Magnetism is a Property of Materials That Respond at an Atomic or Subatomic Level to an Applied Magnetic Field

8/6/2019 Magnetism is a Property of Materials That Respond at an Atomic or Subatomic Level to an Applied Magnetic Field

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Magnetism is a property of materials that respond at an atomic or subatomic level to an applied

magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is

responsible for the behavior ofpermanent magnets, which produce their own persistent magneticfields, as well as the materials that are attracted to them. However, all materials are influenced to

a greater or lesser degree by the presence of a magnetic field. Some are attracted to a magnetic

field (paramagnetism); others are repulsed by a magnetic field (diamagnetism); others have amuch more complex relationship with an applied magnetic field. Substances that are negligibly

affected by magnetic fields are known as non-magnetic substances. They include copper,

aluminium, gases, andplastic.

The magnetic state (or phase) of a material depends on temperature (and other variables such aspressure and applied magnetic field) so that a material may exhibit more than one form of

magnetism depending on its temperature, etc.

[edit] Diamagnetism

Main article:Diamagnetism

Diamagnetism appears in all materials, and is the tendency of a material to oppose an applied

magnetic field, and therefore, to be repelled by a magnetic field. However, in a material withparamagnetic properties (that is, with a tendency to enhance an external magnetic field), the

paramagnetic behavior dominates.[9] Thus, despite its universal occurrence, diamagnetic behavior

is observed only in a purely diamagnetic material. In a diamagnetic material, there are nounpaired electrons, so the intrinsic electron magnetic moments cannot produce any bulk effect.

In these cases, the magnetization arises from the electrons' orbital motions, which can be

understoodclassicallyas follows:

When a material is put in a magnetic field, the electrons circling the nucleus willexperience, in addition to theirCoulomb attraction to the nucleus, a Lorentz force from

the magnetic field. Depending on which direction the electron is orbiting, this force may

increase the centripetal forceon the electrons, pulling them in towards the nucleus, or itmay decrease the force, pulling them away from the nucleus. This effect systematically

increases the orbital magnetic moments that were aligned opposite the field, and

decreases the ones aligned parallel to the field (in accordance withLenz's law). This

results in a small bulk magnetic moment, with an opposite direction to the applied field.

Note that this description is meant only as an heuristic; a proper understanding requires a

quantum-mechanical description.

Note that all materials undergo this orbital response. However, in paramagnetic and

ferromagnetic substances, the diamagnetic effect is overwhelmed by the much stronger effectscaused by the unpaired electrons.

[edit] Paramagnetism

Main article:Paramagnetism
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In a paramagnetic material there are unpaired electrons, i.e. atomic ormolecular orbitals with

exactly one electron in them. While paired electrons are required by the Pauli exclusion principle

to have their intrinsic ('spin') magnetic moments pointing in opposite directions, causing theirmagnetic fields to cancel out, an unpaired electron is free to align its magnetic moment in any

direction. When an external magnetic field is applied, these magnetic moments will tend to align

themselves in the same direction as the applied field, thus reinforcing it.

[edit] Ferromagnetism

Main article:Ferromagnetism

A ferromagnet, like a paramagnetic substance, has unpaired electrons. However, in addition tothe electrons' intrinsic magnetic moment's tendency to be parallel to an applied field, there is also

in these materials a tendency for these magnetic moments to orient parallel to each otherto

maintain a lowered energy state. Thus, even when the applied field is removed, the electrons inthe material maintain a parallel orientation.

Every ferromagnetic substance has its own individual temperature, called the Curie temperature,

or Curie point, above which it loses its ferromagnetic properties. This is because the thermal

tendency to disorder overwhelms the energy-lowering due to ferromagnetic order.

Some well-known ferromagnetic materials that exhibit easily detectable magnetic properties (to

form magnets) are nickel,iron, cobalt, gadolinium and theiralloys.

[edit] Magnetic domains

Magnetic domains in ferromagnetic material.Main article: Magnetic domains

The magnetic moment of atoms in a ferromagnetic material cause them to behave something liketiny permanent magnets. They stick together and align themselves into small regions of more or

less uniform alignment called magnetic domains orWeiss domains. Magnetic domains can beobserved with a magnetic force microscope to reveal magnetic domain boundaries that resemble

white lines in the sketch.There are many scientific experiments that can physically show

magnetic fields.
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Effect of a magnet on the domains.

When a domain contains too many molecules, it becomes unstable and divides into two domains

aligned in opposite directions so that they stick together more stably as shown at the right.

