Ferromagnetism

Ferromagnetism is the basic mechanism by which certain materials (such as iron) form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished. Ferromagnetism (along with the similar effect ferrimagnetism) is the strongest type and is responsible for the common phenomena of magnetism in magnets encountered in everyday life.[1] Substances respond weakly to magnetic fields with three other types of magnetism, paramagnetism, diamagnetism, and antiferromagnetism, but the forces are usually so weak that they can only be detected by sensitive instruments in a laboratory. An everyday example of ferromagnetism is a refrigerator magnet used to hold notes on a refrigerator door. The attraction between a magnet and ferromagnetic material is "the quality of magnetism first apparent to the ancient world, and to us today".[2]

Permanent magnets (materials that can be magnetized by an external magnetic field and remain magnetized after the external field is removed) are either ferromagnetic or ferrimagnetic, as are the materials that are noticeably attracted to them. Only a few substances are ferromagnetic. The common ones are iron, nickel, cobalt and most of their alloys, and some compounds of rare earth metals. Ferromagnetism is very important in industry and modern technology, and is the basis for many electrical and electromechanical devices such as electromagnets, electric motors, generators, transformers, and magnetic storage such as tape recorders, and hard disks, and nondestructive testing of ferrous materials.

MagnetEZ
A magnet made of alnico, an iron alloy, with its keeper.

History and distinction from ferrimagnetism

Ferromagnetic ordering
Ferromagnetic ordering in the strict sense
Ferrimagnetic ordering
Ferrimagnetic ordering

Historically, the term ferromagnetism was used for any material that could exhibit spontaneous magnetization: a net magnetic moment in the absence of an external magnetic field. This general definition is still in common use.[3]

However, in a landmark paper in 1948, Louis Néel showed there are two levels of magnetic alignment that result in this behavior. One is ferromagnetism in the strict sense, where all the magnetic moments are aligned. The other is ferrimagnetism, where some magnetic moments point in the opposite direction but have a smaller contribution, so there is still a spontaneous magnetization.[4][5]:28–29

In the special case where the opposing moments balance completely, the alignment is known as antiferromagnetism; but antiferromagnets do not have a spontaneous magnetization.

Ferromagnetic materials

Curie temperatures for some crystalline ferromagnetic materials[6][7]
Material Curie
temp. (K)
Co 1388
Fe 1043
Fe2O3[a] 948
FeOFe2O3[a] 858
NiOFe2O3[a] 858
CuOFe2O3[a] 728
MgOFe2O3[a] 713
MnBi 630
Ni 627
MnSb 587
MnOFe2O3[a] 573
Y3Fe5O12[a] 560
CrO2 386
MnAs 318
Gd 292
Tb 219
Dy 88
EuO 69
  1. ^ a b c d e f g Ferrimagnetic material
  1. ^ a b c d e f g Ferrimagnetic material

The table above lists a selection of ferromagnetic and ferrimagnetic compounds, along with the temperature above which they cease to exhibit spontaneous magnetization (see Curie temperature).

Ferromagnetism is a property not just of the chemical make-up of a material, but of its crystalline structure and microstructure. There are ferromagnetic metal alloys whose constituents are not themselves ferromagnetic, called Heusler alloys, named after Fritz Heusler. Conversely there are non-magnetic alloys, such as types of stainless steel, composed almost exclusively of ferromagnetic metals.

Amorphous (non-crystalline) ferromagnetic metallic alloys can be made by very rapid quenching (cooling) of a liquid alloy. These have the advantage that their properties are nearly isotropic (not aligned along a crystal axis); this results in low coercivity, low hysteresis loss, high permeability, and high electrical resistivity. One such typical material is a transition metal-metalloid alloy, made from about 80% transition metal (usually Fe, Co, or Ni) and a metalloid component (B, C, Si, P, or Al) that lowers the melting point.

A relatively new class of exceptionally strong ferromagnetic materials are the rare-earth magnets. They contain lanthanide elements that are known for their ability to carry large magnetic moments in well-localized f-orbitals.

