Domain theory of ferromagnetism
Encyclopedia
Domain theory of ferromagnetism explains two significant observations of materials such as iron:
For example, when a refrigerator magnet
is
applied to a refrigerator door,
the iron under the magnet becomes magnetized,
causing the magnet to be attracted to the door.
When the magnet is removed, the spot on the door loses its magnetization.
According to domain theory, quantum mechanical exchange forces
make magnetic moments of nearby atoms tend to point in the same direction. Collections of nearby atoms pointing in the same direction are called magnetic domains. Over longer distances, domains point in random directions, canceling each other, and leaving the material unmagnetized. When an external magnetic field is applied, the domains line up in the direction of the field, and add to the external field. Although an external field would have little influence on individual atoms, it has a stronger effect on the atoms in a domain, because they all point the same way. This explains why a weak external field, can cause a ferromagnetic material to become strongly magnetized.
Below a certain temperature called the Curie temperature, quantum mechanical exchange forces overcome thermal energy, which would otherwise randomize the magnetic moments of individual atoms.
The existence of sufficient exchange forces in some materials makes them ferromagnetic
.
Each ferromagnetic material has a unique Curie temperature.
Above the Curie temperature thermal energy dominates, and the material becomes paramagnetic
. Domain theory also explains other magnetic properties, such as the existence of permanent magnets.
This is easy to demonstrate. When two bar magnets are lined up next to each other, with their north poles pointing in the same direction, they will tend to spin around with the north pole of one magnet next to the south pole of the other magnet. The energy to spin the magnets around, came from magnetic fields. After spinning around, the system contains less energy, and is more stable.
As ferromagnetic domains become smaller, the material has less magnetic energy, however, the exchange energy increases, because atoms on opposite sides of the domain boundaries are not pointing in the same direction. The magnetic energy goes down as the number of domains increases, but the energy at the boundaries goes up in proportion to the surface area of the boundaries.
There are several types of energies the influence the size, shape, and orientation of domains:
which makes adjacent dipole
s
line up in the same direction is called exchange energy.
energy depends upon the direction of magnetization. This direction dependency is called Magnetic anisotropy
, and the directions are called easy and hard:
For example, iron atoms are arranged in a
cubic
latice,
and the easy direction is along the
<100> edges
of the cube,
with the hard directions along the
face diagonals <110>.
Nickel is also cubic, but the easy direction is
along the body <111> diagonals of the cube,
with the hard direction along the <100> edges.
is a transition layer which separates the adjacent domains magnetised in different directions. Domain wall energy is due to both exchange energy and anisotropy energy.
and energy produced is called magnetostriction energy.
. It is understandable from the thermodynamic principle
.
- The material may become strongly magnetized by application of a weak external magnetizing field.
- The same specimen may return to the demagnetized state when the external field is removed.
For example, when a refrigerator magnet
Refrigerator magnet
A refrigerator magnet is an ornament, often whimsical, attached to a small magnet which is used to post items such as shopping lists or report cards on a refrigerator door, or which simply serves as decoration. Refrigerator magnets come in a wide variety of shapes and sizes, including but not...
is
applied to a refrigerator door,
the iron under the magnet becomes magnetized,
causing the magnet to be attracted to the door.
When the magnet is removed, the spot on the door loses its magnetization.
According to domain theory, quantum mechanical exchange forces
Exchange interaction
In physics, the exchange interaction is a quantum mechanical effect without classical analog which increases or decreases the expectation value of the energy or distance between two or more identical particles when their wave functions overlap...
make magnetic moments of nearby atoms tend to point in the same direction. Collections of nearby atoms pointing in the same direction are called magnetic domains. Over longer distances, domains point in random directions, canceling each other, and leaving the material unmagnetized. When an external magnetic field is applied, the domains line up in the direction of the field, and add to the external field. Although an external field would have little influence on individual atoms, it has a stronger effect on the atoms in a domain, because they all point the same way. This explains why a weak external field, can cause a ferromagnetic material to become strongly magnetized.
Below a certain temperature called the Curie temperature, quantum mechanical exchange forces overcome thermal energy, which would otherwise randomize the magnetic moments of individual atoms.
The existence of sufficient exchange forces in some materials makes them ferromagnetic
Ferromagnetism
Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...
.
Each ferromagnetic material has a unique Curie temperature.
Above the Curie temperature thermal energy dominates, and the material becomes paramagnetic
Paramagnetism
Paramagnetism is a form of magnetism whereby the paramagnetic material is only attracted when in the presence of an externally applied magnetic field. In contrast with this, diamagnetic materials are repulsive when placed in a magnetic field...
