Physics%20of%20Magnetism

1
Physics of Magnetism
2
Physical Principles of Magnetism
In order to understand how rocks, or, more
correctly, the magnetic minerals present within
the rock, retain a record of the Earths magnetic
field we need to have some understanding of the
basic physics behind the process. This is
inextricable from quantum mechanics. We cannot,
however, cover the complete quantum mathematical
formulations instead we will try to gain a
qualitative / semi-quantitative understanding of
the physical principles underlying the phenomenon.
3
Physics of Magnetism
The movement of an electrically charged particle
produces a magnetic field. The result is that
all materials display some magnetic properties.
The fundamental units of magnetic charge are
dipoles a combination of positive and negative
charge (m and -m respectively), which exhibit a
dipole moment. Two kinds of electron motion
define the magnetic properties exhibited by an
element.
4
Physics of Magnetism

• Firstly, electrons orbiting the nucleus have an
  orbital angular momentum L, such that
•  
• L Mass x Radius of orbit x Velocity
• The orbiting electron forms a loop of current,
  which generates a magnetic field (a magnetic
  moment ?)
• ? iA, where i is the current and A is the area
  of the loop
•  
• This magnetic moment is quantised in units of ?B
  (The Bohr Magnetron)
• m ?B, where ?B eh/4?me (9.27x10-24 Am2)
• (e is the electron charge, me is the mass of the
  electron and h is Plancks constant).

5
Physics of Magnetism
Secondly, the electron has a spin and a spin
angular momentum S. Each electron spins around
an axis, and that axis can have one of two
possible orientations either parallel or
antiparallel to an external magnetic field. This
spinning charge gives rise to a magnetic
field ?S ? ?B The superposition of
these forms of electron motion gives the total
angular momentum of the atom. Magnetism in
solids, however, is dominated by the magnetic
moment associated with electron spin.
6
Physics of Magnetism
The magnetic characteristics displayed by an atom
depend on the arrangement of its electrons.
Electrons are arranged around the nucleus of an
atom in shells (states of successively higher
energy). Within a shell, electrons exist in
orbitals, which are described by quantum numbers.
Each orbital contains no more than two electrons
(Pauli exclusion principle) and these have
opposite spins.
7
Physics of Magnetism Electron orbitals
Orbitals are filled with electrons in the order
of increasing energy.
8
Physics of Magnetism
Electrons occupy specific energy levels, or
orbitals, as they orbit the nucleus of an atom.
9
Physics of Magnetism
n the principal quantum number defines the energy
level of the orbital. Electrons with the same n
are said to be in the same shell. Increasing n
indicates shells farther away from the
nucleus. l the orbital quantum number defines the
total angular momentum of the orbital. l can
vary from 0 to n-1. Electrons with l values of
0, 1, 2, 3 are known as s, p, d and f
electrons. m the momentum quantum number defines
the component of angular momentum in the
direction of the applied field. m is an integer
value 1, 0 -1. S the spin quantum number defines
the spin of the electron. This can be ½ or -½,
and is summed over the full number of electrons
in a shell. A full shell has S 0, whereas for
Fe S2.
