MAIN MAGNETIC BEHAVIOR OF SEMICONDUCTOR MATERIALS

Hello friends of steemit, this time I write to make a brief review about the main magnetic orderings observed in semiconductor materials.

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DIAMAGNETISM

Diamagnetism is a behavior that derives from the change in the movement of the electron around the nucleus, produced by the application of a magnetic field, where the electrons move in such a way that they produce a magnetic dipole moment in the opposite direction to the field.

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PARAMAGNETISM

Paramagnetism is a type of magnetic behavior that is related to the differences in the number of inhabitants between states allowed for unpaired electrons in a given system of particles. The law of Curie is the equation that defines paramagnetism and is as follows:

Where:

is the magnetic susceptibility.

is the temperature expressed in degrees Kelvin (K).

is a constant known as the Curie constant. Your unit is

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Although Curie's law accounted for paramagnetic behavior, it was observed that most non-ferromagnetic metals had a magnetic susceptibility independent of temperature. W. Pauli showed that many conduction electrons in a metal, do not have the possibility of orienting when a magnetic field is applied, and that only electrons in a range of energies KbT, at the top of the Fermi distribution, have the opportunity to orient when a field is applied, and therefore, a fraction T / Tf of the total number of electrons, is the one that contributes to the magnetic susceptibility of the material. Using the Fermi-Dirac statistic the expression is reached:

Where:

is the concentration of unpaired electrons.

it's Boltzmann's constant.

is the temperature of Fermi.

is the Bohr magneton.

On the other hand, the Dutch physicist J.H. Van Vleck, found that there is a paramagnetic contribution to the magnetic susceptibility of a material which takes into account the average change of the dipole moments present in the system, going from the state of minimum energy to any other allowed state of energy. The expression of J.H. Van Vleck is:

Where:

is the Bohr magneton.

is the gyromagnetic factor of the free electron

is the concentration of unpaired electrons with components of angular momentum and spin on the z axis.

they are the base states, which have energies respectively.

FERROMAGNETISM

This is a behavior in which there is a long-range ordering of the magnetic dipole moments of the particles and their spins. This is due to the cooperative effect that exists between the particles, that is, the orientation of the spin of a particle is influenced by that of the other particles in its environment, so it differs from the previous cases, where the magnetism is not cooperative.

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The ferromagnetic arrangement corresponds to the parallel orientation with respect to a sufficiently large magnetic field from the spins of all the particles present, at temperatures close to absolute zero.

In this type of materials, when the temperature decreases, a transition of the ferromagnetic-paramagnetic type (F-P) is observed, this happens at a specific temperature, known as the Curie temperature.

The magnetic susceptibility of ferromagnetic materials at temperatures higher than the Curie temperature is given by the Curie-Weiss Law:

Where:

it's Curie's constant.

is the temperature measured in Kelvin degrees.

is the temperature of Curie-Weiss.

The above equation is only valid for

To find the magnetic susceptibility for the ferromagnets below the Curie-Weiss temperature one must resort to the following more general expression:

Where:

it is the magnetic free energy.

is the intensity of the magnetic field.

FERRIMAGNETISM

This is an order in which there is a cooperative effect, in which two subnetworks of atoms can be identified, which present spins of different magnitude and aligned in opposite directions, one with respect to the other subnet.

The ferrimagnetic materials present a transition to paramagnetism at a temperature known as the ferrimagnetic Curie temperature and as with ferromagnetism, below this temperature, the behavior of ferrimagnetic materials is complex.

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ANTIFERROMAGNETISM

(a) paramagnetic materials. (b) ferromagnetic materials. (c) antiferromagnetic materials

This is a long-range order, which corresponds to the anti-parallel orientation of the spins in a material.

The antiferromagnetic materials present an antiferromagnetic-paramagnetic phase change (AF-P), at a temperature known as the temperature of Néel (Tn), in honor of the French physicist Lois Néel, who in 1936, postulated the existence of this magnetic ordering .

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REFERENCES:

Morrish, A. H. The physical principles of magnetism. John Willey & sons, INC. New York (1965).
Nobel foundations. Nobel lectures in physics (1971-1980).World Scientific Publishing Co. Singapore (1992).
Bersohn, M. Baird, J. C. An introduction to electron paramagnetic resonance. W. A. Benjamin, INC. New York (1966).
Kittel, C. Introduction to solid state physics. John Willey & sons, INC. New York (1964).
Poole, Charles P. Electron spin resonance: A compresive treatise on experimental techniques. John Wille & sons, INC. Second edition.Ontario (1983).