Most ferromagnetic materials are metals, since the conducting electrons are often responsible for mediating the ferromagnetic interactions. It is therefore a challenge to develop ferromagnetic insulators, especially multiferroic materials, which are both ferromagnetic and ferroelectric.[8]

Actinide ferromagnets

A number of actinide compounds are ferromagnets at room temperature or exhibit ferromagnetism upon cooling. PuP is a paramagnet with cubic symmetry at room temperature, but which undergoes a structural transition into a tetragonal state with ferromagnetic order when cooled below its TC = 125 K. In its ferromagnetic state, PuP's easy axis is in the <100> direction.[9]

In NpFe2 the easy axis is <111>.[10] Above TC ≈ 500 K NpFe2 is also paramagnetic and cubic. Cooling below the Curie temperature produces a rhombohedral distortion wherein the rhombohedral angle changes from 60° (cubic phase) to 60.53°. An alternate description of this distortion is to consider the length c along the unique trigonal axis (after the distortion has begun) and a as the distance in the plane perpendicular to c. In the cubic phase this reduces to c/a = 1.00. Below the Curie temperature

which is the largest strain in any actinide compound.[11] NpNi2 undergoes a similar lattice distortion below TC = 32 K, with a strain of (43 ± 5) × 10−4.[11] NpCo2 is a ferrimagnet below 15 K.

Lithium gas

In 2009, a team of MIT physicists demonstrated that a lithium gas cooled to less than one kelvin can exhibit ferromagnetism.[12] The team cooled fermionic lithium-6 to less than 150 nK (150 billionths of one kelvin) using infrared laser cooling. This demonstration is the first time that ferromagnetism has been demonstrated in a gas.

Tetragonal ruthenium

In 2018, a team of University of Minnesota physicists demonstrated that body-centered tetragonal ruthenium exhibits ferromagnetism at room temperature.[13]

Explanation

The Bohr–van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of magnetism, including ferromagnetism. Magnetism is now regarded as a purely quantum mechanical effect. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle.[14]

Origin of magnetism

One of the fundamental properties of an electron (besides that it carries charge) is that it has a magnetic dipole moment, i.e., it behaves like a tiny magnet, producing a magnetic field. This dipole moment comes from the more fundamental property of the electron that it has quantum mechanical spin. Due to its quantum nature, the spin of the electron can be in one of only two states; with the magnetic field either pointing "up" or "down" (for any choice of up and down). The spin of the electrons in atoms is the main source of ferromagnetism, although there is also a contribution from the orbital angular momentum of the electron about the nucleus. When these magnetic dipoles in a piece of matter are aligned, (point in the same direction) their individually tiny magnetic fields add together to create a much larger macroscopic field.

However, materials made of atoms with filled electron shells have a total dipole moment of zero, because the electrons all exist in pairs with opposite spin, every electron's magnetic moment is cancelled by the opposite moment of the second electron in the pair. Only atoms with partially filled shells (i.e., unpaired spins) can have a net magnetic moment, so ferromagnetism only occurs in materials with partially filled shells. Because of Hund's rules, the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment.

These unpaired dipoles (often called simply "spins" even though they also generally include orbital angular momentum) tend to align in parallel to an external magnetic field, an effect called paramagnetism. Ferromagnetism involves an additional phenomenon, however: in a few substances the dipoles tend to align spontaneously, giving rise to a spontaneous magnetization, even when there is no applied field.

Exchange interaction

When two nearby atoms have unpaired electrons, whether the electron spins are parallel or antiparallel affects whether the electrons can share the same orbit as a result of the quantum mechanical effect called the exchange interaction. This in turn affects the electron location and the Coulomb (electrostatic) interaction and thus the energy difference between these states.

The exchange interaction is related to the Pauli exclusion principle, which says that two electrons with the same spin cannot also be in the same spatial state (orbital). This is a consequence of the spin-statistics theorem and that electrons are fermions. Therefore, under certain conditions, when the orbitals of the unpaired outer valence electrons from adjacent atoms overlap, the distributions of their electric charge in space are farther apart when the electrons have parallel spins than when they have opposite spins. This reduces the electrostatic energy of the electrons when their spins are parallel compared to their energy when the spins are anti-parallel, so the parallel-spin state is more stable. In simple terms, the electrons, which repel one another, can move "further apart" by aligning their spins, so the spins of these electrons tend to line up. This difference in energy is called the exchange energy.

