Explanation Ferromagnetism

1 explanation

1.1 origin of magnetism
1.2 exchange interaction
1.3 magnetic anisotropy
1.4 magnetic domains
1.5 magnetized materials
1.6 curie temperature

explanation

the bohr–van leeuwen theorem, discovered in 1910s, showed classical physics theories unable account form of magnetism, including ferromagnetism. magnetism regarded purely quantum mechanical effect. ferromagnetism arises due 2 effects quantum mechanics: spin , pauli exclusion principle.

origin of magnetism

one of fundamental properties of electron (besides carries charge) has magnetic dipole moment, i.e., behaves tiny magnet, producing magnetic field. dipole moment comes more fundamental property of electron has quantum mechanical spin. due quantum nature, spin of electron can in 1 of 2 states; magnetic field either pointing or down (for choice of , down). spin of electrons in atoms main source of ferromagnetism, although there contribution orbital angular momentum of electron nucleus. when these magnetic dipoles in piece of matter aligned, (point in same direction) individually tiny magnetic fields add create larger macroscopic field.

however, materials made of atoms filled electron shells have total dipole moment of zero, because electrons exist in pairs opposite spin, every electron s magnetic moment cancelled opposite moment of second electron in pair. atoms partially filled shells (i.e., unpaired spins) can have net magnetic moment, ferromagnetism occurs in materials partially filled shells. because of hund s rules, first few electrons in shell tend have same spin, thereby increasing total dipole moment.

these unpaired dipoles (often called spins though include angular momentum) tend align in parallel external magnetic field, effect called paramagnetism. ferromagnetism involves additional phenomenon, however: in few substances dipoles tend align spontaneously, giving rise spontaneous magnetization, when there no applied field.

exchange interaction

when 2 nearby atoms have unpaired electrons, whether electron spins parallel or antiparallel affects whether electrons can share same orbit result of quantum mechanical effect called exchange interaction. in turn affects electron location , coulomb (electrostatic) interaction , energy difference between these states.

the exchange interaction related pauli exclusion principle, says 2 electrons same spin cannot in same spatial state (orbital). consequence of spin-statistics theorem , electrons fermions. therefore, under conditions, when orbitals of unpaired outer valence electrons adjacent atoms overlap, distributions of electric charge in space farther apart when electrons have parallel spins when have opposite spins. reduces electrostatic energy of electrons when spins parallel compared energy when spins anti-parallel, parallel-spin state more stable. in simple terms, electrons, repel 1 another, can move further apart aligning spins, spins of these electrons tend line up. difference in energy called exchange energy.

this energy difference can orders of magnitude larger energy differences associated magnetic dipole-dipole interaction due dipole orientation, tends align dipoles antiparallel. in doped semiconductor oxides rkky interactions have been shown bring periodic longer-range magnetic interactions, phenomenon of significance in study of spintronic materials.

the materials in exchange interaction stronger competing dipole-dipole interaction called magnetic materials. instance, in iron (fe) exchange force 1000 times stronger dipole interaction. therefore, below curie temperature virtually of dipoles in ferromagnetic material aligned. in addition ferromagnetism, exchange interaction responsible other types of spontaneous ordering of atomic magnetic moments occurring in magnetic solids, antiferromagnetism , ferrimagnetism. there different exchange interaction mechanisms create magnetism in different ferromagnetic, ferrimagnetic, , antiferromagnetic substances. these mechanisms include direct exchange, rkky exchange, double exchange, , superexchange.

magnetic anisotropy

although exchange interaction keeps spins aligned, not align them in particular direction. without magnetic anisotropy, spins in magnet randomly change direction in response thermal fluctuations , magnet superparamagnetic. there several kinds of magnetic anisotropy, common of magnetocrystalline anisotropy. dependence of energy on direction of magnetization relative crystallographic lattice. common source of anisotropy, inverse magnetostriction, induced internal strains. single-domain magnets can have shape anisotropy due magnetostatic effects of particle shape. temperature of magnet increases, anisotropy tends decrease, , there blocking temperature @ transition superparamagnetism occurs.

