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 Paul Langevin (1872-1946)  
 (c) Marcel Cerf, 1936
Paul Langevin
 John H. Van Vleck  (1899-1980) 
 Nobel Prize in 1977
John H. Van Vleck

Final Answers
© 2000-2016   Gérard P. Michon, Ph.D.

Electromagnetic Properties of Matter

[ ... ]   electricity itself is to be understood as
not an accident, but an essence of matter
Lord Kelvin  (1824-1907) 

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Electromagnetism and Magnetism  in  Treatise of Physics  (1935).
The Seven Ages of Magnetism  (Trinity College Dublin)
EM Fields & Sources  by  Steven Errede  (Physics 435, UIUC).
Electromagnetic Theory  by  Kentaro Hori  (Physics 352F, U. of Toronto).
Advanced Classical Electromagnetism  by  Richard Fitzpatrick  (UT Austin).
Classical Electrodynamics  by  Robert G. Brown  (Duke University).
Introduction to the Theory of Ferromagnetism  by  Amikam Aharoni.
Simulating Glauber dynamics for the Ising model  by  Raissa D'Souza.
Quantum Mechanics: The key to understanding magnetism  by  J.H. Van Vleck.
Post's constraint for EM constitutive relations  by  de Lange  &  Raab
Spin valve  and  giant magnetoresistance  (GMR).  Nobel Prize in Physics 2007.
Magnetic Levitation at your Fingertips  (Nature, July 22, 1999)
Magnetic Dipole Moment  by  Rod Nave.
Magnet Formulas  by  Eric Dennison.

Wikipedia:   Magnetization  |  Polarization Density  |  Neodymium Magnet  |  Pyrolytic Carbon
Meissner Effect (1933)

Video:  MIT OpenCourseWare   Electricity & Magnetism  by  Walter Lewin.
Visualizing Electricity and Magnetism :  Physics 8.02 at MIT.

Electromagnetic Properties of Matter

This discussion is the  second part  of our presentation of electromagnetism.  Familiarity with  vector calculus  and  Maxwell's equations  (in a vacuum)  is a prerequisite.

(2008-03-20)   Magnetization  (M)  and Electric Polarization  (P)
The densities of magnetic dipoles and electric dipoles, respectively.

Although Maxwell's equations do describe electromagnetism  both  in vacuum and in the midst of matter,  it's useful to make a distinction between electromagnetic sources which are either  free  or  bound  to matter  at the atomic level.

Ultimately, this allows a  different presentation  of Maxwell's equations  (where bound sources are suitably hidden)  which can be better suited to a description of electromagnetism within the bulk of dense matter.  First things first:

In one nice continuous model of matter, the microscopic electromagnetic sources  bound  to matter are simply approximated by a distribution of dipoles.  (This  dipolar  approximation usually captures directly the main aspects of things, but it may be awkward in some cases, including  antiferromagnetic materials.)  The fields created by those so-called  molecular  sources is simply superimposed to the field created by the  free  charges and currents  (henceforth subscripted with a nought).

The total current density  j  (which appears in the ordinary Maxwell equations)  is the sum of three terms:  free current, magnetization current and polarization current.  Likewise, the total electric charge density is the sum of the free charge density and the density  (-div P)  implied by the conservation of  bound  charges:

j   =   jo  rot M  +  P/t
r   =   ro  -  div P

Some authors  (including Tobias Brandes) argue that, from a purely mathematical perspective, the traditional distinction between free and bound sources is arbitrary.  Thus, Brandes "simplifies" the above by discarding entirely the "free" parts of the above  (for which we use nought subscripts).  We do not adopt that viewpoint here.

Of the three components of the total current density, the  magnetization current  or  bound current  (rot M)  is the most difficult to fathom.  Let's explain...

 Come back later, we're
 still working on this one...

(2008-03-23)   Electric Polarization and Magnetization Gauge

Mathematically, the fields produced by any smooth distribution of electromagnetic sources can be equated to what's produced by some smooth distribution of electromagnetic dipoles.  However, this may involve "unphysical" dipolar densities  (P and M)  which grow without bounds over time, or over space.  Thus, there's a finiteness requirement which helps define mathematically what portion of the electromagnetic sources ought to be considered  free  in the above sense.