This energy difference can be orders of magnitude larger than the energy differences associated with the magnetic dipole-dipole interaction due to dipole orientation,[15] which tends to align the dipoles antiparallel. In certain doped semiconductor oxides RKKY interactions have been shown to bring about periodic longer-range magnetic interactions, a phenomenon of significance in the study of spintronic materials.[16]

The materials in which the exchange interaction is much stronger than the competing dipole-dipole interaction are frequently called magnetic materials. For instance, in iron (Fe) the exchange force is about 1000 times stronger than the dipole interaction. Therefore, below the Curie temperature virtually all of the dipoles in a ferromagnetic material will be aligned. In addition to ferromagnetism, the exchange interaction is also responsible for the other types of spontaneous ordering of atomic magnetic moments occurring in magnetic solids, antiferromagnetism and ferrimagnetism. There are different exchange interaction mechanisms which create the magnetism in different ferromagnetic, ferrimagnetic, and antiferromagnetic substances. These mechanisms include direct exchange, RKKY exchange, double exchange, and superexchange.

Magnetic anisotropy

Although the exchange interaction keeps spins aligned, it does not align them in a particular direction. Without magnetic anisotropy, the spins in a magnet randomly change direction in response to thermal fluctuations and the magnet is superparamagnetic. There are several kinds of magnetic anisotropy, the most common of which is magnetocrystalline anisotropy. This is a dependence of the energy on the direction of magnetization relative to the crystallographic lattice. Another common source of anisotropy, inverse magnetostriction, is induced by internal strains. Single-domain magnets also can have a shape anisotropy due to the magnetostatic effects of the particle shape. As the temperature of a magnet increases, the anisotropy tends to decrease, and there is often a blocking temperature at which a transition to superparamagnetism occurs.[17]

Magnetic domains

Electromagnetic dynamic magnetic domain motion of grain oriented electrical silicon steel
Electromagnetic dynamic magnetic domain motion of grain oriented electrical silicon steel.
Weiss-Bezirke1
Kerr micrograph of metal surface showing magnetic domains, with red and green stripes denoting opposite magnetization directions.

The above would seem to suggest that every piece of ferromagnetic material should have a strong magnetic field, since all the spins are aligned, yet iron and other ferromagnets are often found in an "unmagnetized" state. The reason for this is that a bulk piece of ferromagnetic material is divided into tiny regions called magnetic domains[18] (also known as Weiss domains). Within each domain, the spins are aligned, but (if the bulk material is in its lowest energy configuration; i.e. unmagnetized), the spins of separate domains point in different directions and their magnetic fields cancel out, so the object has no net large scale magnetic field.

Ferromagnetic materials spontaneously divide into magnetic domains because the exchange interaction is a short-range force, so over long distances of many atoms the tendency of the magnetic dipoles to reduce their energy by orienting in opposite directions wins out. If all the dipoles in a piece of ferromagnetic material are aligned parallel, it creates a large magnetic field extending into the space around it. This contains a lot of magnetostatic energy. The material can reduce this energy by splitting into many domains pointing in different directions, so the magnetic field is confined to small local fields in the material, reducing the volume of the field. The domains are separated by thin domain walls a number of molecules thick, in which the direction of magnetization of the dipoles rotates smoothly from one domain's direction to the other.

Magnetized materials

Moving magnetic domains by Zureks
Moving domain walls in a grain of silicon steel caused by an increasing external magnetic field in the "downward" direction, observed in a Kerr microscope. White areas are domains with magnetization directed up, dark areas are domains with magnetization directed down.

Thus, a piece of iron in its lowest energy state ("unmagnetized") generally has little or no net magnetic field. However, the magnetic domains in a material are not fixed in place; they are simply regions where the spins of the electrons have aligned spontaneously due to their magnetic fields, and thus can be altered by an external magnetic field. If a strong enough external magnetic field is applied to the material, the domain walls will move by the process of the spins of the electrons in atoms near the wall in one domain turning under the influence of the external field to face in the same direction as the electrons in the other domain, thus reorienting the domains so more of the dipoles are aligned with the external field. The domains will remain aligned when the external field is removed, creating a magnetic field of their own extending into the space around the material, thus creating a "permanent" magnet. The domains do not go back to their original minimum energy configuration when the field is removed because the domain walls tend to become 'pinned' or 'snagged' on defects in the crystal lattice, preserving their parallel orientation. This is shown by the Barkhausen effect: as the magnetizing field is changed, the magnetization changes in thousands of tiny discontinuous jumps as the domain walls suddenly "snap" past defects.

This magnetization as a function of the external field is described by a hysteresis curve. Although this state of aligned domains found in a piece of magnetized ferromagnetic material is not a minimal-energy configuration, it is metastable, and can persist for long periods, as shown by samples of magnetite from the sea floor which have maintained their magnetization for millions of years.