magnetic domains

electromagnetic dynamic magnetic domain motion of grain oriented electrical silicon steel



kerr micrograph of metal surface showing magnetic domains, red , green stripes denoting opposite magnetization directions.

the above seem suggest every piece of ferromagnetic material should have strong magnetic field, since spins aligned, yet iron , other ferromagnets found in unmagnetized state. reason bulk piece of ferromagnetic material divided tiny regions called magnetic domains (also known weiss domains). within each domain, spins aligned, (if bulk material in lowest energy configuration, i.e. unmagnetized), spins of separate domains point in different directions , magnetic fields cancel out, object has no net large scale magnetic field.

ferromagnetic materials spontaneously divide magnetic domains because exchange interaction short-range force, on long distances of many atoms tendency of magnetic dipoles reduce energy orienting in opposite directions wins out. if dipoles in piece of ferromagnetic material aligned parallel, creates large magnetic field extending space around it. contains lot of magnetostatic energy. material can reduce energy splitting many domains pointing in different directions, magnetic field confined small local fields in material, reducing volume of field. domains separated thin domain walls number of molecules thick, in direction of magnetization of dipoles rotates smoothly 1 domain s direction other.

magnetized materials

moving domain walls in grain of silicon steel caused increasing external magnetic field in downward direction, observed in kerr microscope. white areas domains magnetization directed up, dark areas domains magnetization directed down.

thus, piece of iron in lowest energy state ( unmagnetized ) has little or no net magnetic field. however, magnetic domains in material not fixed in place; regions spins of electrons have aligned spontaneously due magnetic fields, , can altered external magnetic field. if strong enough external magnetic field applied material, domain walls move process of spins of electrons in atoms near wall in 1 domain turning under influence of external field face in same direction electrons in other domain, reorienting domains more of dipoles aligned external field. domains remain aligned when external field removed, creating magnetic field of own extending space around material, creating permanent magnet. domains not go original minimum energy configuration when field removed because domain walls tend become pinned or snagged on defects in crystal lattice, preserving parallel orientation. shown barkhausen effect: magnetizing field changed, magnetization changes in thousands of tiny discontinuous jumps domain walls snap past defects.

this magnetization function of external field described hysteresis curve. although state of aligned domains found in piece of magnetized ferromagnetic material not minimal-energy configuration, metastable, , can persist long periods, shown samples of magnetite sea floor have maintained magnetization millions of years.

heating , cooling (annealing) magnetized material, subjecting vibration hammering it, or applying rapidly oscillating magnetic field degaussing coil tends release domain walls pinned state, , domain boundaries tend move lower energy configuration less external magnetic field, demagnetizing material.

commercial magnets made of hard ferromagnetic or ferrimagnetic materials large magnetic anisotropy such alnico , ferrites, have strong tendency magnetization pointed along 1 axis of crystal, easy axis . during manufacture materials subjected various metallurgical processes in powerful magnetic field, aligns crystal grains easy axes of magnetization point in same direction. magnetization, , resulting magnetic field, built in crystal structure of material, making difficult demagnetize.

curie temperature

as temperature increases, thermal motion, or entropy, competes ferromagnetic tendency dipoles align. when temperature rises beyond point, called curie temperature, there second-order phase transition , system can no longer maintain spontaneous magnetization, ability magnetized or attracted magnet disappears, although still responds paramagnetically external field. below temperature, there spontaneous symmetry breaking , magnetic moments become aligned neighbors. curie temperature critical point, magnetic susceptibility theoretically infinite and, although there no net magnetization, domain-like spin correlations fluctuate @ length scales.

the study of ferromagnetic phase transitions, via simplified ising spin model, had important impact on development of statistical physics. there, first shown mean field theory approaches failed predict correct behavior @ critical point (which found fall under universality class includes many other systems, such liquid-gas transitions), , had replaced renormalization group theory.