. Domain theory also explains other magnetic properties, such as the existence of permanent magnets.
Energy minimization
A system is more stable, when it contains less energy. A magnetic field contains energy. When magnetic fields cancel each other, they contain less energy.This is easy to demonstrate. When two bar magnets are lined up next to each other, with their north poles pointing in the same direction, they will tend to spin around with the north pole of one magnet next to the south pole of the other magnet. The energy to spin the magnets around, came from magnetic fields. After spinning around, the system contains less energy, and is more stable.
As ferromagnetic domains become smaller, the material has less magnetic energy, however, the exchange energy increases, because atoms on opposite sides of the domain boundaries are not pointing in the same direction. The magnetic energy goes down as the number of domains increases, but the energy at the boundaries goes up in proportion to the surface area of the boundaries.
There are several types of energies the influence the size, shape, and orientation of domains:
Exchange energy
The interaction of energyEnergy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
which makes adjacent dipole
Dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
s
line up in the same direction is called exchange energy.
Anisotropy energy
In ferromagnetic crystals the magnetizationMagnetization
In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material...
energy depends upon the direction of magnetization. This direction dependency is called Magnetic anisotropy
Magnetic anisotropy
Magnetic anisotropy is the direction dependence of a material's magnetic properties. In the absence of an applied magnetic field, a magnetically isotropic material has no preferential direction for its magnetic moment while a magnetically anisotropic material will align its moment with one of the...
, and the directions are called easy and hard:
- Easy direction, a weak magnetic fieldMagnetic fieldA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
has to be applied. - Hard direction, a strong magnetic field has to be applied.
For example, iron atoms are arranged in a
cubic
Cubic crystal system
In crystallography, the cubic crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals....
latice,
and the easy direction is along the
<100> edges
Miller index
Miller indices form a notation system in crystallography for planes and directions in crystal lattices.In particular, a family of lattice planes is determined by three integers h, k, and ℓ, the Miller indices. They are written , and each index denotes a plane orthogonal to a direction in the...
of the cube,
with the hard directions along the
face diagonals <110>.
Nickel is also cubic, but the easy direction is
along the body <111> diagonals of the cube,
with the hard direction along the <100> edges.
Domain wall energy
Domain wallDomain wall
A domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...
is a transition layer which separates the adjacent domains magnetised in different directions. Domain wall energy is due to both exchange energy and anisotropy energy.
Magnetostrictive energy
When domain walls are magnetized in different directions, they will either expand or shrink. This results in deformation. This effect is called magnetostrictionMagnetostriction
Magnetostriction is a property of ferromagnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of material's magnetization due to the applied magnetic field changes the magnetostrictive strain until reaching its saturation value, λ...
and energy produced is called magnetostriction energy.
Magnetostatic energy
- The self-energy of a permanent magnet acting on its own field.
- The energy of interaction of a permanent magnet acting an external field.
History
Domain theory of ferromagnetism was developed by Pierre WeissPierre Weiss
Pierre-Ernest Weiss was a French physicist who developed the domain theory of ferromagnetism in 1907. Weiss domains and the Weiss magneton are named after him. Weiss also developed the Molecular or Mean field theory, which is often called Weiss-mean-field theory.Weiss was born in Mulhouse and...
. It is understandable from the thermodynamic principle
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
.
See also
- Bohr–van Leeuwen theoremBohr–van Leeuwen theoremThe Bohr–van Leeuwen theorem is a theorem in the field of statistical mechanics. The theorem shows that when statistical mechanics and classical mechanics are applied consistently, the thermal average of the magnetization is always zero...
proves classical physics cannot account for ferromagnetism - ferromagnetismFerromagnetismFerromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...
- Magnetic domain
- Bloch wallBloch wallA Bloch wall is a narrow transition region at the boundary between magnetic domains, over which the magnetization changes from its value in one domain to that in the next. The magnetization rotates along an axis that is perpendicular to the plane of the wall unlike the Néel wall where the...
- Domain wallDomain wallA domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...
- Weiss domain
- Weiss magnetonWeiss magnetonThe Weiss magneton was an experimentally derived unit of magnetic moment equal to joules per tesla, which is about 20% of the Bohr magneton. It was suggested in 1911 by Pierre Weiss.-Origin:...
- Bohr magneton
- Barkhausen effectBarkhausen effectThe Barkhausen effect is a name given to the noise in the magnetic output of a ferromagnet when the magnetizing force applied to it is changed...
- CoercivityCoercivityIn materials science, the coercivity, also called the coercive field or coercive force, of a ferromagnetic material is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation...