![Ferrimagnetic ordering](https://upload.wikimedia.org/wikipedia/commons/8/81/Ferrimagnetic_ordering.svg)
A ferrimagnetic material is a material that has populations of atoms with opposing
magnetic moment
In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electroma ...
s, as in
antiferromagnetism
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. ...
, but these moments are unequal in magnitude so a
spontaneous magnetization
Spontaneous magnetization is the appearance of an ordered spin state ( magnetization) at zero applied magnetic field in a ferromagnetic or ferrimagnetic material below a critical point called the Curie temperature or .
Overview
Heated to temper ...
remains. This can for example occur when the populations consist of different
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, a ...
s or
ions (such as Fe
2+ and Fe
3+).
Ferrimagnetism has often been confused with
ferromagnetism
Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
. The oldest known magnetic substance,
magnetite
Magnetite is a mineral and one of the main iron ores, with the chemical formula Fe2+Fe3+2O4. It is one of the oxides of iron, and is ferrimagnetic; it is attracted to a magnet and can be magnetized to become a permanent magnet itself. With ...
(Fe
3O
4), was classified as a ferromagnet before
Louis Néel discovered ferrimagnetism in 1948. Since the discovery, numerous uses have been found for ferrimagnetic materials, such as
hard drive platters and
biomedical
Biomedicine (also referred to as Western medicine, mainstream medicine or conventional medicine) applications.
History
Until the twentieth century, all naturally occurring magnetic substances were called ferromagnets. In 1936,
Louis Néel published a paper proposing the existence of a new form of cooperative magnetism he called antiferromagnetism. While working with Mn
2Sb, French physicist Charles Guillaud discovered that the current theories on magnetism were not adequate to explain the behavior of the material, and made a model to explain the behavior. In 1948, Néel published a paper about a third type of cooperative magnetism, based on the assumptions in Guillaud's model. He called it ferrimagnetism. In 1970, Néel was awarded for his work in magnetism with the
Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
.
Physical origin
![Ferrimagnetism - magnetic moment as a function of temperature](https://upload.wikimedia.org/wikipedia/commons/c/c4/Ferrimagnetism_-_magnetic_moment_as_a_function_of_temperature.svg)
Ferrimagnetism has the same physical origins as
ferromagnetism
Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
and
antiferromagnetism
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. ...
. In ferrimagnetic materials the magnetization is also caused by a combination of dipole-dipole interactions and exchange interactions resulting from the
Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formula ...
. The main difference is that in ferrimagnetic materials there are different types of atoms in the material's
unit cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
. An example of this can be seen in the figure on the right. Here the atoms with a smaller magnetic moment point in the opposite direction of the larger moments. This arrangement is similar to that present in antiferromagnetic materials, but in ferrimagnetic materials the net moment is nonzero because the opposed moments differ in magnitude.
Ferrimagnets have a critical temperature above which they become
paramagnetic
Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, ...
just as ferromagnets do. At this temperature (called the
Curie temperature
In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Cur ...
) there is a second order phase transition and the system can no longer maintain a spontaneous magnetization. This is because at higher temperatures the thermal motion is strong enough that it exceeds the tendency of the dipoles to align.
Derivation
There are various ways to describe ferrimagnets, the simplest of which is with
mean-field theory
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of ...
. In mean-field theory the field acting on the atoms can be written as:
Where
is the
applied magnetic field and
is field caused by the interactions between the atoms. The following assumption then is:
Here
is the average magnetization of the lattice and
is the molecular field coefficient. When we allow
and
to be position and orientation dependent we can then write it in the form:
Here
is the field acting on the i
th substructure and
is the molecular field coefficient between the i
th and the k
th substructure. For a diatomic lattice we can designate two types of sites, A and B. We can designate
the number of magnetic ions per unit volume,
the fraction of the magnetic ions on the A sites, and
the fraction on the B sites. This then gives:
It can be shown that
and that
unless the structures are identical.
favors a parallel alignment of
and
, while
favors an anti-parallel alignment. For ferrimagnets,
, so it will be convenient to take
as a positive quantity and write the minus sign explicitly in front of it. For the total fields on A and B this then gives:
Furthermore we will introduce the parameters
and
which give the ratio between the strengths of the interactions. At last we will introduce the reduced magnetizations:
with
the spin of the i
th element. This then gives for the fields:
The solutions to these equations (omitted here) are then given by
where
is the
Brillouin function. The simplest case to solve now is
. Since
. This then gives the following pair of equations:
with
and
. These equations do not have a known analytical solution, so they must be solved numerically to find the temperature dependence of
.
Effects of temperature
Unlike ferromagnetism, the shapes of the magnetization curves of ferrimagnetism can take many different shapes depending on the strength of the interactions and the relative abundance of atoms. The most notable instances of this property are that the direction of magnetization can reverse while heating a ferrimagnetic material from
absolute zero
Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibra ...
to its critical temperature, and that strength of magnetization can increase while heating a ferrimagnetic material to the critical temperature, both of which cannot occur for ferromagnetic materials. These temperature dependencies have also been experimentally observed in NiFe
2/5Cr
8/5O
4 and Li
1/2Fe
5/4Ce
5/4O
4.
A temperature lower than the
Curie temperature
In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Cur ...
, but at which the opposing magnetic moments are equal (resulting in a net magnetic moment of zero) is called a magnetization compensation point. This compensation point is observed easily in garnets and rare-earth–transition-metal alloys (RE-TM). Furthermore, ferrimagnets may also have an
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
compensation point, at which the net angular momentum vanishes. This compensation point is a crucial point for achieving high speed magnetization reversal in magnetic memory devices.
Effect of external fields
When ferrimagnets are exposed to an external magnetic field, they display what is called
magnetic hysteresis
Magnetic hysteresis occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become '' ...
