# Magnetic Properties (Homework 8)

1. (a) Please explain why some atoms are paramagnetic and others are diamagnetic.

(b) Define Ferromagnetism, Antiferromagnetism, Ferrimagnetism, and Itinerant Ferromagnetism.

a)

$M=χH$    ($M$ is magnetization, $H$ is magnetic field)

$\left\{\begin{matrix}χ≫1 \text{ is feromagnetism}\\χ>≈1 \text{ is paramagnetism}\\χ<0\text{ is diamagnetism}\end{matrix}\right.$

Atoms have valence electrons on the last level. All electrons have spins. The spin of un-paired electrons on the last energy level give a non-zero magnetic field. The sum of each magnetic moment of each un-paired electron on the last level, due to its spin) is called magnetization. Because they are oriented at random, the total sum of the magnetic moments of all un-paired valence electrons is usually zero. (All these remaining spins can be compared with tiny current loops).

Diamagnetism explanation:

The Faraday law says that an external applied magnetic field induces in a material a current such that its magnetic field is opposite to the external applied field (the tiny currents that correspond to electrons spins). Therefore the substance tend to be repelled by an external magnetic field.  Therefore all materials have a diamagnetic component.

Paramagnetism explanation

All unpaired electrons on the last energy level, from different neighboring atoms have exchange interaction between them.  Thus they will align their spins (the exchange interaction of the valence electrons of two neighboring atoms is minimum when their spins are parallel). The magnetic moments of these aligned spins give a total weak magnetic moment (on the overall all the valence electrons spins remain randomly oriented) .  When an external magnetic field is applied these weak magnetic moments (aligned spins) will further align with the magnetic field.This is responsible for the paramagnetism

Feromagnetism explanation

In some materials, there are microscopic domains (containing some hundreds of atoms) where the spins align parallel for all valence electrons of all atoms (not just for some neighboring atoms). When an external field is applied all the magnetic moments from all the domains align with the applied magnetic field and thus a very strong magnetization is produced. This alignment of magnetic moments from neighboring domains remains in place after the external field is removed. This is responsible for ferromagnetism.

b)

Ferromagnetism, Ferrimagnetism and Ferrimagnetism are all due to the existence of magnetic domains (of some hundreds of atoms) as explained at a).

For Feromagnetism all spins of all neighboring atoms from a domain are parallel on to each other.  However is a lattice sometimes neighboring atoms individual magnetic moments are opposite one to the other (when for example there are two types of atoms in a lattice). When the resultant moment of two anti parallel moments gives a (smaller) magnetic moment (aligned with the external field) , this is Ferimagnetism. When the resultant moment of two anti parallel moments gives a (smaller) magnetic moment (opposite to the external field) thus is Antiferomagnetism.

Feromagnetism, ferimagnetism and Antiferomagnetism happen when there are big domains (with aligned spins of all valence electron atoms) in the substance. However in gases there cannot exist big domains and some different aligned spins (from neighboring atoms) wander through the system (gas). This is called Itinerant Magnetism (the magnetic moments domains move through the substance).