Single domain (magnetic)
Encyclopedia
Single domain, in magnetism
, refers to the state of a ferromagnet in which the magnetization
does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a single domain particle (but other definitions are possible; see below). Such particles are very small (generally below a micrometre
in diameter). They are also very important in a lot of applications because they have a high coercivity
. They are the main source of hardness in hard magnets, the carriers of magnetic memory
in tape drives, and the best recorders of the ancient Earth's magnetic field
(see paleomagnetism
).
in ferromagnets assumed that ferromagnets are divided into magnetic domains
and that the magnetization changed by the movement of domain wall
s. However, as early as 1930, Frenkel and Dorfman predicted that sufficiently small particles could only hold one domain, although they greatly overestimated the upper size limit for such particles. The possibility of single domain particles received little attention until two developments in the late 1940's: (1) Improved calculations of the upper size limit by Kittel and Néel, and (2) a calculation of the magnetization curves for systems of single-domain particles by Stoner and Wohlfarth. The Stoner–Wohlfarth model has been enormously influential in subsequent work and is still frequently cited.
is consistent with the single-domain state. More recently it was realized that a particle's state could be single-domain for some range of magnetic fields and then change continuously into a non-uniform state.
Another common definition of single-domain particle is one in which the single-domain state has the lowest energy of all possible states (see below).
is pointed in the same direction. It therefore has the largest possible magnetic moment
for a particle of that size and composition. The magnitude of this moment is
, where 
is the volume of the particle and 
is the saturation magnetization.
The magnetization at any point in a ferromagnet can only change by rotation. If there is more than one magnetic domain, the transition between one domain and its neighbor involves a rotation of the magnetization to form a domain wall
. Domain walls move easily within the magnet and have a low coercivity
. By contrast, a particle that is single-domain in all magnetic fields changes its state by rotation of all the magnetization as a unit. This results in a much larger coercivity
.
The most widely used theory for hysteresis in single-domain particle is the Stoner–Wohlfarth model. This applies to a particle with uniaxial magnetocrystalline anisotropy
.
nanometers and 
nanometers. The size range is bounded below by the transition to superparamagnetism
and above by the formation of multiple magnetic domains
.
cause the magnetization
to dance around in a random manner. In the single-domain state, the moment rarely strays far from the local stable state. Energy barriers (see also activation energy
) prevent the magnetization from jumping from one state to another. However, if the energy barrier gets small enough, the moment can jump from state to state frequently enough to make the particle superparamagnetic. The frequency of jumps has a strong exponential dependence on the energy barrier, and the energy barrier is proportional to the volume, so there is a critical volume at which the transition occurs. This volume can be thought of as the volume at which the blocking temperature
is at room temperature.
. This field tends to rotate the magnetization in a way that reduces the total moment of the magnet, and in larger magnets the magnetization is organized in magnetic domains
. The demagnetizing energy is balanced by the energy of the exchange interaction
, which tends to keep spins aligned. There is a critical size at which the balance tips in favor of the demagnetizing field and the multidomain
state is favored. Most calculations of the upper size limit for the single-domain state identify it with this critical size.
Magnetism
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 of permanent magnets, which produce their own persistent magnetic fields, as well...
, refers to the state of a ferromagnet in which the magnetization
Magnetization
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...
does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a single domain particle (but other definitions are possible; see below). Such particles are very small (generally below a micrometre
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...
in diameter). They are also very important in a lot of applications because they have a high coercivity
Coercivity
In 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...
. They are the main source of hardness in hard magnets, the carriers of magnetic memory
Magnetic memory
Magnetic memory may refer to:* Magnetic storage, the storage of data on a magnetized medium* Remanence, or residual magnetization, the magnetization left behind in a ferromagnet after an external magnetic field is removed...
in tape drives, and the best recorders of the ancient Earth's magnetic field
Earth's magnetic field
Earth's magnetic field is the magnetic field that extends from the Earth's inner core to where it meets the solar wind, a stream of energetic particles emanating from the Sun...
(see paleomagnetism
Paleomagnetism
Paleomagnetism is the study of the record of the Earth's magnetic field in rocks. Certain minerals in rocks lock-in a record of the direction and intensity of the magnetic field when they form. This record provides information on the past behavior of Earth's magnetic field and the past location of...
).
History
Early theories of 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...
in ferromagnets assumed that ferromagnets are divided into magnetic domains
Magnetic domains
A magnetic domain describes a region within a magnetic material which has uniform magnetization. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction...
and that the magnetization changed by the movement of domain wall
Domain 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,...
s. However, as early as 1930, Frenkel and Dorfman predicted that sufficiently small particles could only hold one domain, although they greatly overestimated the upper size limit for such particles. The possibility of single domain particles received little attention until two developments in the late 1940's: (1) Improved calculations of the upper size limit by Kittel and Néel, and (2) a calculation of the magnetization curves for systems of single-domain particles by Stoner and Wohlfarth. The Stoner–Wohlfarth model has been enormously influential in subsequent work and is still frequently cited.