The same distribution of charges and currents is obtained if  P  and  M  are respectively replaced by the following electric polarization and magnetization densities  (for arbitrary fields  Z  and  k  of respective units  C/m  and A) :

P  +  rot Z                  M  -  Z/t  -  grad k

 Come back later, we're
 still working on this one...

(2008-02-24)   Electric Displacement  D  and Magnetic Field Strength  H
Maxwell's equations "in matter" feature  free  charges and currents  only.

Defining magnetization and polarization densities  (M & P)  as above,  the two equations of Maxwell involving electromagnetic sources become:

div (e0 E)   =   ro - div P
rot (B / m0 )  -  (e0 E) /t   =   jo  +  rot M  +  P/t

This strongly suggests bundling  P  with  E  and  M  with  B  as follows...

The  electric displacement  D  is defined as a function of the  electric field  E  and  electric polarization density  P  (in  C/m2 )  namely:

D   =   e0 E  +  P

Likewise, the  magnetic field strength  H  (also called  magnetizing field  or magnetizing force, in the magnet trade)  depends on the  magnetic induction  B  and  magnetization  M  (magnetic moment per unit of volume, in  A/m) :

H   =   B / m0  -  M

Those definitions give Maxwell's equations the following simple form:

Maxwell's Equations in Matter  (1864)
rot E  +    B   =   0   div D  =   ro
rot H  -    D   =   jo div B  =   0

If and when there's no risk of confusion, the nought subscripts  (denoting  free  charges and currents)  may be dropped.

The misleading term  "displacement current"  for  D/t  was coined by Maxwell himself, in 1861, when he had to introduce it to make  Ampère's Law  come out right!  In a dense medium, some of it can be interpreted as an actual current  (the polarization current  P/t ).  In vacuum, however,  none  of this "current" is real; it's simply a mathematical artefact which makes Maxwell's equations consistent.

The above equations form a framework which must be supplemented by specific relations giving  D  and  H  in terms of  E  and  B  for a particular medium.  Such relations are known as  electromagnetic constitutive relations.

This may be applied to the  D  and  H  fields which result from non-dipolar expressions of bound sources,  although the  constitutive relations  for  multipolar  expressions of  D  and  H  are rarely considered.

(2008-02-24)   Electric and magnetic susceptibilities  (ce  and   c)
A medium responds to a field with  polarization densities  (P and M).

An external electromagnetic field can disturb the equilibrium of charges and spins in ordinary matter.  Some of the ensuing disturbances may be described classically in such terms that the macroscopic electromagnetic fields appear to obey a modified version of Maxwell's equations.

A simple way matter can react to a driving electromagnetic field is by creating electric and magnetic dipoles in its midst with densities  P  and  M, respectively.

The simplest response of matter to a driving electromagnetic field at a given frequency is the creation of varying dipoles  proportional  to the fields.  The coefficients of proportionality are scalars in an  isotropic  medium, but they are generally  tensors.  The coordinates of those tensors are complex numbers whose imaginary part vanishes at low frequency  (because the lag time in the response of matter to electromagnetic excitations can then be neglected).

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 still working on this one...

Magnetic Field Strength (H)  by  Rod Nave.
Wikipedia:   Skin Depth  |  Complex Permittivity  |  Electric Susceptibility  |  Magnetic Susceptibility

(2008-02-25)   Electric Permittivity and Magnetic Permeability
Functions of  electric susceptibility  and  magnetic susceptibility.

In an isotropic nondispersive medium...

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 still working on this one...

 Pierre Curie 

 Signature of 
 Pierre Curie
(2008-03-03)   Paramagnetism   (Pierre Curie, 1895)
A susceptibility inversely proportional to temperature.

Permanent magnetic dipoles in thermal equilibrium tend to align themselves with the applied magnetic field.  Such a model of matter yields a magnetic susceptibility which is inversely proportional to the temperature T:

cm   =   C / T

The constant of proportionality  C  is called the  Curie constant.  Such a relation was first recorded  (in the case of oxygen) by Pierre Curie in 1895.

To account for this, Langevin proposed (in 1905) that molecules have permanent magnetic moments of magnitude  m,  oriented according to Boltzmann statistics.

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 still working on this one...

