Magnetic Properties

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  • Topic: Magnetism, Magnetic field, Paramagnetism
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Magnetic Properties of Solids

Magnetic Properties
Magnetic (with unpaired electron) Materials Non-magnetic or diamagnetic (electrons all paired up)

Paramagnetic Ferromagnetic Antiferromagnetic Ferrimagnetic

Magnetic Behavior
B = μH B = μ0H + μ0M
Induction generated Induction generated by the field by the sample

B: magnetic flux density μ: permittivity (m0: free space) H: magnetic field M: Magnetization

χ = M/H

χ: magnetic susceptibility

B = μ0H + μ0Hχ B = μ0H (1 + χ) = μH μ0 (1 + χ) = μ (1 + χ) = μ / μ0 = μr μr: relative permittivity

Behavior of Substances in a Magnetic Field

Magnetic behavior may be distinguished by the values of χ and μ and by their temperature and field dependence 1. Positive vs. negative value: only diamagnetic materials show negative χ 2. Absolute value: ferromagnetic materials show huge positive value 3. Temperature dependence: diamagnetism is not temp. dependence, antiferromagentic materials increase with increasing temp, and para- and ferromagnetic materials decrease with increasing temp 4. Field dependence: only ferro- and antiferromagnetic materials show field dependence

Effect of Temperature
Paramagnetic substance: obey Curie Law
C: Curie constant T: temperature

There is no spontaneous interaction between adjacent unpaired electrons. With increasing temperature the alignment is more difficult and χ decreases.

Paramagnetic substance show some magnetic ordering (ferro- or antiferro): Curie-Weiss Law χ= C Τ-θ θ: Weiss constant

There is some spontaneous interaction between adjacent spins. A better fit to the high temperature behavior in the paramagnetic region is provided by Curie-Weiss Law (with additional Weiss constant).

Effect of Temperature

Paramagnetic: Curie law; T decrease, c increase (alignment easier) Robert John Lancashire (wwwchem.uwimona.edu.jm)

Tc: ferromagnetic Curie temperature (below Tc, sample is ferromagnetic) TN: Néel Temperature (below TN, sample is antiferromagnetic)

Magnetic Moments
Magnetic moment (μ): relates directly to the number of unpaired electrons

Susceptibility and magnetic moment can be determined experimentally using a Guoy Balance:

For paramagnetic substance, unpaired electrons are attracted by the magnetic field and an apparent increase in mass of the sample occurs when the field is switch on

www.geneq.com

Electron Spin Magnetic Moment
Magnetic properties of unpaired electrons arise from electron spin and electron orbital motion Bohr magneton (BM): A natural constant which arises in the treatment of magnetic effects. The magnetic moment is usually expressed as a multiple of the Bohr magneton. BM = eh 4πmc e: electron charge h: Planck’s constant m: electron mass c: velocity of light

Magnetic moments of single electron

μs = g√s(s+1) μs = 1.73 BM μs = g√S(S+1)

g: gyromagnetic ratio ~2 (for electron spin magnetic moment) s: spin quantum number S: sum of spin quantum number

> 1 unpaired electron

Electron-Orbit Magnetic Moment
The motion of an electron around the nucleus may in some materials, give rise to an orbital moment, which contributes to the overall magnetic moment μS+L = [4S(S+1) + L(L+1)]½ L: orbital angular momentum quantum number

Simplified approach: a single unpaired electron is set equal to 1 BM μ = gS

Mechanisms of Magnetic Ordering
The spontaneous alignment of magnetic dipoles in ferro / antiferromagnetic states need some positive energy of interaction between neighboring spins. The origin of this coupling is quantum mechanical. Antiferromagnetism in NiO: superexchange

• The unpaired electrons in these eg orbitals couple with electrons in the p orbitals of the O2- ions. • p orbitals of the O2- ions contain two electron each, which are coupled antiparallel.

Origin of Para- and Ferromagnetism in Metals

Pauli Paramagnetism (paramagnetism of free electrons) Ferromagnetism

Magnetic Materials-Metal and Alloys
Five transition metals: Cr, Mn, Fe,...
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