples.
26
Physics of Magnetism Hysteresis
(After Butler, 1992)
27
Natural Remanent Magnetization (NRM)
The natural remanent magnetization (NRM) of a
rock is the magnetization present in a rock prior
to laboratory treatment and depends on the
geomagnetic field and geological processes that
have operated on the rock during and after its
formation. NRM can typically contain a number of
components of magnetization of differing ages.
The NRM component acquired during the formation
of a rock is usually referred to as primary NRM
and those acquired subsequent to rock formation
as secondary NRMs. Secondary NRMs can often mask
or sometimes completely obscure the primary NRM.
Therefore understanding the modes of acquisition
of NRM by a rock is of critical importance in
interpreting the significance of measured
components of NRM.
28
Natural Remanent Magnetization (NRM)

• The principal forms of NRM are
• Thermoremanent magnetization
• Chemical remanent magnetization
• Detrital remanent magnetization
• Viscous remanent magnetization.

29
NRM Thermoremanent Magnetization (TRM)
A thermoremanent magnetization (TRM) is the NRM
produced in a rock when cooling it from above the
Curie temperature in the presence of a magnetic
field. However this magnetization will, in time,
reach magnetic equilibrium with the surrounding
field. A measure of this time is the relaxation
time (t). Relaxation time is given in the
equation   where C is a frequency factor, v is
the volume of the grain, Bc is the grain's
coercivity, Js is the spontaneous magnetization,
k is Boltzmans constant and T is the absolute
temperature.
30
NRM Thermoremanent Magnetization (TRM)
(After Van der Voo, 1990)
31
NRM Thermoremanent Magnetization (TRM)
(After Butler, 1992)
32
NRM Thermoremanent Magnetization (TRM)
One of the most important features of this
equation is that the relaxation time is strongly
dependent on the absolute temperature and
directly related to the coercivity. At the Curie
temperature the mineral will have a short
relaxation time and will rapidly align with the
applied field. The temperature at which a
particular mineral acquires its magnetization is
known as its blocking temperature (Tb). As a
mineral phase can have a blocking temperature
below the Curie point, albeit with a longer
relaxation time, a TRM can be acquired over a
range of blocking temperatures that are
distributed from the Curie point down. As the
temperature decreases through the Tb of an
individual grain, the grain experiences a large
increase in its relaxation time, effectively
freezing in the magnetization relative to
geological or experimental time scales.
33
NRM Thermoremanent Magnetization (TRM)
In the case of igneous rocks the magnetization is
acquired as the rock cools through the Curie
temperature of the particular magnetic mineral
(at temperatures above the Curie Temperature
magnetic minerals lose their magnetic
properties). As the mineral cools through the
Curie Temperature it retains a record of the
direction and strength of the Earths magnetic
field.
34
NRM Thermoremanent Magnetization (TRM)
If the acquisition of a magnetization through a
range of Tbs is regarded as a stepwise process,
the TRM acquired over a particular temperature
interval is termed Partial TRM or PTRM. The sum
of all PTRMs should give the total TRM (Thellier,
1951).
(After Van der Voo, 1990)
35
NRM Thermoremanent Magnetization (TRM)
A theoretical model for the acquisition of TRM in
single domain ferromagnetic grains was given by
Néel (1955). This model adequately explained the
acquisition of TRM in cases where the assemblage
of grains has a uniaxial anisotropy and grains
are of equal size with a single Tb. In practice
rocks would be expected to have a random
distribution of isotropic axes and a variety of
grain sizes with corresponding variations in Tb.
36
NRM Chemical Remanent Magnetization (CRM)
Chemical remanent magnetization (CRM) is produced
by chemical reactions involving ferromagnetic
minerals including precipitation of a new
magnetic mineral phase and alteration of
pre-existing minerals (both ferromagnetic and
non-magnetic). The new ferromagnetic mineral
locks in a record of the earth's magnetic field
direction at the time of its formation. In
contrast with TRM, where grains acquire a
magnetization at a constant volume and decreasing
temperature, CRMs are acquired at a constant
temperature with changes in volume.
37
NRM Chemical Remanent Magnetization (CRM)
During chemical formation of a ferromagnetic
mineral grains grow from a zero initial volume.
Newly nucleated particles are small, have short
relaxation times and are super-paramagnetic.
During the growth of the grains they become
ferromagnetic and relaxation times increase
dramatically. The diameter at which the grains
change from being super-paramagnetic to
ferromagnetic is known as the blocking diameter
(0.02mm for haematite. As grains pass through
the blocking diameter they record the applied
magnetic field, and continued grain growth can
produce a remanent magnetization that is stable
over geological time.