Magnetic Susceptibility  (ppm)
Air  (because of 21% of O2 ) +0.4
Oxygen  (O2, gas) +2.09
  Nitrogen Dioxide  (NO2, gas)    
Nitric Oxide  (NO, gas) 
Magnesium  (Mg) +12
Aluminum  (Al) +22
Tungsten  (W) +68
Platinum  (Pt) +260
Uranium  (U) +400
Liquid Oxygen  (at 90 K) +3500
Iron Oxide  (FeO) +7200

Magnetic Materials   |   Magnetic Properties of Solids  by  Rod Nave   (Table of Susceptibilities)
Paramagnetic Oxygen Analyzer  (PDF data sheet, Fuji Electric Systems)
Wikipedia:   Paramagnetism   |   Electron Paramagnetic Resonance (EPR)

(2008-03-02)   Diamagnetism   (Brugmans in 1778,  Faraday in 1845)
Materials with  negative  susceptibilities repel both poles of a magnet.

In 1778, S.J. Brugmans  (of Leyden University)  noted that  bismuth  weakly repels both poles of a magnet.  In 1827, Le Baillif described the same effect for antimony  (see p. 144 of Light on Electricity  by John Tyndall, 1871).  Also in 1827, [Antoine César] Becquerel noticed the effect for wood.  In 1828, Seebeck reported it for several other substances...

Antoine César Becquerel (1788-1878; X1806)  was the father of the physicist [Alexandre] Edmond Becquerel (1820-1891) who also investigated diamagnetism and paramagnetism.  The son of Edmond was  [Antoine] Henri Becquerel (1852-1908; X1872)  who shared the Nobel prize in physics in 1903 for his discovery of natural radioactivity  Jean Becquerel (1878-1953, X1897) was the son of Henri.  Like his great-grandfather, grandfather and father before him, Jean held the chair of physics at the Muséum national d'histoire naturelle (MNHN).
The SI unit of activity (Bq) was named after  Henri  Becquerel.

In 1845, Michael Faraday (1791-1867) started to investigate the phenomenon systematically and called it  diamagnetism,  because a small rod of a diamagnetic substance  (like bismuth)  tends to align itself  across  the magnetic field lines  (as each part of the rod tries to get as far away from the nearest magnetic pole as possible).

It turns out that  all  substances have diamagnetic properties but the diamagnetic repulsion is usually masked by attractive paramagnetic or ferromagnetic properties, which are much stronger if at all present  (especially the latter).

If measured for a given number of atoms or moles,  diamagnetism (unlike paramagnetism and ferromagnetism) does  not  depend on temperature.  Thus, for a given volume of a certain substance, diamagnetism simply varies with temperature as the density of the substance  (this amounts to very little dependence on temperature for solids or liquids).

Magnetic Susceptibility  (ppm)
Pyrolytic Graphite  (PG) -85 -595
Bismuth  (Bi) -166
Antimony  (Sb) -73
Mercury  (Hg) -29
Gold  (Au) -28
Silver  (Ag) -23
Diamond  (C) -22
Lead  (Pb) -18
Sodium Chloride  (NaCl) -14
Copper  (Cu) -9.8
Water  (H2O, liquid) -9.035
Soft Human Tissue -8.9
Ammonia  (NH3 , gas at 20°C) -2.6
Nitrogen  (N2 , gas at 20°C) -0.005
Hydrogen  (H2 , gas at 20°C) -0.0021
Vacuum 0

Here is how diamagnetism could be explained in semi-classical terms:  The  Lorentz force  applied to an orbiting electron changes its centripetal acceleration and modifies its orbital magnetic moment in a direction  opposing  the applied external magnetic field.  The size of the orbits would have to be obtained from quantum considerations.

Classical Diamagnetism  (Paul Langevin, 1905)

  c   =    - N   m0 q 2   åi ri2
6 m

Paul Langevin obtained that result in 1905 by a classical argument which takes into account the Larmor precession of each electron about the applied magnetic field.  In the above formula,  N  is the number of atoms per unit of volume,  q  and  m  are the charge and the mass of the electron.  The summation extends over all the electrons in each atom to yield the sum of the mean squares of their orbital radii.

Quantum Diamagnetism  (Lev Davidovich Landau, 1930)

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 still working on this one...

Magnetic Materials   |   Magnetic Properties of Solids  by  Rod Nave   (Table of Susceptibilities)
Diamagnetic Shims in fMRI   |   Wikipedia:   Diamagnetism   |   Magnetic Susceptibility

(2008-03-05)   Magnetic Levitation
Levitation  without  active devices defies Earnshaw's Theorem (1842).