When exposed to a magnetic field, the domain boundaries move so that the domains aligned with

the magnetic field grow and dominate the structure as shown at the left. When the magnetizing

field is removed, the domains may not return to an unmagnetized state. This results in the

ferromagnetic material's being magnetized, forming a permanent magnet.

When magnetized strongly enough that the prevailing domain overruns all others to result in only

one single domain, the material is magnetically saturated. When a magnetized ferromagnetic

material is heated to theCurie point temperature, the molecules are agitated to the point that themagnetic domains lose the organization and the magnetic properties they cause cease. When the

material is cooled, this domain alignment structure spontaneously returns, in a manner roughly

analogous to how a liquid can freeze into a crystalline solid.

[edit] Antiferromagnetism

Antiferromagnetic ordering

Main article:Antiferromagnetism

In an antiferromagnet, unlike a ferromagnet, there is a tendency for the intrinsic magneticmoments of neighboring valence electrons to point in opposite directions. When all atoms are

arranged in a substance so that each neighbor is 'anti-aligned', the substance isantiferromagnetic. Antiferromagnets have a zero net magnetic moment, meaning no field isproduced by them. Antiferromagnets are less common compared to the other types of behaviors,
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and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be

seen to exhibit diamagnetic and ferrimagnetic properties.

In some materials, neighboring electrons want to point in opposite directions, but there is nogeometrical arrangement in which each pair of neighbors is anti-aligned. This is called aspin

glass, and is an example ofgeometrical frustration.

[edit] Ferrimagnetism

Ferrimagnetic ordering

Main article:Ferrimagnetism

Like ferromagnetism, ferrimagnets retain their magnetization in the absence of a field.

However, like antiferromagnets, neighboring pairs of electron spins like to point in oppositedirections. These two properties are not contradictory, because in the optimal geometrical

arrangement, there is more magnetic moment from the sublattice of electrons that point in one

direction, than from the sublattice that points in the opposite direction.

The first discovered magnetic substance,magnetite, was originally believed to be a ferromagnet;Louis Nel disproved this, however, with the discovery of ferrimagnetism.

[edit] Superparamagnetism

Main article: Superparamagnetism

When a ferromagnet or ferrimagnet is sufficiently small, it acts like a single magnetic spin that is

subject to Brownian motion. Its response to a magnetic field is qualitatively similar to the

response of a paramagnet, but much larger.

[edit] Electromagnet

An electromagnet is a type ofmagnet whose magnetism is produced by the flow of electric

current. The magnetic field disappears when the current ceases.
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Electromagnets attracts paper clips when current is applied creating a magnetic field. The

electromagnet loses them when current and magnetic field are removed.

Permeability

As previously mentioned, permeability () is a material property that describes the ease withwhich a magnetic flux is established in a component. It is the ratio of the flux density (B) createdwithin a material to the magnetizing field (H) and is represented by the following equation:

= /

It is clear that this equation describes the slope

of the curve at any point on the hysteresis loop.The permeability value given in papers and

reference materials is usually the maximum

permeability or the maximum relativepermeability. The maximum permeability is the

point where the slope of the B/H curve for the

unmagnetized material is the greatest. This point

is often taken as the point where a straight linefrom the origin is tangent to the B/H curve.

The relative permeability is arrived at by takingthe ratio of the material's permeability to the

permeability in free space (air).

(relative) = (material) / (air)

where: (air) = 1.256 x 10-6 H/m

The shape of the hysteresis loop tells a great deal about the material being magnetized. Thehysteresis curves of two different materials are shown in the graph.
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Relative to other materials, a material with a

wider hysteresis loop has:

Lower Permeability

Higher Retentivity

Higher Coercivity Higher Reluctance

Higher Residual Magnetism

Relative to other materials, a material with the

narrower hysteresis loop has:

Higher Permeability

Lower Retentivity

Lower Coercivity

Lower Reluctance

Lower Residual Magnetism.

In magnetic particle testing, the level of residual magnetism is important. Residual magneticfields are affected by the permeability, which can be related to the carbon content and alloying of

the material. A component with high carbon content will have low permeability and will retain

more magnetic flux than a material with low carbon content.

Magnetisation

The output from a magnetometer, a single value of magnetic moment for the sample, is a

combination of the magnetic moments on the atoms within the sample, the type and level of

magnetic ordering and the physical dimensions of the sample itself. The moment is also affectedby external parameters such as temperature and applied magnetic field.