38
NRM Chemical Remanent Magnetization (CRM)
(After Butler, 1992)
39
NRM Chemical Remanent Magnetization (CRM)
A number of factors govern the rate of CRM
acquisition. Chemically immature sediments (those
with an abundance of low-oxidation-state
minerals) experience more rapid oxidation than
chemically mature sediments and therefore acquire
most of their CRM quickly. Therefore the chemical
maturity of the sediment is a possible tool in
recognising whether a sediment acquired its CRM
rapidly or over a longer period of time.
Secondly, the grain size of the sediment is of
importance, given that fine-grained sediments
have a larger surface to volume ratio and are
likely to undergo more rapid chemical changes
than coarser sediments. Finally the plaeo-climate
and depositional environment also play a role. An
oxygenating depositional environment is much more
likely to result in rapid oxidation and warm
moist paleo-climates tend to prolong the
magnetization process in red beds.
40
NRM Detrital Remanent Magnetization (DRM)
Detrital remanent magnetization (DRM) is produced
by the alignment of small magnetized particles
during the deposition and lithification of
sediments. The acquisition of DRM is a
complicated process given the large number of
processes involved during the formation of
sedimentary rocks. There is a large variety of
initial mineralogies, many minerals not being in
equilibrium with each other or their depositional
environment, and sediments are subject to large
variety of post-depositional processes, such as
bioturbation, prior to lithification.
41
NRM Detrital Remanent Magnetization (DRM)
(Modified after Cox Hart, 1986)
In sediments magnetic minerals make up a tiny
proportion of the rock (lt0.1). As the magnetic
grains sink through the water column they align
themselves with the ambient magnetic field (in
this case the Earths magnetic field). When the
sediment accumulates and solidifies into a rock
the magnetic grains become locked in and thus
preserve a record of the magnetic field at the
time of formation of the rock.
42
NRM Detrital Remanent Magnetization (DRM)
The classic model of DRM acquisition was proposed
by Collinson (1965) which dealt only with the
aligning effect of the applied magnetic field on
a particle at the sediment-water interface. This
yielded a characteristic alignment time of 1
second, implying rapid and complete alignment of
ferromagnetic particles with the geomagnetic
field. However this model does not hold for
natural cases or laboratory experiments as a
number of other important considerations were not
taken into account.
43
NRM Detrital Remanent Magnetization (DRM)
Firstly, magnetic grains and especially
inequidimensional ones interact with each other,
and the final alignment of the grains is
therefore a compromise between alignment with the
magnetic field and adjacent magnetic particles.
Secondly, laboratory experiments indicate that
the inclination of DRM tends to be consistently
shallower than the applied field. A simple
explanation for this is that grains tend to be
magnetized along the long axis of the particle
due to shape anisotropy. These long axes are
subject to gravitational torque which tends to
rotate them toward the horizontal.
44
NRM Detrital Remanent Magnetization (DRM)
There are a number of problems with this
explanation as measurements of the inclination
error in natural sediments tend to be less than
those in laboratory experiments, indicating that
there are other factors to be taken into account,
notably the possibility of further
post-depositional DRM (pDRM). PDRM has been
attributed to Brownian motion, where magnetized
particles are reoriented by the Brownian motion
of the surrounding water. PDRM has been shown to
be free of the inclination problem of DRM and it
seems likely that DRMs in natural sediments are
DRMs with some portion of later pDRM.
45
NRM Detrital Remanent Magnetization (DRM)
Experimental production of PDRM in the laboratory
plotted versus the inclination of the applied
field.
(After Kent, 1973)
Most sediments, and particularly red beds, are
thought to carry CRM, both DRM and pDRM being
subject to CRM overprinting early in the
diagenetic history of the rock.
46
NRM Viscous Remanent Magnetization (VRM)
Viscous remanent magnetization (VRM) is the
magnetization acquired during exposure to weak
magnetic fields. It is proportional to the
intensity of the ambient field and proportional
to the logarithm of the time of exposure to the
field. VRM at a given temperature is given
by where t is the time of exposure to the
field and S is the viscosity coefficient. The
viscosity coefficient (S) has been shown to be
proportional to temperature. Because of the
logarithmic growth of VRM with time, viscous
magnetizations tend to be dominated by recent
magnetic fields and generally rocks with a high
proportion of VRM tend to have NRM aligned with
the present geomagnetic field.