In 1842, Samuel Earnshaw (1805-1888) proved that permanent magnets are unable to produce stable levitation.  This theorem can be extended to include ferromagnetic or paramagnetic materials.

In 1845, Faraday rediscovered diamagnetism.  In 1847, Lord Kelvin recognized that Earnshaw's theorem would not apply to diamagnetic materials.  Static magnetic levitation is indeed possible if  diamagnets  are involved.

Because of their negative susceptibility, diamagnetic bodies seek equilibrium at a  minimum  of the magnetic field...  Although diamagnetic effects are small, they can be large enough to oppose Earth gravity (for thin shim of pyrographite) or, at least, combine with stronger magnetic fields to obtain stable levitation in midair, at room temperature.

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Martin D. Simon designed a diamagnetic levitation stand  (see video)  at UCLA which included two disks of pyrolytic graphite (PG).  According to Meredith Lamb, it was on January 17, 2000 that those PG disks were first used to make thin floaters that could levitate over a pattern of  alternating poles  formed by four neodymium block magnets.

We are not discussing here the use of electromagnets  (which consume  some  power)  to achieve the illusion of stability by a dynamic control of the magnetic field, using sensors which monitor the position of a permanent magnet floating over another one.  This does have great entertainment value, though.

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 still working on this one...

The Frog That Learned to Fly at the Nijmegen High Field Magnet Laboratory (1997)
Diamagnetic Levitation by Roger Schmidt   |   Diamagnetic Levitation by Martin D. Simon (UCLA)
Diamagnetically stabilized magnet levitation by M.D. Simon, L.O. Heflinger, A.K. Geim
Levitating Pyrolytic Graphite over Neodymium Magnets by Simon Quellen Field

(2008-06-23)   Pyrolytic Carbon  (Pyrolytic Graphite, or PyroCarbon)
At room temperature, this is the  most diamagnetic  substance known.

Pyrolytic graphite  (PG or PyC)  is a layered form of pure carbon with a density between 1.7 and 2.0.

It's obtained from short hydrocarbon gases  (mostly methane or propane)  by  chemical vapor deposition  (CVD)  at high temperature  (up to  2000°C)  under a low partial pressure  (10 mmHg or less)  which prevents the formation of  carbon black  (this can be achieved by dilution in an  inert gas,  like helium, argon, nitrogen or hydrogen).  The process is fairly slow:  A thickness of just  1 mm  requires typically  48 hours  (but as little as  1 hour  for low-grade stuff).

In medical applications  (replacement joints and heart valves)  material coated with pyrolytic carbon is marketed under the name of  PyroCarbon  by companies like  Ascension Orthopedics  (Austin, Texas)  and Nexa  (the Tornier group acquired the relevant implant technology from the French firm  BioProfile).  PyroCarbon was first used to manufacture heart valves in 1968.

For experimental purposes,  pyrolytic graphite  is available from  SciToys.

Pyrolytic Graphite  by  Simon Quellen Field   (SciToys)   |   Pyrolytic Carbon  (Wikipedia)
Pyrocarbone  at  LeCarbone.com  by  Thermya S.A.  (Bordeaux, France)
The possibility of increasing the diamagnetic susceptibility of pyrocarbon  (pdf)
by  Brandt, Kotosonov, Kuvshinnikov & Semenov  (1979)

(2008-03-18)   The theorem of Bohr and Van Leeuwen   (1911, 1919)
Classical diamagnetism and paramagnetism cancel each other...

As part of his doctoral dissertation  (Copenhagen 1911)  Niels Bohr (1885-1962)  introduced a classical argument which would later be developed by  Hendrika Johanna Van Leeuwen (1887-1974)  in her own doctoral dissertation  (Leiden 1919,  Journal de Physique 1921)  under the guidance of  H.A. Lorentz  and  Paul Ehrenfest.

The remark, known as the  Bohr-Van Leeuwen Theorem,  is that the ordinary laws of classical and statistical physics  (outside of quantum theory)  imply that an external magnetic field will not induce any net magnetization in a set of moving electric charges at thermal equilibrium.  Thus, classically, the diamagnetic and paramagnetic effects cancel each other  exactly !