Heating and then cooling (annealing) a magnetized material, subjecting it to vibration by hammering it, or applying a rapidly oscillating magnetic field from a degaussing coil tends to release the domain walls from their pinned state, and the domain boundaries tend to move back to a lower energy configuration with less external magnetic field, thus demagnetizing the material.

Commercial magnets are made of "hard" ferromagnetic or ferrimagnetic materials with very large magnetic anisotropy such as alnico and ferrites, which have a very strong tendency for the magnetization to be pointed along one axis of the crystal, the "easy axis". During manufacture the materials are subjected to various metallurgical processes in a powerful magnetic field, which aligns the crystal grains so their "easy" axes of magnetization all point in the same direction. Thus the magnetization, and the resulting magnetic field, is "built in" to the crystal structure of the material, making it very difficult to demagnetize.

Curie temperature

As the temperature increases, thermal motion, or entropy, competes with the ferromagnetic tendency for dipoles to align. When the temperature rises beyond a certain point, called the Curie temperature, there is a second-order phase transition and the system can no longer maintain a spontaneous magnetization, so its ability to be magnetized or attracted to a magnet disappears, although it still responds paramagnetically to an external field. Below that temperature, there is a spontaneous symmetry breaking and magnetic moments become aligned with their neighbors. The Curie temperature itself is a critical point, where the magnetic susceptibility is theoretically infinite and, although there is no net magnetization, domain-like spin correlations fluctuate at all length scales.

The study of ferromagnetic phase transitions, especially via the simplified Ising spin model, had an important impact on the development of statistical physics. There, it was first clearly shown that mean field theory approaches failed to predict the correct behavior at the critical point (which was found to fall under a universality class that includes many other systems, such as liquid-gas transitions), and had to be replaced by renormalization group theory.

See also

References

  1. ^ Chikazumi, Sōshin (2009). Physics of ferromagnetism. English edition prepared with the assistance of C.D. Graham, Jr (2nd ed.). Oxford: Oxford University Press. p. 118. ISBN 9780199564811.
  2. ^ Bozorth, Richard M. Ferromagnetism, first published 1951, reprinted 1993 by IEEE Press, New York as a "Classic Reissue." ISBN 0-7803-1032-2.
  3. ^ Somasundaran, P., ed. (2006). Encyclopedia of surface and colloid science (2nd ed.). New York: Taylor & Francis. p. 3471. ISBN 9780849396083.
  4. ^ Cullity, B.D.; Graham, C.D. (2011). "6. Ferrimagnetism". Introduction to Magnetic Materials. John Wiley & Sons. ISBN 9781118211496.
  5. ^ Aharoni, Amikam (2000). Introduction to the theory of ferromagnetism (2nd ed.). Oxford: Oxford University Press. ISBN 9780198508090.
  6. ^ Kittel, Charles (1986). Introduction to Solid State Physics (sixth ed.). John Wiley and Sons. ISBN 0-471-87474-4.
  7. ^ Jackson, Mike (2000). "Wherefore Gadolinium? Magnetism of the Rare Earths" (PDF). IRM Quarterly. Institute for Rock Magnetism. 10 (3): 6.
  8. ^ Hill, Nicola A. (2000-07-01). "Why Are There so Few Magnetic Ferroelectrics?". The Journal of Physical Chemistry B. 104 (29): 6694–6709. doi:10.1021/jp000114x. ISSN 1520-6106.
  9. ^ Lander GH, Lam DJ (1976). "Neutron diffraction study of PuP: The electronic ground state". Phys. Rev. B. 14 (9): 4064–67. Bibcode:1976PhRvB..14.4064L. doi:10.1103/PhysRevB.14.4064.
  10. ^ Aldred AT, Dunlap BD, Lam DJ, Lander GH, Mueller MH, Nowik I (1975). "Magnetic properties of neptunium Laves phases: NpMn2, NpFe2, NpCo2, and NpNi2". Phys. Rev. B. 11 (1): 530–44. Bibcode:1975PhRvB..11..530A. doi:10.1103/PhysRevB.11.530.
  11. ^ a b Mueller MH, Lander GH, Hoff HA, Knott HW, Reddy JF (Apr 1979). "Lattice distortions measured in actinide ferromagnets PuP, NpFe2, and NpNi2" (PDF). J Phys Colloque C4, supplement. 40 (4): C4–68–C4–69.
  12. ^ G-B Jo; Y-R Lee; J-H Choi; C.A. Christensen; T.H. Kim; J.H. Thywissen; D.E. Pritchard; W. Ketterle (2009). "Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms". Science. 325 (5947): 1521–24. arXiv:0907.2888. Bibcode:2009Sci...325.1521J. doi:10.1126/science.1177112. PMID 19762638.
  13. ^ Quarterman, P.; Sun, Congli; Garcia-Barriocanal, Javier; DC, Mahendra; Lv, Yang; Manipatruni, Sasikanth; Nikonov, Dmitri E.; Young, Ian A.; Voyles, Paul M.; Wang, Jian-Ping (2018). "Demonstration of Ru as the 4th ferromagnetic element at room temperature". Nature Communications. 9. Bibcode:2018NatCo...9.2058Q. doi:10.1038/s41467-018-04512-1.
  14. ^ Feynman, Richard P.; Robert Leighton; Matthew Sands (1963). The Feynman Lectures on Physics, Vol. 2. Addison-Wesley. pp. Ch. 37.
  15. ^ Chikazumi, Sōshin (2009). Physics of ferromagnetism. English edition prepared with the assistance of C.D. Graham, Jr (2nd ed.). Oxford: Oxford University Press. pp. 129–30. ISBN 9780199564811.
  16. ^ Assadi, M.H.N; Hanaor, D.A.H (2013). "Theoretical study on copper's energetics and magnetism in TiO2 polymorphs" (PDF). Journal of Applied Physics. 113 (23): 233913. arXiv:1304.1854. Bibcode:2013JAP...113w3913A. doi:10.1063/1.4811539.
  17. ^ Aharoni, Amikam (1996). Introduction to the Theory of Ferromagnetism. Clarendon Press. ISBN 0-19-851791-2. Archived from the original on 2011-06-29.
  18. ^ Feynman, Richard P.; Robert B. Leighton; Matthew Sands (1963). The Feynman Lectures on Physics, Vol. I. Pasadena: California Inst. of Technology. pp. 37.5–37.6. ISBN 0465024939.

