This document summarizes key concepts related to magnetism in condensed matter: 1. Magnetism originates from magnetic materials like magnetite, which was the first known magnetic material. It was later discovered that magnetite could make iron magnetic through contact or rubbing. 2. Magnetite was also found to point approximately north when floating on water, leading to its use in early compasses. 3. Materials exhibit different types of magnetism (diamagnetism, paramagnetism, ferro/ferrimagnetism) depending on the arrangement and cancellation of magnetic moments within their atomic or molecular structures. 4. The magnetization of a material depends on both its intrinsic properties and external magnetic fields

1. Mangnetism in Condensed
Matter

2. The story of magnetism begins with a mineral called
magnetite (Fe3O4), the first magnetic
material known to man. Its early history is obscure, but
its power of attracting iron was cer tainly known 2500
years ago. Magnetite is widely distributed. In the
ancient world the most
plentiful deposits occurred in the district of Magnesia,
in what is now modern Turkey, and
our word magnet is derived from a similar Greek
word, said to come from the name of this
district. It was also known to the Greeks that a piece of
iron would itself become magnetic if
it were touched, or, better, rubbed with magnetite

3. Later on, but at an unknown date, it was found that
a properly shaped piece of magnetite,
if supported so as to float on water, would turn until it
pointed approximately north and
south. So would a pivoted iron needle, if
previously rubbed with magnetite. Thus was
the mariner’s compass born. This north-pointing
property of magnetite accounts for the
old English word lodestone for this substance; it
means “waystone,” because it points
the way.

4. It is the moment of the torque exerted on
the magnet when it is at right angles to a uniform
field of 1 Oe.
When dealing with small volumes like the unit
cell, the magnetic moment is often given in units
called Bohr magnetons, uB, where 1 Bohr
magneton = 9.27*10^-21 erg/Oe.

5. We are now in a position to consider how
magnetization can be measured and what the
measurement reveals about the magnetic behavior
of various kinds of substances.
Figure shows one method of measurement. The
specimen is in the form of a ring,3
wound with a large number of closely spaced turns
of insulated wire, connected through
a switch S and ammeter A to a source of variable
current. This winding is called the
primary, or magnetizing, winding

8. M is zero only for empty space. The
magnetization, even for applied fields H of
many thousands of
oersteds, is very small and negative for
diamagnetics, very small and positive for
paramag netics and antiferromagnetics, and
large and positive for ferro- and ferrimagnetics.
H is the “fundamental” mag netic field, which
produces magnetization M in magnetic
materials. The flux density B is a
useful quantity primarily because changes in B
generate voltages through Faraday’s law.

9. The ratio of these
two

10. The magnetization curve is nonlinear, so that x
varies with H and passes through a maximum value
(about 40 for the curve shown).
Two other phenomena appear:
1.Saturation. At large enough values of H, the
magnetization M becomes constant at its
saturation value of Ms.
2. Hysteresis, or irreversibility. After saturation, a
decrease in H to zero does not reduce
M to zero. Ferro- and ferrimagnetic materials can
thus be made into permanent
magnets.
The word hysteresis is from a Greek word
meaning “to lag behind,” and
is today applied to any phenomenon in which the
effect lags behind the cause,

12. The ratio of B to H is called the permeability
m

13. 1.Permeability varies greatly with the level of the
applied field, and soft magnetic
materials are almost never used at constant field.
2.Permeability is strongly structure-sensitive,
and so depends on purity, heat treatment,
deformation, etc.

14. the susceptibility of weakly magnetic substances
and
the saturation magnetization of strongly magnetic
ones,they do not depend on details of structural
elements
such as grain size, crystal orientation, strain,lattice
imperfections, or small amounts of
impurities.

15. Magnetic moments of electrons

18. Atoms contain many electrons, each spinning about
its own axis and moving in its own orbit.
The magnetic moment associated with each kind of
motion is a vector quantity, parallel to the
axis of spin and normal to the plane of the orbit,
respectivel
1. The magnetic moments of all the electrons are so
oriented that they cancel one
another out, and the atom as a whole has no net
magnetic moment. This condition
leads to diamagnetism

19. 2. The cancellation of electronic moments is only
partial and the atom is left with a net
magnetic moment. Such an atom is often referred to,
for brevity, as a magnetic
atom. Substances composed of atoms of this kind are
para-, ferro-, antiferro-, or
ferrimagnetic
spin and orbital moments oriented so that the
atom as a whole has no net moment.
the effect of an applied field on a single electron
orbit is to reduce the effective current of the orbit,
and so to produce a magnetic moment opposing
the applied field.

20. Electrons which constitute a closed shell in an atom
usually have their spin and orbital
moments oriented so that the atom as a whole has no
net moment. Thus the monoatomic
rare gases He, Ne, A, etc., which have closed-
shell electronic structures, are all diamagnetic.
So are most polyatomic gases, such as H2, N2, etc.,
because the process of molecule
formation usually leads to filled electron shells and no
net magnetic moment per molecule.

22. called the Curie–Weiss law. Here u is a constant,
with the dimensions of temperature, for
any one substance, and equal to zero for those
substances which obey Curie’s law. Some
authors write the denominator of Equation 3.8 as (Tþu).
Curie’s measurements on paramagnetics went without
theoretical explanation for 10
years, until Langevin in 1905 took up the problem in
the
same paper in which he presented
his theory of diamagnetism. Qualitatively, his theory of
paramagnetism is simple. He
assumed a paramagnetic to consist of atoms, or
molecules, each of which has the same
net magnetic moment m, because all the spin and
orbital moments of the electrons do

23. these atomic moments point at random
and cancel one another, so that the magnetization of
the specimen is zero. When a field
is applied, there is a tendency for each atomic moment
to turn toward the direction of the field; if no opposing
force acts, complete alignment of the atomic moments
would be produced and the specimen as a whole would
acquire a very large moment in the direction
of the field. But thermal agitation of the atoms opposes
this tendency and tends to keep
the atomic moments pointed at random

25. Crystal field theory (CFT)
describes the breaking of degeneracies of electron orbital states,
usually d or f orbitals, due to a static electric field produced by a
surrounding charge distribution (anion neighbors). This theory has
been used to describe various spectroscopies of transition
metal coordination complexes, in particular optical spectra (colors).
CFT successfully accounts for some magnetic properties,
colors, hydration enthalpies, and spinel structures of transition
metal complexes, but it does not attempt to describe bonding. CFT
was developed by physicists Hans Bethe[1] and John Hasbrouck
van Vleck[2] in the 1930s. CFT was subsequently combined
with molecular orbital theory to form the more realistic and
complex ligand field theory (LFT), which delivers insight into the
process of chemical bonding in transition metal complexes.

26. Jahn–Teller effect :
(JT effect or JTE) is an important mechanism
of spontaneous symmetry breaking in molecular
and solid-state systems which has far-reaching
consequences in different fields, and is
responsible for a variety of phenomena
in spectroscopy, stereochemistry, crystal
chemistry, molecular and solid-state physics,
and materials science. The effect is named
for Hermann Arthur Jahn and Edward Teller, who
first reported studies about it in 1937.
The Jahn–Teller effect is most often encountered
in octahedral complexes of the transition
metals.[3] The phenomenon is very common in
six-coordinate copper(II)
complexes.[4] The d9 electronic configuration of
this ion gives three electrons in the two
degenerate eg orbitals, leading to a doubly