Ferromagnetism

Not to be confused withFerrimagnetism.

Amagnetmade ofalnico,a ferromagnetic iron alloy, with itskeeper

Paramagnetism, ferromagnetism, and spin waves

Ferromagnetismis 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 thecoercivityof 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 materialmagnetismhave been distinguished. Ferromagnetism (along with the similar effectferrimagnetism) is the strongest type and is responsible for the common phenomenon of everyday magnetism.An example of a permanent magnet formed from a ferromagnetic material is arefrigerator magnet.

Substances respond weakly to 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 bemagnetizedby an externalmagnetic fieldand remain magnetized after the external field is removed) are either ferromagnetic or ferrimagnetic, as are the materials that are attracted to them. Relatively few materials are ferromagnetic. They are typically pure forms, alloys, or compounds ofiron,cobalt,nickel,and certainrare-earth metals.

Ferromagnetism is vital in industrial applications and modern technologies, forming the basis for electrical and electromechanical devices such aselectromagnets,electric motors,generators,transformers,magnetic storage(includingtape recordersandhard disks), andnondestructive testingof ferrous materials.

Ferromagnetic materials can be divided into magnetically soft materials (likeannealediron), which do not tend to stay magnetized, and magnetically hard materials, 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 internalmicrocrystallinestructure, making them difficult to demagnetize. To demagnetize a saturated magnet, a magnetic field must be applied. The threshold at which demagnetization occurs depends on thecoercivityof the material. Magnetically hard materials have high coercivity, whereas magnetically soft materials have low coercivity.

The overall strength of a magnet is measured by itsmagnetic momentor, alternatively, its totalmagnetic flux.The local strength of magnetism in a material is measured by itsmagnetization.

Terms

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 termferromagnetismwas 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.

In a landmark paper in 1948,Louis Néelshowed 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.

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

Materials

See also:Category:Ferromagnetic materials

Curie temperatures for some crystalline ferromagnetic materials

Material	Curie temp.(K)
Co	1388
Fe	1043
Fe2O3	948
NiOFe2O3	858
CuOFe2O3	728
MgOFe2O3	713
MnBi	630
Ni	627
Nd2Fe14B	593
MnSb	587
MnOFe2O3	573
Y3Fe5O12	560
CrO2	386
MnAs	318
Gd	292
Tb	219
Dy	88
EuO	69

Ferromagnetism is an unusual property that occurs in only a few substances. The common ones are thetransition metalsiron,nickel,andcobalt,as well as theiralloysand 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,lowhysteresisloss, high permeability, and high electrical resistivity. One such typical material is a transition metal-metalloidalloy, made from about 80% transition metal (usually Fe, Co, or Ni) and a metalloid component (B,C,Si,P,orAl) that lowers the melting point.

A relatively new class of exceptionally strong ferromagnetic materials are therare-earth magnets.They containlanthanideelements 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(T_C), above which they cease to exhibit spontaneous magnetization.

Unusual materials

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, especiallymultiferroicmaterials, which are both ferromagnetic andferroelectric.

A number ofactinidecompounds are ferromagnets at room temperature or exhibit ferromagnetism upon cooling.PuPis a paramagnet withcubic symmetryatroom temperature,but which undergoes a structural transition into atetragonalstate with ferromagnetic order when cooled below itsT_C= 125 K.In its ferromagnetic state, PuP'seasy axisis in the ⟨100⟩ direction.

InNpFe₂the easy axis is ⟨111⟩.AboveT_C≈ 500 K,NpFe₂is also paramagnetic and cubic. Cooling below the Curie temperature produces arhombohedraldistortion wherein the rhombohedral angle changes from 60° (cubic phase) to 60.53°. An alternate description of this distortion is to consider the lengthcalong the unique trigonal axis (after the distortion has begun) andaas the distance in the plane perpendicular toc.In the cubic phase this reduces toc/a= 1.00.Below the Curie temperature

${\frac {c}{a}}-1=-(120\pm 5)\times 10^{-4},$

which is the largest strain in anyactinidecompound.NpNi₂undergoes a similar lattice distortion belowT_C= 32 K,with a strain of (43 ± 5) × 10⁻⁴.NpCo₂is a ferrimagnet below 15 K.

In 2009, a team ofMITphysicists demonstrated that alithiumgas cooled to less than onekelvincan exhibit ferromagnetism.The team cooledfermioniclithium-6to 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-blockand p-block elements, such asrubidium sesquioxide.