External links

  • Electromagnetism – ch. 11, from an online textbook
  • Sandeman, Karl (January 2008). "Ferromagnetic Materials". DoITPoMS. Dept. of Materials Sci. and Metallurgy, Univ. of Cambridge. Retrieved 2008-08-27. Detailed nonmathematical description of ferromagnetic materials with animated illustrations
  • Magnetism: Models and Mechanisms in E. Pavarini, E. Koch, and U. Schollwöck: Emergent Phenomena in Correlated Matter, Jülich 2013, ISBN 978-3-89336-884-6
Antiferroelectricity

Antiferroelectricity is a physical property of certain materials. It is closely related to ferroelectricity; the relation between antiferroelectricity and ferroelectricity is analogous to the relation between antiferromagnetism and ferromagnetism.

An antiferroelectric material consists of an ordered (crystalline) array of electric dipoles (from the ions and electrons in the material), but with adjacent dipoles oriented in opposite (antiparallel) directions (the dipoles of each orientation form interpenetrating sublattices, loosely analogous to a checkerboard pattern). This can be contrasted with a ferroelectric, in which the dipoles all point in the same direction.

In an antiferroelectric, unlike a ferroelectric, the total, macroscopic spontaneous polarization is zero, since the adjacent dipoles cancel each other out.

Antiferroelectricity is a property of a material, and it can appear or disappear (more generally, strengthen or weaken) depending on temperature, pressure, external electric field, growth method, and other parameters. In particular, at a high enough temperature, antiferroelectricity disappears; this temperature is known as the Néel point or Curie point.

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. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism.

Generally, antiferromagnetic order may exist at sufficiently low temperatures, but vanishes at and above the Néel temperature – named after Louis Néel, who had first identified this type of magnetic ordering. Above the Néel temperature, the material is typically paramagnetic.

Calcium hexaboride

Calcium hexaboride (sometimes calcium boride) is a compound of calcium and boron with the chemical formula CaB6. It is an important material due to its high electrical conductivity, hardness, chemical stability, and melting point. It is a black, lustrous, chemically inert powder with a low density. It has the cubic structure typical for metal hexaborides, with octahedral units of 6 boron atoms combined with calcium atoms. CaB6 and lanthanum-doped CaB6 both show weak ferromagnetic properties, which is a remarkable fact because calcium and boron are neither magnetic, nor have inner 3d or 4f electronic shells, which are usually required for ferromagnetism.

