Ferromagnetism is a property of certain materials (such asiron) that results in a significant, observablemagnetic permeability, and in many cases, a significantmagnetic coercivity, allowing the material to form apermanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability.
Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. For example, this temporary magnetization inside a steel plate accounts for the plate's attraction to a magnet. Whether or not that steel plate then acquires permanent magnetization depends on both the strength of the applied field and on thecoercivity of that particular piece of steel (which varies with the steel's chemical composition and any heat treatment it may have undergone).
Inphysics, multiple types of materialmagnetism have been distinguished. Ferromagnetism (along with the similar effectferrimagnetism) is the strongest type and is responsible for the common phenomenon of everyday magnetism.[1] A common example of a permanent magnet is arefrigerator magnet.[2] Substances respond weakly to magnetic fields by three other types of magnetism—paramagnetism,diamagnetism, andantiferromagnetism—but the forces are usually so weak that they can be detected only by lab instruments.
Permanent magnets (materials that can bemagnetized by an externalmagnetic field and remain magnetized after the external field is removed) are either ferromagnetic or ferrimagnetic, as are the materials that are strongly attracted to them. Relatively few materials are ferromagnetic; the common ones are the metalsiron,cobalt,nickel and most of theiralloys, and certainrare-earth metals.
Ferromagnetic materials can be divided into magnetically "soft" materials (likeannealediron) having low coercivity, which do not tend to stay magnetized, and magnetically "hard" materials having high coercivity, which do. Permanent magnets are made from hard ferromagnetic materials (such asalnico) and ferrimagnetic materials (such asferrite) that are subjected to special processing in a strong magnetic field during manufacturing to align their internalmicrocrystalline structure, making them difficult to demagnetize. To demagnetize a saturated magnet, a magnetic field must be applied. The threshold at which demagnetization occurs depends on thecoercivity of the material. The overall strength of a magnet is measured by itsmagnetic moment or, alternatively, its totalmagnetic flux. The local strength of magnetism in a material is measured by itsmagnetization.
Ferromagnetic material: all the molecular magnetic dipoles are pointed in the same direction
Ferrimagnetic material: some of the dipoles point in the opposite direction, but their smaller contribution is overcome by the others
Historically, the termferromagnetism was used for any material that could exhibitspontaneous magnetization: a net magnetic moment in the absence of an external magnetic field; that is, any material that could become amagnet. This definition is still in common use.[3]
In a landmark paper in 1948,Louis Néel showed that two levels of magnetic alignment result in this behavior. One is ferromagnetism in the strict sense, where all the magnetic moments are aligned. The other isferrimagnetism, where some magnetic moments point in the opposite direction but have a smaller contribution, so spontaneous magnetization is present.[4][5]: 28–29
In the special case where the opposing moments balance completely, the alignment is known asantiferromagnetism; antiferromagnets do not have a spontaneous magnetization.
Ferromagnetism is an unusual property that occurs in only a few substances. The common ones are thetransition metalsiron,nickel, andcobalt, as well as theiralloys and alloys ofrare-earth metals. It is a property not just of the chemical make-up of a material, but of its crystalline structure and microstructure. Ferromagnetism results from these materials having many unpaired electrons in their d-block (in the case of iron and its relatives) or f-block (in the case of the rare-earth metals), a result ofHund's rule of maximum multiplicity. There are ferromagnetic metal alloys whose constituents are not themselves ferromagnetic, calledHeusler alloys, named afterFritz Heusler. Conversely, there are non-magnetic alloys, such as types ofstainless steel, composed almost exclusively of ferromagnetic metals.
Amorphous (non-crystalline) ferromagnetic metallic alloys can be made by very rapidquenching (cooling) of an alloy. These have the advantage that their properties are nearly isotropic (not aligned along a crystal axis); this results in lowcoercivity, lowhysteresis 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, orAl) that lowers themelting point.
A relatively new class of exceptionally strong ferromagnetic materials are therare-earth magnets. They containlanthanide elements that are known for their ability to carry large magnetic moments in well-localizedf-orbitals.