47
NRM Isothermal Remanent Magnetization (IRM)
Isothermal remanent magnetization (IRM) is
acquired in the presence of a direct field at a
constant temperature. IRM curves or hysteresis
loops are often used in laboratory experiments to
identify magnetic carriers in rocks. A
demagnetized sample is subjected to an applied
magnetic field (H) and the induced magnetization
(Ji) is then measured. The induced magnetization
per unit volume (J) is plotted against H, where H
is increased in a series of steps up to maximum
and then reversed and increased to a maximum in
the reversed direction. The resultant hysteresis
loop is characteristic of the remanence
carrier(s) in the rock. The maximum induced
magnetization is known as the saturation
magnetization (Js) and depends linearly on the
concentration of the ferromagnetic mineral
involved.
48
Physics of Magnetism Hysteresis
When a ferromagnet is subjected to a cyclic
change in the external field the magnetisation is
not directly proportional to the applied field by
there is a lag in the magnetisation, which is
known as hysteresis. H is the applied field, J is
the induced magnetization. Js is the saturation
magnetization, Jr is the saturation remanence and
Hc is the coercivity. The various hysteresis
properties are not solely intrinsic properties
but are dependent on grain size, domain state,
stresses and temperature. Because hysteresis
parameters are dependent on grain size, they are
useful for magnetic grain sizing of natural
samples.
49
NRM Isothermal Remanent Magnetization (IRM)
The applied field (H) required to achieve
saturation (gt700mT for haematite, 300mT for
magnetite) can be used as an indication of the
identity and domain states of the magnetic
carriers. The reversed field required to reduce
Js to zero is known as the coercivity of
remanence (Hcr). Typical values of Hcr for
magnetite are 20-80mT and gt300mT for haematite,
though higher values are not unknown, indicating
hard magnetic components.
50
NRM Isothermal Remanent Magnetization (IRM)
In nature occurrences of IRM tend to be
restricted to outcrops that have been subjected
to lightning strikes. Electrical currents of
lightning can exceed 104-105 amperes and induce
magnetic fields of up 10mT within 1m of the
strike. These can generally be recognised by
abnormally high NRM intensities and in some
instances by a high scatter in the NRM directions.
www.gsfc.nasa.gov/
51
NRM Isothermal Remanent Magnetization (IRM)
The current travels radially from the point of
impact, and the distance it travels depends on
the conductivity of the rock, and whether it is
wet. The resulting magnetic directions are
usually highly scattered.
52
NRM AF Demagnetization
Alternating field (AF) demagnetization is
achieved by the cycling of a magnetized rock
sample through hysteresis loops with decreasing
amplitude in a zero Dc field. The magnetic moment
of grains with a coercivity less than the peak
field applied is thereby nullified. The process
is repeated for successively higher fields until
the NRM is effectively demagnetized or the
maximum peak field is attained.
(After Van der Voo, 1990)
53
NRM Thermal Demagnetization
Progressive thermal demagnetization is achieved
by stepwise heating to the maximum unblocking
temperature. Samples are then cooled in a
field-free chamber which allows for random
orientation of particles or domain moments. The
magnetization of the rock sample is measured at
room temperature between each heating cycle. The
lower blocking temperature components are
progressively removed leaving those of high
thermal stability. Treatments are typically in
20-100C steps though this depends on the nature
of the NRM. Treatments are usually concentrated
over temperature intervals where a large
proportion of magnetic grains un-block, (i.e. a
thermally discrete spectrum or where detailed
analysis is required.
54
NRM Thermal Demagnetization
(After Van der Voo, 1990)
55
NRM Thermal Demagnetization
(After Butler, 1992)
56
NRM Thermal Demagnetization
(After Butler, 1992)
57
NRM Thermal Demagnetization
58
NRM Thermal Demagnetization
One drawback with the technique is that the
heating cycle can produce mineralogical
alteration within the rock and for the magnetic
minerals these alteration products include
production of Maghemite from Magnetite at
150-250C, Hematite from Maghemite at 350-450C,
Hematite from Magnetite at gt500C and the
reduction of Hematite to Magnetite at gt550C.
Alterations such as these will change the
magnetic characteristics of the sample and it
becomes particularly important that
field-cancellation in the furnace be as complete
as possible to avoid the acquisition of spurious
TRM during cooling.
59
Magnetism in Oxides
Ilmeno- Haematite series
Titano-Magnetite series
60
NRM Thermal Demagnetization
Up, W
NRM
520oC
530oC
540oC
N
550oC
500mA/m
GP35 (Hornblendite)