Origins of magnetism in materials

Both the orbital and the effective spinning motions of the electron have associated angular moments quantized in units of ii = 1.055 x 10-34 Js. It is an elementary exercise in physics to show that the relationship between the magnetic dipole moment / and the angular momentum L for a moving particle of mass m and charge Q is 

It follows that once the total angular momentum of an ion, atom or molecule is known, so too is its magnetic moment. Most free atoms possess net angular momentum and therefore have magnetic moments, but when atoms combine to form molecules or solids, the electrons interact so that the resultant angular momentum is nearly always zero. Exceptions are atoms of the elements of the three transition series which, because of their incomplete inner electron shells, have a resultant magnetic moment. 

There are two major contributions to the magnetic moment of an atom - from the orbiting electrons and from their spin. There is also a nuclear magnetic moment, but because it is of the order of 10 3 of that of the Bohr magneton, it is insignificant in the present context and will be disregarded. 

The description of the orbital and spin states of an electron in terms of the quantum numbers n, /, m, and s, and the calculation of the total angular momentum of a number of electrons in an atom in terms of J are outlined in Chapter 2. From that discussion, together with the above, it follows that an electron with orbital quantum number / possesses a total magnetic moment /(/ + and this can be oriented with respect to a magnetic field in 

The field vector determining the Forentz force on a current is the magnetic induction B, which is measured in teslas. In principle, B at a point P can be 

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