10
Physics of Magnetism
Atomic Number Element K L L M M N
Atomic Number Element 1s 2s 2p 3s 3p 4s
11 Na ?? ?? 6 ?
12 Mg ?? ?? 6 ??
13 Al ?? ?? 6 ?? ?
14 Si ?? ?? 6 ?? ? ?
15 P ?? ?? 6 ?? ? ? ?
16 S ?? ?? 6 ?? ?? ? ?
17 Cl ?? ?? 6 ?? ?? ?? ?
18 Ar ?? ?? 6 ?? ?? ?? ??
19 K ?? ?? 6 ?? ?? ?? ?? ?
20 Ca ?? ?? 6 ?? ?? ?? ?? ??
11
ES2 Electron orbitals
1s2
2s2
2p6
3s2
3p6
3d10
4s2
4p6
4d10
4f14
5s2
5p6
5d10
5f14
6s2
6p6
6d10
7s2
7p6
8s2
12
Physics of Magnetism
Atomic Number Element Inner Shells
Atomic Number Element Inner Shells 3d 4s
21 Sc 1s22s22p63s23p6 ? ??
22 Ti 1s22s22p63s23p6 ? ? ??
23 V 1s22s22p63s23p6 ? ? ? ??
24 Cr 1s22s22p63s23p6 ? ? ? ? ? ?
25 Mn 1s22s22p63s23p6 ? ? ? ? ? ??
26 Fe 1s22s22p63s23p6 ?? ? ? ? ? ??
27 Co 1s22s22p63s23p6 ?? ?? ? ? ? ??
28 Ni 1s22s22p63s23p6 ?? ?? ?? ? ? ??
29 Cu 1s22s22p63s23p6 ?? ?? ?? ?? ? ??
30 Zn 1s22s22p63s23p6 ?? ?? ?? ?? ?? ??
13
Physics of Magnetism
The net magnetic moment of an atom (J)
orbital angular momentum ? spin angular
momentum. These combine to minimise J and,
hence, the net magnetic moment. When J 0, the
atom is non-magnetic When J ? 0, the atom acts as
a magnet.
14
Physics of Magnetism
As the magnetic moment in solids is dominated by
the magnetic moment associated with electron
spin, an atom will possess an overall magnetic
moment where there are unpaired electrons in an
orbital (i.e. the spin moments are not
cancelled). As single electrons are added the
spin moments are combined, and the resultant
magnetic moment (from spin) is at a maximum when
the outer shell is half-full, and decreases as
further electrons are added to the outer shell
until it is full.
15
Physics of Magnetism Magnetic Susceptibility
Regardless of the arrangements of the electrons a
basic response is common to all materials on the
application of a magnetic field. This is because
the applied field exerts an aligning torque on
electron orbits, causing them to rotate and,
hence, producing a magnetisation, which is
parallel or anti-parallel to the applied field.
The response is dependent on its magnetic
susceptibility (?). Magnetic susceptibility can
therefore be most simply regarded as the ease
with which a material can be magnetised, and is a
dimensionless parameter which links the magnetic
moment of the material with the applied
field J ?H Where J is the magnetic moment
(A/m) and H is the applied field (Tesla).
16
Physics of Magnetism Magnetic Moments
17
Physics of Magnetism Diamagnetism
Diamagnetic materials are those which, when a
magnetic field is applied, acquire a small
induced magnetization opposite to the applied
field (e.g. Quartz). The induced magnetization
is linearly dependant on the applied field and
decays to zero when the field is removed.
Diamagnetism is a property of all matter but the
effect is swamped in substances whose atoms
possess atomic magnetic moments.
18
Physics of Magnetism Paramagnetism
19
Physics of Magnetism Paramagnetism
Paramagnetic substances are those which, when a
magnetic field is applied, acquire an induced
magnetization parallel to the applied field (e.g.
Fayalite an iron-rich Olivine). Paramagnetic
substances contain atoms with atomic magnetic
moments but with no interaction between adjacent
atomic moments (i.e. atoms with unfilled shells).
Again the magnetization is linearly dependant on
the applied field and decays to zero when the
field is removed. The effect is much stronger
than the diamagnetic behaviour by a factor of
about 10 to 100.
20
Physics of Magnetism Permanent magnetism
21
Physics of Magnetism Ferromagnetism
The transition metals and rare earth elements
(and their compounds) behave as through J S not
J L ? S. The orbital moment is said to be
quenched. This occurs because the 3d (or 4f)
electrons (which occupy the outermost orbitals)
have highly eccentric orbitals, which extend
proportionately farther form the nucleus, and
interact with surrounding atoms. These 3d (or
4f) electrons experience an electrostatic
crystal field with outweighs the electrostatic
L-S coupling. The Spin dominates. As the 3d
states are filled progressively, the electrons
are added with parallel spins until all 5
orbitals are filled, and all rotate in unison
with the applied field. There is, however, no
linkage between the spin directions in adjacent
atoms.
