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In materials that exhibit antiferromagnetism, the
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 electromagnets ...
s of
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, and ...
s or
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 ...
s, usually related to the spins of
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s, align in a regular pattern with neighboring
spins The spins (as in having "the spins")Diane Marie Leiva. ''The Florida State University College of Education''Women's Voices on College Drinking: The First-Year College Experience"/ref> is an adverse reaction of intoxication that causes a state of v ...
(on different sublattices) pointing in opposite directions. This is, like
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
ferrimagnetism A ferrimagnetic material is a material that has populations of atoms with opposing magnetic moments, as in antiferromagnetism, but these moments are unequal in magnitude so a spontaneous magnetization remains. This can for example occur when t ...
, a manifestation of ordered
magnetism Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
. The phenomenon of antiferromagnetism was first introduced by
Lev Landau Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet- Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His a ...
in 1933. Generally, antiferromagnetic order may exist at sufficiently low temperatures, but vanishes at and above the
Néel 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 ...
– named after
Louis Néel Louis Eugène Félix Néel (22 November 1904 – 17 November 2000) was a French physicist born in Lyon who received the Nobel Prize for Physics in 1970 for his studies of the magnetic properties of solids. Biography Néel studied at the Lycée ...
, who had first identified this type of magnetic ordering. Above the Néel temperature, the material is typically
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, d ...
.


Measurement

When no external field is applied, the antiferromagnetic structure corresponds to a vanishing total magnetization. In an external magnetic field, a kind of
ferrimagnetic A ferrimagnetic material is a material that has populations of atoms with opposing magnetic moments, as in antiferromagnetism, but these moments are unequal in magnitude so a spontaneous magnetization remains. This can for example occur when t ...
behavior may be displayed in the antiferromagnetic phase, with the absolute value of one of the sublattice magnetizations differing from that of the other sublattice, resulting in a nonzero net magnetization. Although the net magnetization should be zero at a temperature of
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 vibration ...
, the effect of
spin canting Some antiferromagnetic materials exhibit a non-zero 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 magn ...
often causes a small net magnetization to develop, as seen for example in
hematite Hematite (), also spelled as haematite, is a common iron oxide compound with the formula, Fe2O3 and is widely found in rocks and soils. Hematite crystals belong to the rhombohedral lattice system which is designated the alpha polymorph of . ...
. The
magnetic susceptibility In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ap ...
of an antiferromagnetic material typically shows a maximum at the Néel temperature. In contrast, at the transition between the
ferromagnetic 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 ...
to the
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, d ...
phases the susceptibility will diverge. In the antiferromagnetic case, a divergence is observed in the ''staggered susceptibility''. Various microscopic (exchange) interactions between the magnetic moments or spins may lead to antiferromagnetic structures. In the simplest case, one may consider an
Ising model The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent ...
on a bipartite lattice, e.g. the simple cubic lattice, with couplings between spins at nearest neighbor sites. Depending on the sign of that interaction,
ferromagnetic 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 ...
or antiferromagnetic order will result.
Geometrical frustration In condensed matter physics, the term geometrical frustration (or in short: frustration) refers to a phenomenon where atoms tend to stick to non-trivial positions or where, on a regular crystal lattice, conflicting inter-atomic forces (each one fa ...
or
competing Competition is a rivalry where two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, indivi ...
ferro- and antiferromagnetic interactions may lead to different and, perhaps, more complicated magnetic structures. The relationship between
magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
and the
magnetizing field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
is
non-linear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
like in
ferromagnetic materials 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 a ...
. This fact is due to the contribution of the
hysteresis loop Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
, which for ferromagnetic materials involves a
residual magnetization Remanence or remanent magnetization or residual magnetism is the magnetization left behind in a ferromagnetic material (such as iron) after an external magnetic field is removed. Colloquially, when a magnet is "magnetized", it has remanence. The ...
.