The ``Intensity of Magnetisation3.2'', , is a measure of the magnetisation of a body. It is

defined as the magnetic moment per unit volume or

(3.2)

with units of Am (emucm in cgs notation).[8]

A sample contains many atoms and their arrangement affects the magnetisation. In Figure3.1(a)

a magnetic moment is contained in unit volume. This has a magnetisation of Am.

Figure3.1(b) shows two such units, with the moments aligned parallel. The vector sum of

moments is in this case, but as the both the moment and volume are doubled remains the
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same. In Figure 3.1(c) the moments are aligned antiparallel. The vector sum of moments is now

0 and hence the magnetisation is 0Am.

Figure 3.1: Effect of moment alignment on magnetisation: (a) Single magnetic moment, , (b)

two identical moments aligned parallel and (c) antiparallel to each other.

Scenarios (b) and (c) are a simple representation of ferro- and antiferromagnetic ordering. Hencewe would expect a large magnetisation in a ferromagnetic material such as pure iron and a small

magnetisation in an antiferromagnet such as -Fe O .

Magnetic domains

A magnetic domain describes a region within a magnetic material which has uniform

magnetization. This means that the individual magnetic momentsof the atoms are aligned with

one another and they point in the same direction. When heated above a temperature called theCurie temperature, a piece of ferromagnetic material undergoes aphase transition, and the

uniform magnetization within a domain spontaneously disappears: each atom has its owndirection of magnetic moment, independent from its neighbouring atoms (typical of the

paramagnetic state). Magnetic domain structure is responsible for the magnetic behavior of

ferromagneticmaterials like iron,nickel, cobaltand theiralloys, ferritesetc. The regionsseparating magnetic domains are called domain walls, where the magnetisation rotates

coherently from the direction in one domain to that in the next domain.

Development of domain theory

Main article:Domain theory of ferromagnetism

Magnetic domain theory was developed by French physicist Pierre-Ernest Weiss[1] who in 1906

suggested their existence in ferromagnets.[2] He suggested that large number of atomic magnetic

moments (typically 1012-1018) were aligned parallel. The direction of alignment varies from
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domain to domain in a more or less random manner although certain crystallographic axis may

be preferred by the magnetic moments, called easy axes. Weiss still had to explain the reason for

the spontaneous alignment of atomic moments within aferromagnetic material, and he came upwith the so-called Weiss mean field : he assumed that a given magnetic moment in a material

experienced a very high effective magnetic field due to the magnetization of its neighbours. In

the original Weiss theory the mean field was proportional to the bulk magnetization M, so that

where is the mean field constant. However this is not applicable to ferromagnets due to the

variation of magnetization from domain to domain. In this case, the interaction field is

Where Ms is the saturation magnetization at 0K.

Later, the quantum theory made it possible to understand the microscopic origin of the Weissfield. The exchange interactionbetween localized spins favored a parallel (in ferromagnets) or an

anti-parallel (in anti-ferromagnets) state of neighbouring magnetic moments.

[edit] Energy considerations

Rotation of orientation and increase in size of magnetic domains due to an externally applied

field (compare Zeeman energy).

The existence of magnetic domains is a result of energy minimisation. Landau and Lifshitz [1]

proposed theoretical domain structures based on a minimum energy concept, which forms the

basis for modern domain theory. The primary reason for the existence of domains within a

crystal is that their formation reduces the magnetic free energy. In the simplest case for such a

crystal, the energy,E, is the sum of several free energy terms:

(3)

whereEex is the exchange energy,Ek is the magnetocrystalline anisotropy energy,E is the

magnetoelastic energy,ED is the magneto-static energy, andEH is the Zeeman energy, i.e. theenergy of the magnetic material in the presence of an external applied field. A wall energyEw
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could also be added. However, sinceEw comprisesEex andEk, it is not necessary to includeEw as

a separate term in the equation. [3]

Magneto-static energy: This is a self-energy, due to the interaction of the magnetic fieldcreated by the magnetization in some part of the sample on other parts of the same

sample. Intrinsically, it has exactly the same nature as the "Zeeman energy" but theinteraction of the material with itself is put in the magnetostatic energy whereas the

interaction with the external magnetic field is put in the "Zeeman energy". This energyterm is the only one responsible for the presence of magnetic domains in magnetic

materials. Minimizing its value requires that the magnetization in the material makes

closed loops, with the magnetization staying parallel to the sample edges.

