ABSTRACT
This chapter treats some properties of systems of independent spins and explains the origin of the exchange interaction in materials. It introduces the spin and shows some principal behaviors of a system of independent spins under the application of a magnetic field. The chapter examines three cases. The first case concerns free electrons at low temperatures. The second case is the system of free atoms where each atom has a permanent magnetic moment. The third case is a diamagnetic case: The reaction of the electrons in an atom to an applied magnetic field gives rise to a negative susceptibility. Exchange interactions, or magnetic interactions, between spins of neighboring atoms can give rise to a magnetic ordering which is responsible for the principal low-temperature properties of the system. Since the spins are independent, their states are affected only by a variation of an external parameter such as the temperature and/or an applied magnetic field.