22
Physics of Magnetism
Atomic Number Element Inner Shells
Atomic Number Element Inner Shells 3d 4s
21 Sc 1s22s22p63s23p6 ? ??
22 Ti 1s22s22p63s23p6 ? ? ??
23 V 1s22s22p63s23p6 ? ? ? ??
24 Cr 1s22s22p63s23p6 ? ? ? ? ? ?
25 Mn 1s22s22p63s23p6 ? ? ? ? ? ??
26 Fe 1s22s22p63s23p6 ?? ? ? ? ? ??
27 Co 1s22s22p63s23p6 ?? ?? ? ? ? ??
28 Ni 1s22s22p63s23p6 ?? ?? ?? ? ? ??
29 Cu 1s22s22p63s23p6 ?? ?? ?? ?? ? ??
30 Zn 1s22s22p63s23p6 ?? ?? ?? ?? ?? ??
23
Physics of Magnetism Ferromagnetism
Ferromagnetic solids have atoms with atomic
magnetic moments which strongly interact with
each other (e.g. magnetite). In these materials
the atoms are packed in the crystal lattice in
such a way that the orbitals of adjacent atoms
overlap (in the case of iron (Fe) the 3d orbitals
are highly eccentric and overlap) . This causes
the electrons to try to adhere to the Pauli
exclusion principle of both atoms simultaneously,
which effectively means that electrons are shared
between adjacent atoms. This results in strong
parallel coupling of electron spin moments
throughout the material and these aligned moments
give rise to a strong permanent magnetisation.
24
Physics of Magnetism Ferromagnetism
In pure ferromagnetic materials, covalent bonding
occurs by exchange of one or more 3d electrons
shared between adjacent atoms, forcing them to
have parallel 3d orbital spins. This is only
favourable in atoms with more than five 3d
electrons as the sharing then brings them closer
to a noble gas state. E.g. CrO2 which was used
extensively in audio tapes.
? ? ? ? ?
Oxygen
Cr 3d orbital
25
Physics of Magnetism Anti-ferromagnetism
In most oxides and sulphides of ferromagnetic
material, the oxygen provide a link between
nearest neighbour Fe cations, which force the
atomic dipoles of the Fe cations to be
anti-parallel. FeO (wustite is an example)
? ? ? ?
? ? ? ?
Fe2
O2-
Fe2
26
Physics of Magnetism Ferrimagnetism
In most oxides and sulphides of ferromagnetic
material, the oxygen provide a link between
nearest neighbour Fe cations, which force the
atomic dipoles of the Fe cations to be
anti-parallel. Fe3O4 (Magnetite is an example)
? ? ?
? ? ? ?
Fe3
O2-
Fe2
27
Physics of Magnetism Magnetic Susceptibility
28
Physics of Magnetism Magnetic Susceptibility
In Ferromagnetic materials applied magnetic
fields induce a magnetization parallel to the
applied field, which can be retained after
removal of the applied field, giving rise to a
remanent magnetization. The magnetization does
not exhibit a linear relationship with the
applied field and for a given ferromagnetic
material and temperature there is maximum
magnetization, known as the saturation
magnetization (Js), beyond which an increased
applied field will not increase the induced
magnetization. The saturation magnetization
decreases with increasing temperature until it is
reduced to zero at a temperature known as the
Curie temperature, which is characteristic of the
particular ferromagnetic material. At
temperatures above the Curie point the material
exhibits paramagnetic behaviour.
29
Physics of Magnetism Hysteresis
When a ferromagnet is subjected to a cyclic
change in the external field the magnetisation is
not directly proportional to the applied field by
there is a lag in the magnetisation, which is
known as hysteresis. H is the applied field, J is
the induced magnetization. Js is the saturation
magnetization, Jr is the saturation remanence and
Hc is the coercivity. The various hysteresis
properties are not solely intrinsic properties
but are dependent on grain size, domain state,
stresses and temperature. Because hysteresis
parameters are dependent on grain size, they are
useful for magnetic grain sizing of natural
samples.
30
Physics of Magnetism
In ionic compounds, such as oxides, more complex
forms of magnetic ordering can occur. Such
compounds can have two atomic sublattices. If
the ferromagnetic effects within these
sublattices oppose and exactly cancel out each
other the material is antiferromagnetic.
Ferrimagnetic and canted antiferromagnetic
substances are those where the two internal
ferromagnetic effects do not completely cancel
each other. These materials behave like
ferromagnetics and have a Curie temperature (or
more correctly a Néel temperature).
31
Physics of Magnetism Temperature Effects
Alignment of magnetic moments at various
temperatures at 0K there is perfect alignment,
but above this the spin moments precess about the
average direction due to thermal activation.
Above the Curie temperature they are random.
32
Physics of Magnetism
33
Magnetism in Oxides
34
Magnetism in Oxides
Ilmeno- Haematite series
Titano-Magnetite series