Magnetoelastic anisotropy energy: This energy is due to the effect ofmagnetostriction,a slight change in the dimensions of the crystal when magnetized. This causes elastic

strains in the lattice, and the direction of magnetization that minimizes these strain

energies will be favoured.

Magnetocrystalline anisotropy energy: The crystal lattice is 'easy' to magnetize in some

directions and 'hard' to magnetize in others. Magnetization in the easy directions lowers

this energy.

Zeeman energy: Energy resulting from the interaction between the magnetic materialand an externally applied magnetic field.

[edit] Domain observation

There are many ways to observe magnetic domains. Each method has a different application

because not all domains are the same. In condensed matter, domains can be circular, square,irregular, elongated, and striped, all of which have varied sizes and dimensions. Large domains,

within the range of 25-100 micrometers can be easily seen by Kerr microscopy, which applies a

physical phenomenon called the magneto-optic Kerr effect. Other domains, such as domainswithin the range of a few nanometers can be documented by the use ofmagnetic force

microscopy.

1.1.3.2 Ferromagnetism. Weiss molecular field

Some materials present very strong magnetization, typically in the order of the saturation

magnetization, also in absence of external field, i.e. they present spontaneous magnetization.

This kind of materials are referred to asferromagnetic materials (Fe, Co, Ni, Gd, alloys, etc.).Typical properties of some ferromagnetic materials can be found in Appendix A. The behavior

of very small regions of ferromagnetic materials can be treated by following the same line of

reasoning used for paramagnetism. With respect to the continuum model introduced in

section 1.1.1, we are now dealing with phenomena occurring inside our elementary volume ,which involve the interactions between single spins. Here we report the theory developed by

Weiss which is very similar to the one used for paramagnetism. In fact, the main difference stays
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in the postulation of an additional magnetic field w whose non magnetic (Maxwellian) origin

is not investigated. This field was called molecular fieldby Weiss [8]; by adding the field w

w ( w is characteristic of the material) to the external field in Eq. (1.24), one ends up

with the following equation:

(1.28)

The latter equation can be linearized for high temperatures, which corresponds to small as seen

before. Then, one can find the well-known Curie-Weiss law that once again expresses thedependance of the susceptibility on the temperature

(1.29)

where is the Curie temperature, characteristic of the material. Thus, for temperatures

the ferromagnetic materials behave like paramagnetic. For temperature , one can use

Eq. (1.28) to derive the relationship between the saturation magnetization and the

temperature . The resulting relationship behaves like in Fig. 1.2. This behaviorqualitatively matches with experimental observations [5].

Figure 1.2: Typical behavior of spontaneous magnetization as function of temperature.

In addition, the phenomenological approach of molecular field was theoretically justified when

Heisenberg introduced the exchange interaction on the basis of quantum theory (1931).

Nevertheless, the Weiss theory gives information about the magnitude of magnetization, but

nothing can be said about the direction. In this respect micromagnetics has the purpose to find
http://wpage.unina.it/mdaquino/PhD_thesis/main/node96.html#Weisshttp://wpage.unina.it/mdaquino/PhD_thesis/main/node8.html#eq:langevinhttp://wpage.unina.it/mdaquino/PhD_thesis/main/node9.html#eq:Weisshttp://wpage.unina.it/mdaquino/PhD_thesis/main/node9.html#fig:Weisshttp://wpage.unina.it/mdaquino/PhD_thesis/main/node96.html#Aharoni_bookhttp://wpage.unina.it/mdaquino/PhD_thesis/main/node96.html#Weisshttp://wpage.unina.it/mdaquino/PhD_thesis/main/node8.html#eq:langevinhttp://wpage.unina.it/mdaquino/PhD_thesis/main/node9.html#eq:Weisshttp://wpage.unina.it/mdaquino/PhD_thesis/main/node9.html#fig:Weisshttp://wpage.unina.it/mdaquino/PhD_thesis/main/node96.html#Aharoni_book


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the direction of magnetization at every location within the magnetic body. In this respect, for

constant temperature, the magnetization vector field can be written as

(1.30)

where is the magnetization unit-vector field.

Hysterisis curve:

Magnetic hysteresis

Hysteresis is well known in ferromagnetic materials. When an externalmagnetic field is applied

to a ferromagnet, the atomicdipolesalign themselves with the external field. Even when theexternal field is removed, part of the alignment will be retained: the material has becomemagnetized. For example, a piece ofiron that is brought into a magnetic field retains somemagnetization, even after the external magnetic field is removed. Once magnetized, the iron will

stay magnetized indefinitely. To demagnetize the iron, it would be necessary to apply a magnetic

field in the opposite direction. This is the effect that provides the element of memory in a harddisk drive.

