Magnetic Moment Essay

Besides of the property possessed by diamagnetic atoms or molecules, paramagnetic ones have unpaired electrons which lead to the major contribution to the overall magnetic moment in the direction of the applied field. This effect is obvious enough that can cancel the diamagnetic effect out. The microscopic magnetic moment of the electrons is quantized and they do Larmor procession in the external magnetic field which results from their motion affected by the external field as well as their spin around its own axis. Consequently, the final angular momentum is represented by J, which is equal to the sum of orbital angular momenta (L ) and the spin ones (S). Then the effective magnetic moment (μeff) can be given by a formula (Russell-Saunders coupling, Fig. 1.2): μeff = gJ μB [j (j+1) ]1/2 J = L + S

Fig. 1.2 The illustration about angular momentum of an atom doing Larmor procession here j is the total angular momentum quantum number which is related to J, gJ is the Landé g-factor (a kind of a g-factor, and Alfred Landé first described it in 1921. It is used for describing the total angular momentum quantum.), and μB is the Bohr magneton.

Seeing from the formula, we can see the importance of unpaired electrons whose number determine the value of the total spin quantum number

This method is based on a apparent mass change of a substance before and after the effect of a magnetic field. There is an alternative named Faraday balance whose principle is almost the same. Afterwards there is another method called Evans balance which is more convenient and is suitable to all forms of samples such as solids, liquids, and gases. This method is not expensive, neither requires a precision weighting device. Then some techniques such as SQUID (superconducting quantum interference device)[14] and Hall-sensors[15] based on it are