Cooperative magnetism
Magnetic behavior is restricted mainly to compounds of transition metals and
lanthanides, most of which possess unpaired d and f electrons, respectively. The
magnetic moments of atoms in solids may interact with each other if they are close
together, this is called cooperative magnetism.
1. Para-, ferro-, antiferro-, ferricmagnetism
Paramagnetism is a form of magnetism that occurs only in the presence of an
externally applied magnetic field. When an external magnetic field acts on a
paramagnetic substance, the magnetic moments of the electrons adopt the orientation
of the field, the sample is magnetized. Paramagnetic materials are characterized by a
random orientation of the magnetic moments and therefore the total magnetic moment
is equal to zero. (Al, Sn, Pt, O2)
Ferromagnetism is a cooperative phenomenon, i.e. many particles in a solid behave in
a coupled manner. In a ferromagnetic substance the magnetic moments of adjacent
atoms orient themselves mutually parallel, and their action is added up. (α-Fe, Ni)
Antiferromagnetism. The coupling of magnetic moments of the atoms can result in
spin having opposite orientations; in this case the material is antiferromagnetic. At
very low temperatures its total magnetic moment is zero. (MnF2,FeF2(rutile Type))
Ferrimagnetism. The particles bearing opposite magnetic moments occur in different
quantities and or their magnetic moments differ in magnitude. The behavior in a
magnetic field is like that of ferromagnetic materials. (FeFe2O,NiFe2O4)
2. Susceptibility an magnetization
When a substance is placed in a magnetic field, H , the density of lines of force in the
sample (magnetic induction or magnetic flux density B) is related to H by the
permeability, of the substance, μ
B=μH
B=μ0H+μ0M
μ0 :the permeability of free space
M: is the magnetization
The magnetic susceptibility χ is defined as the ratio of magnetization to field.
χ=M/H , therefore μ=μ0(1+χ)
the ratio μ/μ0 is equal to 1+χ and is called the relative permeability, μr.
3.Temperature dependence of susceptibility: Curie-Weiss law
Many paramagnetic substances obey the simple Curie law, especially at high
temperatures. It states that magnetic susceptibility is inversely proportional to
temperature:
χmol=C/T
(C = Curie constant.)
Such Curie response occurs when there is no spontaneous interaction between adjacent
unpaired electrons. When there is some spontaneous interaction between adjacent
spins, which may develop into ferro- and antiferromagnetism at low temperatures, a
better fit to high temperature behavior in paramagnetic region is often provided by the
Curie-Weiss law:
χmol=C/T-θ
(θ = Weiss constant)
Reference:
U.Müller,Inorganic Structural Chemistry,2ndEdition,John Wiley&Sons Ltd,Chichester,
2007
A.R.West,Basic Solid State Chemistry,2ndEdition,John Wiley&Sons Ltd, Chichester,
2009
1.
Compare the interaction between unpaired spins in a ferromagnetic material to
the one for an antiferromagnet material. Explain the difference.
2.
When the temperature is increasing, the magnetic susceptibility of paramagnetic
will decrease. Explain why.