Of course, this flies in the face of experimental results and merely goes to show that classical physics by itself  cannot  produce an adequate theory of magnetism.  Some form of quantization is needed to resolve this and other issues and reconcile theory with experiment  (the magnetic dipoles postulated by Langevin in his theory of paramagnetism can be construed as a good substitute for such a quantization).

John Hasbrouck Van Vleck (1899-1980)  discusses the theorem in  Theory of Electric and Magnetic Susceptibilities  (1934).  In his Nobel lecture (1970)  he argues that this particular point may have been one of the main motivations which led  Niels Bohr  himself to propose quantum conditions for the structure of the atom, in 1913  (thereby founding the so-called  Old Quantum Theory).

Proof :   (The following argument is based on what Richard Feynman says in section 34-6 (vol. 2 and vol. 3) of  The Feynman Lectures on Physics.)

A system of moving charges has a probability proportional to  e-U/kT  to have a state of motion of energy  U  at thermal equilibrium  (temperature T).  This energy  U  includes only the kinetic energy of the particles and their  electric  potential energy.  It's unaffected by the existence of any additional  magnetic  field.

Thus, the exact same statistical distribution of charge velocities is achieved at thermal equilibrium whether an external magnetic field is applied or not.

If we assume, as we do within a strict classical framework, that magnetic moments are entirely due to the circulating currents formed by moving charges, then we come to the conclusion that no magnetic moments at all are induced.  In other words, the net magnetic susceptibility is zero!  QED

This conclusion cannot be reached if  intrinsic  magnetic moments exists which are not explained by the classical motions of point charges.  Such things are allowed in Quantum Theory and they can be postulated  ad hoc  in semiclassical models, like the Langevin theory of paramagnetism.  For example, a pointlike electron has a quantum spin which endows it with angular momentum and magnetic moment in spite of its lack of structure and the subsequent lack of a dubious explanation in terms of the rotation of  some other stuff...

Physics Forum:   Is non-electric magnetism possible?

(2008-03-18)   Thermodynamics of Electromagnetism
Electromagnetic interactions of moving charges  and  magnetic dipoles.

To avoid the blatant contradiction of experimental evidence embodied by the above Theorem of Bohr and Van Leeuwen, a semiclassical discussion of magnetism should at least allow the existence of fundamental magnetic dipoles  (elementary particles endowed with a magnetic moment not due to a rotation of electric charges).  The energy of such a beast does depend on the magnetic field it is subjected to.

 Come back later, we're
 still working on this one...

(2008-03-05)   Ferromagnetism   (Pierre Weiss, 1906)
Magnets, hysteresis, Weiss domains and Bloch Walls.
 Pierre Weiss 
Pierre Weiss

Pierre-Ernest Weiss (1865-1940)  was born in Mulhouse, France.  He attended the Zürich Polytechnikum (ETH) graduating at the head of his class in 1887 with a degree in mechanical engineering  Then, Weiss was admitted to the  Ecole normale supérieure  (ENS) becoming  agrégé  in 1893.  He was a student of  Jules Violle (1841-1923)  and  Marcel Brillouin (1854-1948).  His doctoral dissertation (1896) on magnetite and iron-antimony alloys established a relation between magnetization and crystal symmetry.  In 1902, he returned to the ETH of Zürich as professor and director of the  Physics Laboratory.  In 1918, Weiss went on to Strasbourg, where he created his own laboratory dedicated to magnetism  (in 1928, he hired Louis Néel, who would receive a Nobel prize in 1970 for the discovery of antiferromagnetism).  Weiss was one of the key founders of the modern study of magnetism.

The Weiss magneton (empirical molecular magneton) is roughly  1.853 10-24 J/T  (or about 20% of a Bohr magneton).

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In  ferromagnetic materials, the magnetization of the medium itself can create a magnetic field which greatly exceeds a typical external field.  Furthermore, a  remanent magnetization  may exist in the absence of  any  external field.  In 1906-1907, Pierre Weiss discovered that such materials are always subdivided into variously oriented  domains  where the magnetization has its full  saturation  value.  Those domains are now known as  Weiss domains.  To explain this, Weiss proposed the so-called  molecular field hypothesis  whereby molecules could be endowed with tiny magnetic dipole moments which tend to align with their neighbors within each Weiss domain.  The boundaries between Weiss domains are called  Bloch walls,  in honor of the Swiss physicist Felix Bloch (1905-1983; Nobel 1952)  who investigated them.