Classical Heisenberg model

The Classical Heisenberg model is the case of the n-vector model, one of the models used in statistical physics to model ferromagnetism, and other phenomena.

Edmund Clifton Stoner

Edmund Clifton Stoner FRS (2 October 1899 – 27 December 1968) was a British theoretical physicist. He is principally known for his work on the origin and nature of itinerant ferromagnetism (the type of ferromagnetic behaviour associated with pure transition metals like cobalt, nickel, and iron), including the collective electron theory of ferromagnetism and the Stoner criterion for ferromagnetism.

Exchange interaction

In physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classical force, it is not a true force as it lacks a force carrier.

The effect is due to the wave function of indistinguishable particles being subject to exchange symmetry, that is, either remaining unchanged (symmetric) or changing sign (antisymmetric) when two particles are exchanged. Both bosons and fermions can experience the exchange interaction. For fermions, this interaction is sometimes called Pauli repulsion and is related to the Pauli exclusion principle. For bosons, the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation.

The exchange interaction alters the expectation value of the distance when the wave functions of two or more indistinguishable particles overlap. This interaction increases (for fermions) or decreases (for bosons) the expectation value of the distance between identical particles (compared to distinguishable particles). Among other consequences, the exchange interaction is responsible for ferromagnetism and the volume of matter. It has no classical analogue.

Exchange interaction effects were discovered independently by physicists Werner Heisenberg and Paul Dirac in 1926.

Felix Bloch

Felix Bloch (23 October 1905 – 10 September 1983) was a Swiss-American physicist and Nobel physics laureate who worked mainly in the U.S. He and Edward Mills Purcell were awarded the 1952 Nobel Prize for Physics for "their development of new ways and methods for nuclear magnetic precision measurements." In 1954–1955, he served for one year as the first Director-General of CERN. Felix Bloch made fundamental theoretical contributions to the understanding of electron behavior in crystal lattices, ferromagnetism, and nuclear magnetic resonance.

Ferroelasticity

Ferroelasticity is a phenomenon in which a material may exhibit a spontaneous strain. In ferroics, ferroelasticity is the mechanical equivalent of ferroelectricity and ferromagnetism. When stress is applied to a ferroelastic material, a phase change will occur in the material from one phase to an equally stable phase, either of different crystal structure (e.g. cubic to tetragonal), or of different orientation (a 'twin' phase). This stress-induced phase change results in a spontaneous strain in the material.

The shape memory effect and superelasticity are manifestations of ferroelasticity. Nitinol (nickel titanium), a common ferroelastic alloy, can display either superelasticity or the shape - memory effect at room temperature, depending on the nickel / titanium ratio.

Ferroelectricity

Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are pyroelectric, with the additional property that their natural electrical polarization is reversible. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in Rochelle salt by Valasek. Thus, the prefix ferro, meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. Materials that are both ferroelectric and ferromagnetic are known as multiferroics.

Ferromagnetic superconductor

Ferromagnetic superconductors are materials that display intrinsic coexistence of ferromagnetism and superconductivity. They include UGe2, URhGe, and UCoGe. Evidence of ferromagnetic superconductivity was also reported for ZrZn2 in 2001, but later reports question these findings. These materials exhibit superconductivity in proximity to a magnetic quantum critical point.

The nature of the superconducting state in ferromagnetic superconductors is currently under debate. Early investigations studied the coexistence of conventional s-wave superconductivity with itinerant ferromagnetism. However, the scenario of spin-triplet pairing soon gained the upper hand. A mean-field model for coexistence of spin-triplet pairing and ferromagnetism was developed in 2005.These models consider uniform coexistence of ferromagnetism and superconductivity, i.e. the same electrons which are both ferromagnetic and superconducting at the same time. Another scenario where there is an interplay between magnetic and superconducting order in the same material is superconductors with spiral or helical magnetic order. Examples of such include ErRh4B4 and HoMo6S8. In these cases, the superconducting and magnetic order parameters entwine each other in a spatially modulated pattern, which allows for their mutual coexistence, although it is no longer uniform. Even spin-singlet pairing may coexist with ferromagnetism in this manner.

