Fundamentals of Magnetism

1.4.1 Fundamentals of Magnetism

The “spin state” of electrons in an atom determine the magnetic property of the atom. Depending on this spin state of the electrons, the atoms may be classified into mainly : Diamagnetic and Paramag- netic.

(a) Diamagnetic atoms (or ions) are those in which there are no uncoupled or uncompensated electron spins.

(b) Paramagnetic atoms (or ions) are those with uncoupled or unpaired electron spins in the orbital giving rise a “net magnetic (spin) moment”.

The magnetic moment of an uncoupled electron is given as Bohr magneton, µ B . One Bohr magneton represents the magnetic moment of ‘one uncoupled’ electron. Therefore, for example, the net magnetic moment for the Fe 3+ atom is 5 µ B , since it has ‘5 uncoupled’ electrons. Different types of magnetism are shown below :

Ferromagnetic Anti-ferromagnetic Anti-ferrimagnetic Although paramagnetic atoms have ‘net magnetic moments’, the overall magnetic moment of

crystalline solid may be zero due to the interaction of the atoms in the crystalline lattice. Depending on the ‘nature’ of this interaction, the atoms may be further classified as ‘ferromagnetic’, ‘anti-ferromagnetic’, ‘ferrimagnetic’.

A crystal is called a ferromagnetic, if the participating atoms are ‘paramagnetic’ and their ‘direc- tions’ are aligned in one direction, which can be switched in the 'opposite direction'. Anti-ferromagnetic crystal is the one whose ‘total magnetic moment’ is zero, since the magnetic moment of the atoms aligned in one direction is compensated by other atoms, whose magnetic moments are aligned in the opposite direction.

In a ferrimagnetic crystal, the magnetic moments of the atoms are arranged in a similar way to anti-ferromagnetic crystal. However, if the magnetic moment in one direction is larger than the other direction, the result is a “non-zero” overall magnetic moment. Even in ferromagnetic crystal, both up and down magnetic moments coexist. The difference between ferromagnetic and ferrimagnetic is that

25 up and down moments coexist ‘intrinsically’ within the crystal for ferrimagnetic → while they are formed

GENERAL INTRODUCTION

by two distinct regions (called ‘domains’) of the crystal in ferromagnetic materials. Hence, only ‘one direction’ of magnetic moment exists in a domain of ferromagnetic crystals.

In this book, we are dealing with nano materials. In chapter – 5, the magnetic properties of the nano particles of magnetite (i.e., a ferrite with a spinel structure) that are embedded in a glassy diamag- netic matrix are discussed in details. These small particles show a phenomenon of ‘super-paramagnet- ism’ and also within the nano domain for a slightly higher particle size, these nano particles show ‘ferrimagnetism’, as per the above description. In the continuation of this section, we would like to give some details on diamagnetism and paramagnetism along with symmetrization and antisymmetrization, which are very important concepts. Moreover, Pauli’s principle on the ‘electron spin’ is discussed with

a mathematical treatment in terms of ‘determinants’ so that a theoretical understanding is developed for the readers to appreciate some intricate details of the ‘magnetic properties’, i.e., the ‘spin properties’, of nano materials. The necessary concept on the ‘magnetic propetries’ of the nano materials can be ob- tained from the theoretical aspects of Mössbauer and ESR spectra, as detailed in the sections – 1.6.1

and 1.6.2.

The concept of antisymmetrization is important in the quantum level, which can have some cosequences on the magnetic properties of solids containing nano particles. So, here is a brief discussion on this subject.