Saturation Magnetization :

Ferromagnetism is such that the magnetic moments created at the atomic level tend to be aligned in each Weiss domain.  It's useful to estimate what the maximum magnetization can be under such conditions.  The contribution of each atom in the material is mostly due to its electrons, either from their orbital motion or their intrinsic spin which are respectively quantized  (nonrelativistically)  to a whole or half-integer multiple of the Bohr magneton.  In the main, we neglect the interesting magnetic effects due to the nucleons, which are 3 orders of magnitude smaller.

The magnetic moment of an atom can be attributed to its unpaired electrons.  It's typically equal to 1 or 2  Bohr magneton,  but can be as high as  10.6  Bohr magnetons  in the case of Holmium (67).  Thus,  holmium  pole pieces can concentrate magnetic flux  by up to   3.96 T  (this theoretical iimit is obtained by multiplying the permeability of the vacuum into the volume density of the magnetic moments).

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Ferromagnetic Materials
Material Permeability
m / m o
Force  Hc
in A/m
Flux Density
B in teslas (T)
SubstanceTreatment InitialMax. Rem.Sat.
Iron, 99.8%annealed 150 5000 801.3
Iron, 99.95%annealed in H2 10000 180000 41.32.15
Ironpressed powder    374000.6
Steel, 0.9% Cquenched 50 100 56001.03
Cobalt, 99%annealed 70 250 8000.5
Nickel, 99%annealed 110 600 560.4
Mumetal ® 80000 350000 0.40.65
Supermalloy  (annealed in H2 )
(15.7 Fe, 79 Ni, 5 Mo, 0.3 Mn)
100000 800000
Silicon Steel  (4.25% Si)   7600 300.811.97
Ceramic Magnet
C8  (Barium Ferrite)
S26  (Sm2Co17 )
N50  (Nd2Fe14B)
   10 61.47

The magnetic energy density of a ferromagnet  (in joules per cubic meter or, equivalently, in pascals)  is the product of the remanent flux density  (i.e., the magnetic induction B, in teslas)  by the density of magnetization  M.  A non-SI unit commonly used in the trade for this is the  megagauss-oersteds (MG.Oe) :

1 T   = 104 G                   1 A/m   =   4 p 10-3  Oe
1 T.A/m   =   1 J/m3   =   1 Pa   =   40 p  G.Oe   =   125.6637... G.Oe
Conversely,  1 MG.Oe   =   106/40p Pa   =   7957.747... J/m3

For example, the  theoretical  maximum for a neodymium-iron-boron magnet  ("NIB" or "neo")  is quoted to be  64 MGOe  while the best available grade is currently  54 MGOe  (that's what the designation "N54" means).  In more readable SI units, those numbers correspond respectively to  0.51 MPa  and  0.43 MPa.  In other words, an N54 neodymium magnet packs ideally a magnetic energy of  0.43 J  per cubic centimeter.

Magnetic Properties of Ferromagnetic Materials  by  Rod Nave
Iron and Magnetism  by Dr James B. Calvert
Wikipedia:   Ferromagnetism   |   Barkhausen Effect

(2008-03-09)   Antiferromagnetism   (Néel 1932, Landau 1933)
Magnetic multipoles dominate when adjacent dipoles cancel.

Louis Néel  (1904-2000)   was a towering figure in French physics. He helped transform Grenoble into a major research center and earned a belated Nobel prize in 1970.  Louis Néel started a scientific career dedicated to magnetism in Strasbourg in 1928, as an assistant to Pierre Weiss (1865-1940).  He is the eponym for the  Néel temperature  (above which antiferromagnetism disappears)  and  Néel walls  (planes separating domains whose magnetizations differ only by components parallel to the walls).

  Louis Neel 
Louis Néel

Antiferromagnetism occurs below a certain transition temperature, called the  Néel temperature  T, which varies from one antiferromagnetic material to the next:

Antiferromagnetic Materials
Nickel Oxide  (NiO)525 K
FCC  Iron-Manganese alloys  (Fe-Mn)> 500 K
Chromium  (Cr)  310.5 K  
HCP  Iron-Manganese  (17% Mn)  240 K
  Heavy-Fermion Superconductor  (URu2Si2 )  17.5 K

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(2008-03-09)   Ferrimagnetism   (Louis Néel, 1947)
Several types of dipoles may partially cancel each other in a crystal.