The table lists a selection of ferromagnetic and ferrimagnetic compounds, along with theirCurie temperature (TC), above which they cease to exhibit spontaneous magnetization.
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, especiallymultiferroic materials, which are both ferromagnetic andferroelectric.[8]
A number ofactinide compounds are ferromagnets at room temperature or exhibit ferromagnetism upon cooling.PuP is a paramagnet withcubic symmetry atroom temperature, but which undergoes a structural transition into atetragonal state with ferromagnetic order when cooled below itsTC = 125 K. In its ferromagnetic state, PuP'seasy axis is in the ⟨100⟩ direction.[9]
InNpFe2 the easy axis is ⟨111⟩.[10] AboveTC ≈ 500 K, NpFe2 is also paramagnetic and cubic. Cooling below the Curie temperature produces arhombohedral distortion wherein the rhombohedral angle changes from 60° (cubic phase) to 60.53°. An alternate description of this distortion is to consider the lengthc along the unique trigonal axis (after the distortion has begun) anda as the distance in the plane perpendicular toc. In the cubic phase this reduces toc/a = 1.00. Below the Curie temperature, the lattice acquires a distortion
which is the largest strain in anyactinide compound.[11] NpNi2 undergoes a similar lattice distortion belowTC = 32 K, with a strain of (43 ± 5) × 10−4.[11] NpCo2 is a ferrimagnet below 15 K.
In 2009, a team ofMIT physicists demonstrated that alithium gas cooled to less than one kelvin can exhibit ferromagnetism.[12] The team cooledfermioniclithium-6 to less than150 nK (150 billionths of one kelvin) using infraredlaser cooling. This demonstration is the first time that ferromagnetism has been demonstrated in a gas.
In rare circumstances, ferromagnetism can be observed in compounds consisting of only s-block and p-block elements, such asrubidium sesquioxide.[13]
In 2018, a team ofUniversity of Minnesota physicists demonstrated that body-centered tetragonalruthenium exhibits ferromagnetism at room temperature.[14]
Recent research has shown evidence that ferromagnetism can be induced in some materials by anelectric current or voltage. Antiferromagnetic LaMnO3 and SrCoO have been switched to be ferromagnetic by a current. In July 2020, scientists reported inducing ferromagnetism in the abundantdiamagnetic materialiron pyrite ("fool's gold") by an applied voltage.[15][16] In these experiments, the ferromagnetism was limited to a thin surface layer.
TheBohr–Van Leeuwen theorem, discovered in the 1910s, showed thatclassical physics theories are unable to account for any form of material magnetism, including ferromagnetism; the explanation rather depends on thequantum mechanical description ofatoms. Each of an atom's electrons has amagnetic moment according to itsspin state, as described by quantum mechanics. ThePauli exclusion principle, also a consequence of quantum mechanics, restricts the occupancy of electrons' spin states inatomic orbitals, generally causing the magnetic moments from an atom's electrons to largely or completely cancel.[17] An atom will have anet magnetic moment when that cancellation is incomplete.
One of the fundamental properties of anelectron (besides that it carries charge) is that it has amagnetic dipole moment, i.e., it behaves like a tiny magnet, producing amagnetic field. This dipole moment comes from a more fundamental property of the electron: its 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). Electron spin in atoms is the main source of ferromagnetism, although there is also a contribution from theorbitalangular momentum of the electron about thenucleus. 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 filledelectron 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 occurs only in materials with partially filled shells. Because ofHund's rules, the first few electrons in an otherwise unoccupied shell tend to have the same spin, thereby increasing the total dipole moment.
Theseunpaired dipoles (often called simply "spins", even though they also generally include orbital angular momentum) tend to align in parallel to an external magnetic field – leading to a macroscopic effect calledparamagnetism. In ferromagnetism, however, the magnetic interaction between neighboring atoms' magnetic dipoles is strong enough that they align witheach other regardless of any applied field, resulting in thespontaneous magnetization of so-calleddomains. This results in the large observedmagnetic permeability of ferromagnetics, and the ability of magnetically hard materials to formpermanent magnets.
