1. Magnetic Properties from Molecules to Solids
Materials may be classified by their response to externally applied magnetic fields as
diamagnetic
paramagnetic
ferromagnetic
antiferromagnetic
ferrimagnetic

2. Magnetic Properties Diamagnetic: unaffected by a magnetic field
no unpaired electrons
Paramagnetic:
influenced by a magnetic field
unpaired electrons
Transition metals and their compounds are often paramagnetic
Have unpaired d-electrons
Eg. Ti2+
Mn2+

3. diamagnetism : systems contain no unpaired electrons

5. Magnetic properties
Magnetic susceptibility (μ) and the spin-only formula.
Materials that are diamagnetic are repelled by a magnetic field, whereas paramagnetic substances are attracted into a magnetic field, i.e. show magnetic susceptibility. The spinning of unpaired electrons in paramagnetic complexes of d-block metal ions creates a magnetic field, and these spinning electrons are in effect small magnets. The magnetic susceptibility, μ, due to the spinning of the electrons is given by the spin-only formula:
μ(spin-only) = n(n + 2)
Where n = number of unpaired electrons.

6. Magnetization and Magnetic Susceptibility
χ = ∂ M / ∂ H
where M : the molar magnetization, a vector,
H : the magnetic field strength , an axial vector,
χ: molar magnetic susceptibility, a second rank tensor.
When H is weak enough, χis independent of H, one can write
M = χ H

7. χ

8. The measurerement of magnetic susceptibility
A Gouy balance, which is used to measure the magnetic susceptibi
lities of substances

9. Electronic configurations of dn complexes from paramagnetism and diamagnetism
Magnet on:
Paramagnetic
Magnet off
Magnet on:
diamagnetic

10. Sample problem
The magnetic moment of an octahedral Co(II) complex is
4.0 µB. What is its electron configuration?
Answer
µ = [N(N+2)]1/2 µB 4.0 = [N(N+2)]1/2 N 3
A Co(II) complex is d7. The two possible configu
Rations are t52ge2g (high spin) with three unpaired electron
Or t62ge1g (low-spin) with one unpaired electron.The spin
Only magnetic moment are 3.87 µB and 1.73 µB,repectively
(see Tab.).Therefore the only consistent assigment is the
High-spin configuration t52ge2g.

13. Magnetic Measurement
Experimental distinctiom between high-spin and low-spin
complexes is based on the dertermination of their megnetic
properties.Complexes are classified as diamagnetic if they
tend to move out magnetic field and paramagnetic if they
tend to move into magnetic field.The extent od paramagnetism
of a complexes is commonly reported in terms of the magnetic
dipol moment.the higher magnetic moment the greater the
paramagnetism of the sample.
The spin-only paramagnetism which is characteristic of many
d-metal complexes.
µ = 2[S(S+1)]1/2 µB
S: Total spin quantum number; each unpair electron has a spin
quantum number of ½, it allows that S= 1/2N, where N is the
number of unpaired electrons;therefore
µ = [N(N+1)]1/2 µB ; µB is known as Bohr magneton
its value is 9.274x10-24 JT-1

14. t42ge2g ( N= 4, µ= 4.90) configuration and a low-spin t62g (N=0, µ=0)
A measurement of the magnetic moment of a d-block complex can be
usually be interpreted in terms of the number of unpaired electrons it
contains, and hence the measurement can be used to distinguish bet-
ween high-spin and low-spin complex. For example, Magnetic measu
Rements on d6 complex permit us to distinguish between a high-spin
t42ge2g ( N= 4, µ= 4.90) configuration and a low-spin t62g (N=0, µ=0)
configuration.
İon N S µ / µB
Calc Exp.
Ti ½ V
Cr / Mn
Fe /

15. Magnetic properties
The spin-only formula applies reasonably well to metal ions from the first row of transition metals: (units = μB,, Bohr-magnetons)
Metal ion dn configuration μeff(spin only) μeff (observed)
Ca2+, Sc d
Ti3+ d
V3+ d
V2+, Cr3+ d
Cr2+, Mn3+ d
Mn2+, Fe3+ d
Fe2+, Co3+ d
Co2+ d
Ni2+ d
Cu2+ d
Zn2+, Ga3+ d

16. Example:
What is the magnetic susceptibility of [CoF6]3-, assuming that the spin-only formula will apply:
[CoF6]3- is high spin Co(III). (you should know this). High-spin Co(III) is d6 with four unpaired electrons, so n = 4.
We have μeff = n(n + 2)
= 4.90 μB
energy eg
t2g
high spin d6 Co(III)

17. Spin and Orbital contributions to Magnetic susceptibility
For the first-row d-block metal ions the main contribution to magnetic susceptibility is from electron spin. However, there is also an orbital contribution from the motion of unpaired electrons from one d-orbital to another. This motion constitutes an electric current, and so creates a magnetic field (see next slide). The extent to which the orbital contribution adds to the overall magnetic moment is controlled by the spin-orbit coupling constant, λ. The overall value of μeff is related to μ(spin-only) by:
μeff = μ(spin-only)(1 - αλ/Δoct)

18. Diagrammatic representation of spin and orbital contributions to μeff
d-orbitals
spinning
electrons
spin contribution – electrons are orbital contribution - electrons
spinning creating an electric move from one orbital to
current and hence a magnetic another creating a current and field hence a magnetic field

19. Ferromagnetism:
In a normal paramagnetic material, the atoms containing the unpaired electrons are magnetically dilute, and so the unpaired electrons in one atom are not aligned with those in other atoms. However, in ferromagnetic materials, such as metallic iron, or iron oxides such as magnetite (Fe3O4), where the paramagnetic iron atoms are very close together, they can create an internal magnetic field strong enough that all the centers remain aligned:
unpaired electrons aligned in their
own common magnetic field
unpaired electrons
oriented randomly
unpaired electrons
paramagnetic,
magnetically
dilute in e.g.
[Fe(H2O)6]Cl2.
b) ferromagnetic,
as in metallic
Fe or some
Fe oxides.
separated by
diamagnetic atoms Fe
atoms
a) b)

20. electron spins in opposite directions in alternate metal atoms
Antiferromagnetism:
Here the spins on the
unpaired electrons
become aligned in
opposite directions so
that the μeff approaches
zero, in contrast to
ferromagnetism, where
μeff becomes very large.
An example of anti-
ferromagnetism is found
in MnO.
electron spins in opposite
directions in alternate metal atoms
antiferromagnetism

21. Ferromagnetism and Antiferromagnetism
Curie-Weiss Law
χ = C / (T-θ)
θ : Weiss constant, have the units of temperature
θ > 0, parallel (ferromagnetic) interactions
θ < 0, antiparallel (antiferromagnetic) interactions

22. Ferromagnet

24. Distribution of high- and low-spin complexes of the d-block metal ions:
Co(III) is big exception – all low-spin except for [CoF6]3-
1st row tend to be high-spin except for CN- complexes
2nd and 3rd row are all low-spin except for PdF2 and [PdF6]4-