, where magnetic behavior depends on the history of the magnet. They also exhibit a saturation magnetization
; this magnetization is reached when the external field is strong enough to make all the moments align in the same direction. When this point is reached, the magnetization cannot increase as there are no more moments to align. When the external field is removed, the magnetization of the ferrimagnet will not disappear but a nonzero magnetization will remain. This effect is often used in applications of magnets. If an external field in the opposite direction is applied subsequently, the magnet will demagnetize further until it eventually reaches a magnetization of
. This behavior results in what is called a ''hysteresis loop''.
Properties and uses
Ferrimagnetic materials have high
resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
and have
anisotropic
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
properties. The
anisotropy
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
is actually induced by an external applied field. When this applied field aligns with the magnetic dipoles, it causes a net magnetic dipole moment and causes the magnetic dipoles to
precess
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
at a frequency controlled by the applied field, called ''
Larmor'' or ''
precession frequency''. As a particular example, a
microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
signal
circularly polarized
In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to t ...
in the same direction as this precession strongly interacts with the
magnetic dipole moments; when it is polarized in the opposite direction, the interaction is very low. When the interaction is strong, the microwave signal can pass through the material. This directional property is used in the construction of microwave devices like
isolators,
circulator
A circulator is a passive, non-reciprocal three- or four-port device that only allows a microwave or radio-frequency signal to exit through the port directly after the one it entered. Optical circulators have similar behavior. Ports are where an ...
s, and
gyrator
A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conventio ...
s. Ferrimagnetic materials are also used to produce
optical isolator
An optical isolator, or optical diode, is an optical component which allows the transmission of light in only one direction. It is typically used to prevent unwanted feedback into an optical oscillator, such as a laser cavity.
The operation ...
s and
circulators
A circulator is a passive, non-reciprocal three- or four-port device that only allows a microwave or radio-frequency signal to exit through the port directly after the one it entered. Optical circulators have similar behavior. Ports are where an ...
. Ferrimagnetic minerals in various rock types are used to study ancient geomagnetic properties of Earth and other planets. That field of study is known as
paleomagnetism
Paleomagnetism (or palaeomagnetismsee ), is the study of magnetic fields recorded in rocks, sediment, or archeological materials. Geophysicists who specialize in paleomagnetism are called ''paleomagnetists.''
Certain magnetic minerals in rock ...
. In addition, it has been shown that ferrimagnets such as
magnetite
Magnetite is a mineral and one of the main iron ores, with the chemical formula Fe2+Fe3+2O4. It is one of the oxides of iron, and is ferrimagnetic; it is attracted to a magnet and can be magnetized to become a permanent magnet itself. With ...
can be used for
thermal energy storage
Thermal energy storage (TES) is achieved with widely different technologies. Depending on the specific technology, it allows excess thermal energy to be stored and used hours, days, months later, at scales ranging from the individual process, ...
.
Examples
The oldest known magnetic material,
magnetite
Magnetite is a mineral and one of the main iron ores, with the chemical formula Fe2+Fe3+2O4. It is one of the oxides of iron, and is ferrimagnetic; it is attracted to a magnet and can be magnetized to become a permanent magnet itself. With ...
, is a ferrimagnetic substance. The
tetrahedral
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
and
octahedral
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
sites of its crystal structure exhibit opposite spin. Other known ferrimagnetic materials include
yttrium iron garnet
Yttrium iron garnet (YIG) is a kind of synthetic garnet, with chemical composition , or Y3Fe5O12. It is a ferrimagnetic material with a Curie temperature of 560 K. YIG may also be known as yttrium ferrite garnet, or as iron yttrium oxide or ...
(YIG); cubic ferrites composed of
iron oxide
Iron oxides are chemical compounds composed of iron and oxygen. Several iron oxides are recognized. All are black magnetic solids. Often they are non-stoichiometric. Oxyhydroxides are a related class of compounds, perhaps the best known of whic ...
s with other elements such as
aluminum
Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It has ...
,
cobalt
Cobalt is a chemical element with the symbol Co and atomic number 27. As with nickel, cobalt is found in the Earth's crust only in a chemically combined form, save for small deposits found in alloys of natural meteoric iron. The free element, pr ...
,
nickel
Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow to ...
,
manganese
Manganese is a chemical element with the symbol Mn and atomic number 25. It is a hard, brittle, silvery metal, often found in minerals in combination with iron. Manganese is a transition metal with a multifaceted array of industrial alloy use ...
, and
zinc
Zinc is a chemical element with the symbol Zn and atomic number 30. Zinc is a slightly brittle metal at room temperature and has a shiny-greyish appearance when oxidation is removed. It is the first element in group 12 (IIB) of the periodi ...
; and hexagonal or spinel type ferrites, including Rhenium Ferrite, ReFe
2O
4, PbFe
12O
19 and BaFe
12O
19 and
pyrrhotite
Pyrrhotite is an iron sulfide mineral with the formula Fe(1-x)S (x = 0 to 0.2). It is a nonstoichiometric variant of FeS, the mineral known as troilite.
Pyrrhotite is also called magnetic pyrite, because the color is similar to pyrite and it is ...
, Fe
1−xS.
Ferrimagnetism can also occur in
single-molecule magnets. A classic example is a dodecanuclear
manganese
Manganese is a chemical element with the symbol Mn and atomic number 25. It is a hard, brittle, silvery metal, often found in minerals in combination with iron. Manganese is a transition metal with a multifaceted array of industrial alloy use ...
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
with an effective spin ''S'' = 10 derived from antiferromagnetic interaction on Mn(IV) metal centers with Mn(III) and Mn(II) metal centers.
See also
*
*
References
External links
*
{{Magnetic states
Magnetic ordering
Quantum phases