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 theexchange interaction. This in turn affects the electron location and theCoulomb (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 thespin–statistics theorem and that electrons arefermions. Therefore, under certain conditions, when theorbitals of the unpaired outervalence electrons from adjacent atoms overlap, the distributions of theirelectric charge in space are farther apart when the electrons have parallel spins than when they have opposite spins. This reduces theelectrostatic energy of the electrons when their spins are parallel compared to their energy when the spins are antiparallel, so the parallel-spin state is more stable. This difference in energy is called theexchange energy. In simple terms, the outer electrons of adjacent atoms, which repel each other, can move further apart by aligning their spins in parallel, so the spins of these electrons tend to line up.
This energy difference can be orders of magnitude larger than the energy differences associated with themagnetic dipole–dipole interaction due to dipole orientation,[18] 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 ofspintronic materials.[19]
The materials in which the exchange interaction is much stronger than the competing dipole–dipole interaction are frequently calledmagnetic materials. For instance, in iron (Fe) the exchange force is about 1,000 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,[20] ferrimagnetic, and antiferromagnetic substances—these mechanisms includedirect exchange,RKKY exchange,double exchange, andsuperexchange.
Although the exchange interaction keeps spins aligned, it does not align them in a particular direction. Withoutmagnetic anisotropy, the spins in a magnet randomly change direction in response tothermal fluctuations, and the magnet issuperparamagnetic. There are several kinds of magnetic anisotropy, the most common of which ismagnetocrystalline anisotropy. This is a dependence of the energy on the direction of magnetization relative to thecrystallographic lattice. Another common source ofanisotropy,inverse magnetostriction, is induced by internalstrains.Single-domain magnets also can have ashape 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 ablocking temperature at which a transition to superparamagnetism occurs.[21]
Electromagnetic dynamic magnetic domain motion of grain-oriented electrical silicon steelKerr micrograph of a metal surface showing magnetic domains, with red and green stripes denoting opposite magnetization directions
The spontaneous alignment of magnetic dipoles in ferromagnetic materials 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. This is because a bulk piece of ferromagnetic material is divided into tiny regions calledmagnetic domains[22] (also known asWeiss 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 bulk material has no net large-scale magnetic field.
Ferromagnetic materials spontaneously divide into magnetic domains because theexchange 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 ofmagnetostatic 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 thindomain 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.
Moving domain walls in a grain ofsilicon 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 via a process in which the spins of the electrons in atoms near the wall in one domain turn 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, and sum to create 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 theBarkhausen effect: as the magnetizing field is changed, the material's magnetization changes in thousands of tiny discontinuous jumps as domain walls suddenly "snap" past defects.
This magnetization as a function of an external field is described by ahysteresis curve. Although this state of aligned domains found in a piece of magnetized ferromagnetic material is not a minimal-energy configuration, it ismetastable, and can persist for long periods, as shown by samples ofmagnetite 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 adegaussing 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, thusdemagnetizing the material.
Commercialmagnets are made of "hard" ferromagnetic or ferrimagnetic materials with very large magnetic anisotropy such asalnico andferrites, 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.
As the temperature of a material increases, thermal motion, orentropy, competes with the ferromagnetic tendency for dipoles to align. When the temperature rises beyond a certain point, called theCurie temperature, there is a second-orderphase 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 respondsparamagnetically to an external field. Below that temperature, there is aspontaneous symmetry breaking and magnetic moments become aligned with their neighbors. The Curie temperature itself is acritical point, where themagnetic 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 simplifiedIsing spin model, had an important impact on the development ofstatistical physics. There, it was first clearly shown thatmean field theory approaches failed to predict the correct behavior at the critical point (which was found to fall under auniversality class that includes many other systems, such as liquid-gas transitions), and had to be replaced byrenormalization group theory.[citation needed]
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^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.ISSN1520-6106.
^Aldred A. T.; Dunlap B. D.; Lam D. J.; Lander G. H.; Mueller M. H.; Nowik I. (1975). "Magnetic properties of neptunium Laves phases: NpMn2, NpFe2, NpCo2, and NpNi2".Phys. Rev. B.11 (1):530–544.Bibcode:1975PhRvB..11..530A.doi:10.1103/PhysRevB.11.530.
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