In 2018, a team ofUniversity of Minnesotaphysicists demonstrated that body-centered tetragonalrutheniumexhibits ferromagnetism at room temperature.

Electrically induced ferromagnetism

Recent research has shown evidence that ferromagnetism can be induced in some materials by an electric current or voltage. Antiferromagnetic LaMnO₃and SrCoO have been switched to be ferromagnetic by a current. In July 2020, scientists reported inducing ferromagnetism in the abundantdiamagneticmaterialiron pyrite( "fool's gold" ) by an applied voltage.In these experiments, the ferromagnetism was limited to a thin surface layer.

Explanation

TheBohr–Van Leeuwen theorem,discovered in the 1910s, showed thatclassical physicstheories are unable to account for any form of material magnetism, including ferromagnetism; the explanation rather depends on thequantum mechanicaldescription ofatoms.Each of an atom's electrons has amagnetic momentaccording to itsspinstate, 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.An atom will have anetmagnetic moment when that cancellation is incomplete.

Origin of atomic magnetism

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 momentumof 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 shellshave 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 a 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 otherregardless of any applied field, resulting in thespontaneous magnetizationof so-calleddomains.This results in the large observedmagnetic permeabilityof ferromagnetics, and the ability of magnetically hard materials to formpermanent magnets.

Exchange interaction

Main article: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 theexchange interaction.This in turn affects the electron location and theCoulomb (electrostatic) interactionand 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 theoremand that electrons arefermions.Therefore, under certain conditions, when theorbitalsof the unpaired outervalence electronsfrom 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 theelectrostatic energyof 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 interactiondue to dipole orientation,which tends to align the dipoles antiparallel. In certain doped semiconductor oxides,RKKY interactionshave been shown to bring about periodic longer-range magnetic interactions, a phenomenon of significance in the study ofspintronic materials.

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,ferrimagnetic, and antiferromagnetic substances—these mechanisms includedirect exchange,RKKY exchange,double exchange,andsuperexchange.

Magnetic anisotropy

Main article:Magnetic anisotropy

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 magnetsalso can have ashape anisotropydue 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 temperatureat which a transition to superparamagnetism occurs.

Magnetic domains

Electromagnetic dynamic magnetic domain motion of grain-oriented electrical silicon steel

Kerr micrographof a metal surface showing magnetic domains, with red and green stripes denoting opposite magnetization directions

Main article:Magnetic domain

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(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 interactionis 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 ofmagnetostaticenergy. 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 wallsa 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 domain walls in a grain ofsilicon steelcaused 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 ofmagnetitefrom 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 coiltends 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, thusdemagnetizingthe material.

Commercialmagnetsare made of "hard" ferromagnetic or ferrimagnetic materials with very large magnetic anisotropy such asalnicoandferrites,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

Main article:Curie temperature

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 transitionand the system can no longer maintain a spontaneous magnetization, so its ability to be magnetized or attracted to a magnet disappears, although it still respondsparamagneticallyto an external field. Below that temperature, there is aspontaneous symmetry breakingand magnetic moments become aligned with their neighbors. The Curie temperature itself is acritical point,where themagnetic susceptibilityis 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 simplifiedIsingspin model, had an important impact on the development ofstatistical physics.There, it was first clearly shown thatmean field theoryapproaches failed to predict the correct behavior at the critical point (which was found to fall under auniversality classthat includes many other systems, such as liquid-gas transitions), and had to be replaced byrenormalization grouptheory.

See also

• Ferromagnetic material properties
• Hysteresis– Dependence of the state of a system on its history
• Orbital magnetization
• Stoner criterion
• Thermo-magnetic motor– Magnet motor
• Neodymium magnet– Strongest type of permanent magnet from an alloy of neodymium, iron and boron

External links

• Media related toFerromagnetismat Wikimedia Commons
• Electromagnetism– ch. 11, from an online textbook
• Sandeman, Karl (January 2008)."Ferromagnetic Materials".DoITPoMS.Dept. of Materials Sci. and Metallurgy, Univ. of Cambridge.Retrieved2019-06-22.Detailed nonmathematical description of ferromagnetic materials with illustrations
• Magnetism: Models and Mechanismsin E. Pavarini, E. Koch, and U. Schollwöck: Emergent Phenomena in Correlated Matter, Jülich 2013,ISBN978-3-89336-884-6