Magnetic Properties

Most compounds of the transition elements are paramagnetic, and this magnetic behaviour is directly tied to the electronic configuration of the atom or ion in question. As established already in Class XI, an electron possesses a magnetic moment arising from two distinct sources: its spin around its own axis, and its orbital motion around the nucleus; both motions, being motions of a charged particle, generate a small local magnetic field. On the basis of their bulk magnetic behaviour, materials can be broadly classified into several categories: (i) paramagnetic materials, (ii) diamagnetic materials, and, going beyond these two simplest categories, (iii) ferromagnetic materials and (iv) antiferromagnetic materials.

Materials with no net elementary magnetic dipoles -- in other words, species in which every electron is paired -- are diamagnetic. Such materials are weakly repelled by an externally applied magnetic field, because the presence of the external field induces a small magnetic response in the material that opposes (rather than reinforces) the applied field.

Paramagnetic solids, by contrast, possess unpaired electrons and therefore carry genuine magnetic dipoles, but in the bulk solid these individual atomic/ionic dipoles are isolated from one another (not strongly coupled). In the absence of an external magnetic field, these dipoles point in random directions, so the sample as a whole shows no net magnetism. But when an external magnetic field is applied, the individual dipoles align (at least partially) parallel to the direction of that field, and the sample is consequently attracted into the field -- the hallmark, defining behaviour of paramagnetism.

Ferromagnetic materials go a step further: they possess an internal domain structure, in which the magnetic dipoles within any single domain are all aligned parallel to one another, giving each domain a strong net moment. However, in the absence of an applied field, the dipole orientations of neighbouring domains are randomly oriented relative to one another, so the bulk unmagnetised sample still shows little or no net external field. Certain transition elements, or ions of transition elements with unpaired d electrons, are capable of showing this ferromagnetic behaviour under suitable conditions.

For 3d transition-metal ions in typical paramagnetic solids, the observed magnetic dipole moment corresponds overwhelmingly to the electron SPIN contribution alone -- the orbital angular-momentum contribution is, in the standard approximation used here, said to be 'quenched' (effectively suppressed by the surrounding crystal/ligand environment) and can be neglected to good approximation. Under this 'spin-only' approximation, the magnetic moment of the ion is given by the formula μ = g√[S(S+1)] μ_B, where S is the total spin quantum number contributed by all the unpaired electrons in the ion, g is the electron's g-factor (very close to 2 for a free electron), and μ_B is the Bohr magneton, the fundamental unit of atomic-scale magnetic moment.

For an ion with n unpaired electrons, the total spin quantum number is simply S = n/2 (each unpaired electron contributing spin 1/2), and taking g = 2 (the standard free-electron value used throughout this simplified treatment), the spin-only magnetic moment reduces to the compact and commonly quoted working formula μ = √[n(n+2)] μ_B. …