Hysteresis

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 the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past. Hysteresis occurs in ferromagnetic and ferroelectric materials, as well as in the deformation of rubber bands and shape-memory alloys and many other natural phenomena. In natural systems it is often associated with irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect.

Hysteresis can be found in physics, chemistry, engineering, biology, and economics. It is incorporated in many artificial systems: for example, in thermostats and Schmitt triggers, it prevents unwanted frequent switching.

Hysteresis can be a dynamic lag between an input and an output that disappears if the input is varied more slowly; this is known as rate-dependent hysteresis. However, phenomena such as the magnetic hysteresis loops are mainly rate-independent, which makes a durable memory possible.

Systems with hysteresis are nonlinear, and can be mathematically challenging to model. Some models such as the Preisach model (originally applied to ferromagnetism) and the Bouc–Wen model attempt to capture general features of hysteresis; and there are also phenomenological models for particular phenomena such as the Jiles–Atherton model for ferromagnetism.

Magnetic domain

A magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction. When cooled below a temperature called the Curie temperature, the magnetization of a piece of ferromagnetic material spontaneously divides into many small regions called magnetic domains. The magnetization within each domain points in a uniform direction, but the magnetization of different domains may point in different directions. Magnetic domain structure is responsible for the magnetic behavior of ferromagnetic materials like iron, nickel, cobalt and their alloys, and ferrimagnetic materials like ferrite. This includes the formation of permanent magnets and the attraction of ferromagnetic materials to a magnetic field. The regions separating magnetic domains are called domain walls, where the magnetization rotates coherently from the direction in one domain to that in the next domain. The study of magnetic domains is called micromagnetics.

Magnetic domains form in materials which have magnetic ordering; that is, their dipoles spontaneously align due to the exchange interaction. These are the ferromagnetic, ferrimagnetic and antiferromagnetic materials. Paramagnetic and diamagnetic materials, in which the dipoles align in response to an external field but do not spontaneously align, do not have magnetic domains.

Magnetic semiconductor

Magnetic semiconductors are semiconductor materials that exhibit both ferromagnetism (or a similar response) and useful semiconductor properties. If implemented in devices, these materials could provide a new type of control of conduction. Whereas traditional electronics are based on control of charge carriers (n- or p-type), practical magnetic semiconductors would also allow control of quantum spin state (up or down). This would theoretically provide near-total spin polarization (as opposed to iron and other metals, which provide only ~50% polarization), which is an important property for spintronics applications, e.g. spin transistors.

While many traditional magnetic materials, such as magnetite, are also semiconductors (magnetite is a semimetal semiconductor with bandgap 0.14 eV), materials scientists generally predict that magnetic semiconductors will only find widespread use if they are similar to well-developed semiconductor materials. To that end, dilute magnetic semiconductors (DMS) have recently been a major focus of magnetic semiconductor research. These are based on traditional semiconductors, but are doped with transition metals instead of, or in addition to, electronically active elements. They are of interest because of their unique spintronics properties with possible technological applications. Doped Wide band-gap metal oxides such as zinc oxide (ZnO) and titanium oxide (TiO2) are among the best candidates for industrial DMS due to their multifunctionality in opticomagnetic applications. In particular, ZnO-based DMS with properties such as transparency in visual region and piezoelectricity have generated huge interest among the scientific community as a strong candidate for the fabrication of spin transistors and spin-polarized light-emitting diodes, while copper doped TiO2 in the anatase phase of this material has further been predicted to exhibit favorable dilute magnetism.Hideo Ohno and his group at the Tohoku University were the first to measure ferromagnetism in transition metal doped compound semiconductors such as indium arsenide and gallium arsenide doped with manganese referred to as GaMnAs. These materials exhibited reasonably high Curie temperatures (yet below room temperature) that scales with the concentration of p-type charge carriers. Ever since, ferromagnetic signals have been measured from various semiconductor hosts doped with different transition atoms.

Magnetism

Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Only a few substances are ferromagnetic; the most common ones are iron, nickel and cobalt and their alloys such as steel. The prefix ferro- refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe3O4.

Although ferromagnetism is responsible for most of the effects of magnetism encountered in everyday life, all other materials are influenced to some extent by a magnetic field, by several other types of magnetism. Paramagnetic substances such as aluminum and are weakly attracted to an applied magnetic field; diamagnetic substances such as copper and carbon are weakly repelled; while antiferromagnetic materials such as chromium and spin glasses have a more complex relationship with a magnetic field. The force of a magnet on paramagnetic, diamagnetic, and antiferromagnetic materials is usually too weak to be felt, and can be detected only by laboratory instruments, so in everyday life these substances are often described as non-magnetic.