Fig. 2. A family of B-H loops for grain-oriented electrical steel in sinusoidally varying

fields with amplitudes from 0.3 T to 1.7 T. BR denotes remanence and HC is the

coercivity.

The relationship between magnetic field strength (H) and magnetic flux density (B) - Fig. 2, isnot linear in such materials. If the relationship between the two is plotted for increasing levels of

field strength, it will follow a curve up to a point where further increases in magnetic field
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strength will result in no further change in flux density. This condition is calledmagnetic

saturation.

If the magnetic field is now reduced linearly, the plotted relationship will follow a different curveback towards zero field strength at which point it will be offset from the original curve by an

amount called the remanent flux density orremanence.

If this relationship is plotted for all strengths of applied magnetic field the result is a sort ofS-shapedloop. The width of the middle section of the loop describes the amount of hysteresis,related to the coercivity of the material.

Its practical effects might be, for example, to cause a relay to be slow to release due to the

remaining magnetic field continuing to attract the armature when the applied electric current to

the operating coil is removed.

This curve for a particular material influences the design of a magnetic circuit,

This is also a very important effect inmagnetic tape and other magnetic storage media likehard

disks. In these materials it would seem obvious to have one polarity represent a bit, say north for

1 and south for 0. However, to change the storage from one to the other, the hysteresis effect

requires the knowledge of what was already there, because the needed field will be different ineach case. In order to avoid this problem, recording systems first overdrive the entire system into

a known state using a process known asbias. Analog magnetic recording also uses this

technique. Different materials require different biasing, which is why there is a selector switchfor this on the front of most cassette recorders.

In order to minimize this effect and the energy losses associated with it, ferromagnetic

substances with low coercivity and low hysteresis loss are used, likepermalloy.

In many applications small hysteresis loops are driven around points in the B-H plane. Loopsnear the origin have a higher. The smaller loops the more they have a soft magnetic (lengthy)

shape. As a special case, a damped AC field demagnetizes any material provided it is initially

sufficiently intense.

Magnetic field hysteresis loss causes heating.[2] This is an energy loss mechanism in powertransformers and electric motors and other apparatus using ferromagnetic cores.

Soft and Hard magnetic materials

Types of magnetic material

Most of magnetic materials of industrial interests are ferromagenetic materials. The ferromagneticmaterials can be categorized into two; one is soft magnetic materials and the other is hard magneticmaterials. As shown in the magnetization curve, ferromagnetic materials with the demagnetized statedoes not show magnetization although they have spontaneous magnetization. This is because theferromagnetic materials are divided into many magnetic domains. Within the magnetic domains, the
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direction of magnetic moment is aligened. However, the direction of magnetic moments vary at magneticdomain walls so that it can reduce the magnetostatic energy in the total volume. In the demagnetizedstate, total magnetization is cancelled because of the random orientation of the magnetizations inmagnetic domains. When external magnetic field is applied, domain walls migrate and disappear when allmagnetic moments are aligened to the direction of the magnetic field. When all magnetic domains arewiped away and magnetizations are all aligned to the direction of the magnetic field, magnetization issaturated. This magnetization is called saturation magnetization, Ms.

When domain wall can easily migrate, the ferromagnetic material can be easily magnetized at lowmagnetic filed. This type of ferromagnetic materials are called soft magnetic material, and is suitable forapplications of magnetic cores or recording heads. Since soft magnetic materials can be demagnetized atlow magnetic field, coercivity Hc is low. As they can be easily magnetized, permeability is high. Forferromagnetic materials to be soft, their magnetocrystalline anisotropy and magnetostriction constantmust be low. In addition, for easy migration of magnetic domains, they must have small number of defectssuch as crytal grains.

When domain wall is difficult to migrate, magnetization of the ferromagnetic material occurs only whenhigh magnetic field is applied. In other words, this type of ferromagnetic materials are difficult otmagnetize, but once magnetized, it is difficult to demagnetize. These materials are called hard magneticmaterials, and are suitable for applications such as permanent magnets and magnetic recording media.

Hard magnetic materials have high magnetocrystalline anisotropy. Since large magnetic field is requiredto demagnetize, their coercivity Hc is usually high, but coercivity is highly sensitive to themicrostructurure.

Documents

Magnetism is a Property of Materials That Respond at an Atomic or Subatomic Level to an Applied Magnetic Field