Antiferromagnetic materials

Antiferromagnetic structures were first shown through
neutron diffraction Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to o ...
of transition metal oxides such as nickel, iron, and manganese oxides. The experiments, performed by
Clifford Shull Clifford Glenwood Shull (September 23, 1915 in Pittsburgh, Pennsylvania – March 31, 2001) was a Nobel Prize-winning American physicist. Biography Shull attended Schenley High School in Pittsburgh, received his BS from Carnegie Institute of Tec ...
, gave the first results showing that magnetic dipoles could be oriented in an antiferromagnetic structure. Antiferromagnetic materials occur commonly among
transition metal In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that can ...
compounds, especially oxides. Examples include
hematite Hematite (), also spelled as haematite, is a common iron oxide compound with the formula, Fe2O3 and is widely found in rocks and soils. Hematite crystals belong to the rhombohedral lattice system which is designated the alpha polymorph of . ...
, metals such as
chromium Chromium is a chemical element with the symbol Cr and atomic number 24. It is the first element in group 6. It is a steely-grey, lustrous, hard, and brittle transition metal. Chromium metal is valued for its high corrosion resistance and hardne ...
, alloys such as iron manganese (FeMn), and oxides such as nickel oxide (NiO). There are also numerous examples among high nuclearity metal clusters. Organic molecules can also exhibit antiferromagnetic coupling under rare circumstances, as seen in radicals such as 5-dehydro-m-xylylene. Antiferromagnets can couple to
ferromagnets 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 ...
, for instance, through a mechanism known as
exchange bias Exchange bias or exchange anisotropy occurs in bilayers (or multilayers) of magnetic materials where the hard magnetization behavior of an antiferromagnetic thin film causes a shift in the soft magnetization curve of a ferromagnetic film. The ex ...
, in which the
ferromagnetic 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 ...
film is either grown upon the antiferromagnet or annealed in an aligning magnetic field, causing the surface atoms of the
ferromagnet 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 a ...
to align with the surface atoms of the antiferromagnet. This provides the ability to "pin" the orientation of a
ferromagnetic 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 ...
film, which provides one of the main uses in so-called spin valves, which are the basis of magnetic sensors including modern
hard disk drive A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magnet ...
read heads. The temperature at or above which an antiferromagnetic layer loses its ability to "pin" the magnetization direction of an adjacent ferromagnetic layer is called the blocking temperature of that layer and is usually lower than the Néel temperature.


Geometric frustration

Unlike ferromagnetism, anti-ferromagnetic interactions can lead to multiple optimal states (ground states—states of minimal energy). In one dimension, the anti-ferromagnetic ground state is an alternating series of spins: up, down, up, down, etc. Yet in two dimensions, multiple ground states can occur. Consider an equilateral triangle with three spins, one on each vertex. If each spin can take on only two values (up or down), there are 23 = 8 possible states of the system, six of which are ground states. The two situations which are not ground states are when all three spins are up or are all down. In any of the other six states, there will be two favorable interactions and one unfavorable one. This illustrates
frustration In psychology, frustration is a common emotional response to opposition, related to anger, annoyance and disappointment. Frustration arises from the perceived resistance to the fulfillment of an individual's will or goal and is likely to inc ...
: the inability of the system to find a single ground state. This type of magnetic behavior has been found in minerals that have a crystal stacking structure such as a
Kagome lattice In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. See in particular Theorem 2.1.3, p. 59 (classification of uniform tilings); Figure 2.1.5, p.63 (illustration of this tiling), Theorem 2. ...
or
hexagonal lattice The hexagonal lattice or triangular lattice is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° ...
.


Other properties

Synthetic antiferromagnets (often abbreviated by SAF) are artificial antiferromagnets consisting of two or more thin ferromagnetic layers separated by a nonmagnetic layer. Dipole coupling of the ferromagnetic layers results in antiparallel alignment of the magnetization of the ferromagnets. Antiferromagnetism plays a crucial role in
giant magnetoresistance Giant magnetoresistance (GMR) is a quantum mechanical magnetoresistance effect observed in multilayers composed of alternating ferromagnetic and non-magnetic conductive layers. The 2007 Nobel Prize in Physics was awarded to Albert Fert and Peter ...
, as had been discovered in 1988 by the
Nobel prize The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...
winners
Albert Fert Albert Fert (; born 7 March 1938) is a French physicist and one of the discoverers of giant magnetoresistance which brought about a breakthrough in gigabyte hard disks. Currently, he is an emeritus professor at Paris-Saclay University in Orsay, ...
and
Peter Grünberg Peter Andreas Grünberg (; 18 May 1939 – 7 April 2018) was a German physicist, and Nobel Prize in Physics laureate for his discovery with Albert Fert of giant magnetoresistance which brought about a breakthrough in gigabyte hard disk d ...
(awarded in 2007) using synthetic antiferromagnets. There are also examples of disordered materials (such as iron phosphate glasses) that become antiferromagnetic below their Néel temperature. These disordered networks 'frustrate' the antiparallelism of adjacent spins; i.e. it is not possible to construct a network where each spin is surrounded by opposite neighbour spins. It can only be determined that the average correlation of neighbour spins is antiferromagnetic. This type of magnetism is sometimes called ''speromagnetism''. An interesting phenomenon occurs in
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 ...
Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...
antiferromagnets in a field, where spin-flop and
supersolid In condensed matter physics, a supersolid is a spatially ordered material with superfluid properties. In the case of helium-4, it has been conjectured since the 1960s that it might be possible to create a supersolid. Starting from 2017, a defin ...
phases may be stabilized. The latter phase has been described first by
Takeo Matsubara was a Japanese physicist. Matsubara proposed a method of statistical mechanics related to Green's function (many-body theory), by applying quantum field theory techniques to statistical physics. This method, commonly known as Matsubara Green's ...
and H. Matsuda in 1956.


See also

* * * * * * * * *


References


External links

*
Magnetism: Models and Mechanisms
in E. Pavarini, E. Koch, and U. Schollwöck: Emergent Phenomena in Correlated Matter, Jülich 2013, {{Authority control Quantum phases Magnetic ordering Quantum lattice models Physical phenomena