The magnetic state (or magnetic phase) of a material depends on temperature and other variables such as pressure and the applied magnetic field. A material may exhibit more than one form of magnetism as these variables change. As with magnetizing a magnet, demagnetsing a magnet is also possible." Passing an alternate current, or hitting a heated magnet in an east west direction are ways of demagnetizing a magnet", quotes Sreekethav.

Molecule-based magnets

Molecule-based magnets are a class of materials capable of displaying ferromagnetism and other more complex magnetic phenomena. This class expands the materials properties typically associated with magnets to include low density, transparency, electrical insulation, and low-temperature fabrication, as well as combine magnetic ordering with other properties such as photoresponsiveness. Essentially all of the common magnetic phenomena associated with conventional transition-metal and rare-earth-based magnets can be found in molecule-based magnets.

Spherical model

The spherical model in statistical mechanics is a model of ferromagnetism similar to the Ising model, which was solved in 1952 by T. H. Berlin and M. Kac. It has the remarkable property that when applied to systems of dimension d greater than four, the critical exponents that govern the behaviour of the system near the critical point are independent of d and the geometry of the system. It is one of the few models of ferromagnetism that can be solved exactly in the presence of an external field.

Unpaired electron

In chemistry, an unpaired electron is an electron that occupies an orbital of an atom singly, rather than as part of an electron pair. Each atomic orbital of an atom (specified by the three quantum numbers n, l and m) has a capacity to contain two electrons (electron pair) with opposite spins. As the formation of electron pairs is often energetically favourable, either in the form of a chemical bond or as a lone pair, unpaired electrons are relatively uncommon in chemistry, because an entity that carries an unpaired electron is usually rather reactive. In organic chemistry they typically only occur briefly during a reaction on an entity called a radical; however, they play an important role in explaining reaction pathways.

Radicals are uncommon in s- and p-block chemistry, since the unpaired electron occupies a valence p orbital or an sp, sp2 or sp3 hybrid orbital. These orbitals are strongly directional and therefore overlap to form strong covalent bonds, favouring dimerisation of radicals. Radicals can be stable if dimerisation would result in a weak bond or the unpaired electrons are stabilised by delocalisation. In contrast, radicals in d- and f-block chemistry are very common. The less directional, more diffuse d and f orbitals, in which unpaired electrons reside, overlap less effectively, form weaker bonds and thus dimerisation is generally disfavoured. These d and f orbitals also have comparatively smaller radial extension, disfavouring overlap to form dimers.Relatively more stable entities with unpaired electrons do exist, e.g. the nitric oxide molecule has one. According to Hund's rule, the spins of unpaired electrons are aligned parallel and this gives these molecules paramagnetic properties.

The most stable examples of unpaired electrons are found on the atoms and ions of lanthanides and actinides. The incomplete f-shell of these entities does not interact very strongly with the environment they are in and this prevents them from being paired. The ions with the largest number of unpaired electrons are Gd3+ and Cm3+ with seven unpaired electrons.

An unpaired electron has a magnetic dipole moment, while an electron pair has no dipole moment because the two electrons have opposite spins so their magnetic dipole fields are in opposite directions and cancel. Thus an atom with unpaired electrons acts as a magnetic dipole and interacts with a magnetic field. Only elements with unpaired electrons exhibit paramagnetism, ferromagnetism, and antiferromagnetism.

Uranium diselenide

Uranium diselenide is a compound of uranium and selenium. It has a β form that has orthorhombic crystal system. The family of crystals it matches is PbCl2. The dimensions of the unit cell are a: 7.455 Å, b: 4.2320 Å, c= 8.964 Å. The compound has the unusual property of ferromagnetism, but only if the temperature is below 14 K.Tellurium can be substituted for selenium in varying quantities, expanding the lattice and increasing the ferromagnetic Curie temperature.

William Fuller Brown Jr.

William Fuller Brown Jr. (21 October 1904–1983) was an American physicist who developed the theory of micromagnetics, a continuum theory of ferromagnetism that has had numerous applications in physics and engineering. He published three books: Magnetostatic Principles in Ferromagnetism, Micromagnetics, and Magnetoelastic Interactions.

This page is based on a Wikipedia article written by authors (here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.