The most famous example of a ferrimagnetic substance is  lodestone  (which Gilbert spelled  loadstone ) which is the traditional name for magnetite, the most magnetic substance among naturally occurring minerals.  In fact,  magnetism  derives its name from  magnetite,  not the other way around...

Magnetite, magnesium and manganese, are actually named after the Greek region of  Magnesia  (central Greece)  because they were first discovered in minerals from that area.

Magnetite  (Fe3O4 )  is also called  ferrous-ferric oxide.  An expanded chemical formula  (FeO, Fe2O3 )  better reflects the structure of its crystal...

In the lattice, ferrous ions (Fe++ ) and ferric ions (Fe+++ ) tend to have antiparallel dipole moments.  However, the ferrous and the ferric magnetic moments are not equal in magnitude, so there's a net local magnetization.

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(2008-04-04)   Magneto-Optical Effect   (Michael Faraday, 1845)
In an  active  crystal, light polarization is rotated by a magnetic field.

Faraday effect (transmitted beam) and Kerr effect (reflected beam). The magnetization may be polar (perpendicular to the diopter) longitudinal (parallel to both the diopter and the plane of incidence) or transverse (parallel to the diopter, perpendicular to the plane of incidence).

The first nonlinear-optical effect was the quadratic Kerr effect  (quadratic electro-optic effect, QEO effect) described in 1875 by the Reverend John C. Kerr (1824-1907).

In 1893, Pockels (1865-1913) discovered that a birefringence proportional to the applied field exists in some crystals (Pockels Effect).

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The Faraday Effect  by  Masud Mansuripur   |   Kerr Effect
Magneto-Optical Imaging of Superconductors

(2008-02-24)   Classical Conductor of Conductivity  s.  Ohm's law.
Current density  (j)  is proportional to the electric field  (E) :   j = s E

In an  ideal  conductor  (a  superconductor)  the conductivity is infinite and, therefore,  E = 0.  There's no electric field and the magnetic field doesn't change.

Ordinary substances have a  finite conductivity  s  which varies with temperature.

Conductivity  sin   S/m = (W.m)-1
Silver (Ag) 6.82   1076.301 107
Copper (Cu) 6.48   1075.96   107
Gold (Au) 4.88   1074.52   107
Aluminum (Al) 4.14   1073.78   107
Tungsten (W) 2.07   1071.89   107
Zinc (Zn)  1.67   107
Brass  1.5     107
Nickel (Ni)  1.44   107
Iron (Fe) 1.167 1071.013 107
Lead (Pb) 5.21   1064.81   106
Mercury (Hg)  1.044 106
Graphite (C)  6.10   104
Pencil Lead  1.869 102
Glass  3.0   10-9
Diamond (C)  1.0   10-12
Polyurethane  1.0   10-15
Sulfur (S)  5.0   10-16
Fused Quartz  2.0   10-16

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Conductivity of chemical elements  |  Electrical resistivities of the elements  |  Wiedemann-Franz Law

(2012-08-05)   Bloch Equations   (1946)
Longitudinal and tranverse relaxation times for magnetization.

A phenomenological description...

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Magnetism, Curie's Law and the Bloch Equations, lecture by  Suzana K. Straus  (chemistry professor at UBC)
Felix Bloch (1905-1983; Nobel 1952) endowed a chair at Stanford, held by Leonard Susskind since 2000.
Wikipedia :   Bloch wave   |   Bloch wall   |   Bloch equations   |   Bloch-Torrey equation

(2015-04-18)   Aimé Auguste Cotton  (1869-1951)
Interaction of light with chiral molecules.  The Cotton effect.

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 still working on this one...

In 1953,  a prestigious yearly prize for promising French researchers was created to honor the memory of  Aimé Cotton.  That prize was awarded in 1971 to  Serge Haroche  (b. 1944)  for his doctoral work.  Haroche went on to earn the Nobel Prize in Physics, in 2012.

Aimé Cotton (1869-1951, ENS 1889, Agrégé 1893, Ph.D. 1896)   |   Laboratoire   |   Prix Aimé Cotton

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