Definitions of a single-domain particle
Early investigators pointed out that a single-domain particle could be defined in more than one way. Perhaps most commonly, it is implicitly defined as a particle that is in a single-domain state throughout the hysteresis cycle, including during the transition between two such states. This is the type of particle that is modeled by the Stoner–Wohlfarth model. However, it might be in a single-domain state except during reversal. Often particles are considered single-domain if their saturation remanenceRemanence
Remanence or remanent magnetization is the magnetization left behind in a ferromagnetic material after an external magnetic field is removed. It is also the measure of that magnetization. Colloquially, when a magnet is "magnetized" it has remanence...
is consistent with the single-domain state. More recently it was realized that a particle's state could be single-domain for some range of magnetic fields and then change continuously into a non-uniform state.
Another common definition of single-domain particle is one in which the single-domain state has the lowest energy of all possible states (see below).
Single domain hysteresis
If a particle is in the single-domain state, all of its internal 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...
is pointed in the same direction. It therefore has the largest possible magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
for a particle of that size and composition. The magnitude of this moment is
, where is the volume of the particle and is the saturation magnetization.The magnetization at any point in a ferromagnet can only change by rotation. If there is more than one magnetic domain, the transition between one domain and its neighbor involves a rotation of the magnetization to form a domain wall
Domain 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,...
. Domain walls move easily within the magnet and have a low coercivity
Coercivity
In 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...
. By contrast, a particle that is single-domain in all magnetic fields changes its state by rotation of all the magnetization as a unit. This results in a much larger coercivity
Coercivity
In 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...
.
The most widely used theory for hysteresis in single-domain particle is the Stoner–Wohlfarth model. This applies to a particle with uniaxial magnetocrystalline anisotropy
Magnetocrystalline anisotropy
Magnetocrystalline anisotropy is the dependence of the internal energy of a ferromagnet on the direction of its magnetization. As a result, certain crystallographic directions are preferred directions, or easy axes, for the magnetization. It is a special case of magnetic anisotropy...
.
Limits on the single-domain size
The size range for which a ferromagnet is single-domain is generally quite narrow. For most magnets it is between about nanometers and nanometers. The size range is bounded below by the transition to superparamagnetismSuperparamagnetism
Superparamagnetism is a form of magnetism, which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the Néel relaxation time...
and above by the formation of multiple magnetic domains
Magnetic domains
A magnetic domain describes a region within a magnetic material which has uniform magnetization. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction...
.
Lower limit: superparamagnetism
Thermal fluctuationsThermal fluctuations
In statistical mechanics, thermal fluctuations are random deviations of a system from its equilibrium. All thermal fluctuations become larger and more frequent as the temperature increases, and likewise they disappear altogether as temperature approaches absolute zero.Thermal fluctuations are a...
cause the magnetization
Magnetization
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...
to dance around in a random manner. In the single-domain state, the moment rarely strays far from the local stable state. Energy barriers (see also activation energy
Activation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...
) prevent the magnetization from jumping from one state to another. However, if the energy barrier gets small enough, the moment can jump from state to state frequently enough to make the particle superparamagnetic. The frequency of jumps has a strong exponential dependence on the energy barrier, and the energy barrier is proportional to the volume, so there is a critical volume at which the transition occurs. This volume can be thought of as the volume at which the blocking temperature
Superparamagnetism
Superparamagnetism is a form of magnetism, which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the Néel relaxation time...
is at room temperature.
Upper limit: transition to multiple domains
As size of a ferromagnet increases, the single-domain state incurs an increasing energy cost because of the demagnetizing fieldDemagnetizing field
The demagnetizing field, also called the stray field, is the magnetic field generated by the magnetization in a magnet. The total magnetic field in a region containing magnets is the sum of the demagnetizing fields of the magnets and the magnetic field due to any free currents or displacement...
. This field tends to rotate the magnetization in a way that reduces the total moment of the magnet, and in larger magnets the magnetization is organized in magnetic domains
Magnetic domains
A magnetic domain describes a region within a magnetic material which has uniform magnetization. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction...
. The demagnetizing energy is balanced by the energy of the exchange interaction
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...
, which tends to keep spins aligned. There is a critical size at which the balance tips in favor of the demagnetizing field and the multidomain
Magnetic domains
A magnetic domain describes a region within a magnetic material which has uniform magnetization. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction...
state is favored. Most calculations of the upper size limit for the single-domain state identify it with this critical size.