Download Properties of magnetic materials

Properties of magnetic materials
In an electrical coil in vaccum (number of turns n,
current I, length l) a magnetic field H is produced and
also a magnetic flux density or inductance B.
H = nI/l
B = μoH
μo is the magnetic permeability in vaccum. If for
example an iron core is placed in the coil B is
greatly increased and we obtain
B = μH
μ > μo
μr = μ/μo
where μr is the relative permeability of the material.
Going back to the coil in vacuum; by what amount M must we
increase the magnetic field in order to obtain the same
inductance B as observed with the iron core? The answer is
B = μH = μo(H+M) ≈ μoM since M >> H with the iron core.
M is the magnetisation. The magnetic suceptibility χ = M/H is
another parameter used to characterize magnetism. It is related
to μr in the following way:
μr = μ/μo = (H+M)/H = 1 + (M/H) = 1+ χ.
A material that enhances the magnetism has μr >1, χ > 0 and a
material that weakens the magnetism has μr <1, χ < 0.
Magnetic electrons
Each electron behaves like a small magnet, i.e. it
has a magntic moment called the Bohr magneton
BM = qh/(4πme )
(where q is the charge of the electron, h Planck’s
constant, and me the mass of the electron).
The magnetic moment is caused by (i) the spin of
the electron and (ii) the electron orbiting the
nucleus of the atom.
Magnetic atoms
In orbitals with two electrons of opposite spin (↑↓) the magnetic
moments cancel, while orbitals with an unpaired electron (↑_)
have a magnetic moment.
Atoms of the transition elements often exhibit d-orbitals with an
unpaired electron, which generates a magnetic moment
associated with each atom.
In a crystal, it is possible for the atomic magnetic moments to
interact. If they have the same orientation, a strongly magnetic
material is created.
Magnetic materials
Diamagnets
μr ≈ 0.99995
χ ≈ -0.00005
All solids and liquids that do not exhibit other types of magnetism are
diamagnetic. Diamagnetism decreases B slightly and is associated with the
orbiting of the electrons around the nucleus. A diamagnet is expelled from
a strong applied magnetic field, compare the levitating frog experiment.
Paramagnets
μr ≈ 1.01
χ ≈ 0.01
Paramagnetism increases B and is proportional to the number of unpaired
electrons of the atoms. The atomic magnets have some tendency to align
with the applied field and a paramagnet is drawn into a strong magnetic
field. Paramagnetism is typical for d- and f-block elements. It also exists in
liquids, for example liquid O2 and aqueous solutions containing ions of
transition elements.
Magnetic materials
Ferromagnets μr and χ high
Ferromagnetism enhances B enormeously and is generated by the alignment of
the atomic magnets in domains of μm-size (↑↑↑↑↑↑↑↑↑). All ferromagnets
are solids and are what we normally call magnets. The magnetism is
retained even when the applied field is turned off. The ferromagnetic
elements are: Fe, Ni, Co, Gd, Tb, C?.
Ferrimagnets μr and χ lower than above, but still high
A weaker type of ferromagnet. Neighbouring atomic magnets partly oppose
each other, but a net magnetisation is produced (↑↑↓↑↑↓↑↑↓). Example:
Fe3O4.
Antiferromagnets
μr and χ as for a paramagnet
Neighbouring atomic magnets oppose each other, so that almost no net
magnetisation is produced (↑↓↑↓↑↓↑↓). Distinguished from paramagnets by
different behaviour of B as function of temperature. Examples: MnO, NiO.
Hysteresis in ferromagnets
Nucleation and growth of domains in ferromagnets require energy. This
creates a hysteresis loop in the B-H diagram. The loop is characteriszed by
three parameters:
Bs saturation magnetisation; the maximum B is obtained when all domains and
atomic magnets are aligned
Br remanence; the magnetisation remaning after the applied magnetic field has
been turned off
Hc coercive field, the field needed to remove the remanence magnetisation, i.e.
to demagnetise the material
The hysteresis loop decreases with increasing temperature and the
ferromagnetism disappears completely at the Curie temperature
Technical magnets
Soft magnets for electrical applications: cores for electromagnets, electric motors,
transformers, generators, read-write heads. The material is continuously cycled
through the hysteresis loop. The loop should be small in the H-direction and large
in the B-direction, so that the magnetisation is strong but easily reversed. Eddy
currents causing heating are avoided by laminating with an insulator (polymer).
Examples: (Fe,Si), Permalloy (Fe,Ni), ferrites MFe2O4, GMR thin layers.
Hard magnets are permanent magnets. The hysteresis loop should be large in both the
H- and the B-direction in order to obtain a strong magnetisation that is not easily
removed. It is advantageous to make materials with small grains that consist of only
one domain, since it is difficult to nucleate a new domain. Examples: Alnico
(Fe,Al,Ni,Co) with precipitates, Co5Sm produced using powder metallurgy,
(Nd,Fe,B).
Materials for computer memories should have a small and square hysterisis loop, so
that the magnetisation is relatively easy to change and north (1) and south (0) are
clearly distingushed. Examples: ferrites MFe2O4, GMR thin layers Fe/Cr or Co/Cu.
Fine tuning of ferrites
Magnetite
Fe3O4 or FeIIO·FeIII2O3 is a ferrimagnet with Tc = 580 oC. Magnetite is attracted by a
standard permanent magnet, but sometimes it is possible to find more strongly
magnetic specimens, “lode stones”, that attract unmagnetised iron. The
magnetite crystal structure is of the spinel-type and it is based on a cubic close
packing of oxide ions. The cations occupy some of the tetrahedral and
octahedral interstitial sites according to the scheme
(FeIII)tetr(FeIIIFeII)octO4.
The Fe(III) ion has 5 unpaired electrons (5 BM) and Fe(II) has 4 unpaired
electrons (4 BM). The atomic magnets on the two Fe(III) ions are coupled so
that they cancel each other. The Fe(II) ions all have their magnetic moment in
the same direction within a domain and give rise to a fairly strong magnetism.
The strength of the magnet can now be fine-tuned by substituting the Fe2+ (4 BM),
with other divalent ions of similar size, but different magnetism :
Zn2+ (0 BM), Cu2+ (1 BM), Ni2+ (2 BM), Co2+ (3 BM), Mn2+ (5BM).
Rock magnets
Mid-Atlantic ridge
Molten lava (1100-1200 oC) rises at the fracture situated in the middle of the
Atlantic ocean. When the lava cools and forms a rock on both sides of the
fracture, the magnetite crystals are magnetised by the Earth’s magnetic
field at T < Tc.
About once every million years, the direction of the magnetic field is reversed
and this also affects the new-forming rock. The magnetisation of the rock
changes polarity after about 10 km in a mirror symmetric pattern with the
fracture at the mirror plane. This observation finally convinced most
scientists that plate tectonics exists!
The magnetic polarity of the rock (10 km-scale) is due to the magnetic
domains (μm-scale) formed in magnetite crystals. The ferrimagnetic
properties depend on the magnetic coupling between the atoms in the
crystal structure (Å-scale). The magnetic properties of the atoms are in turn
determined by the magnetic properties of the electrons.