Heisenberg Interpretation on Internal Field: (Quantum Theory)

HEISENBERG INTERPRETATION ON INTERNAL FIELD: (QUANTUM THEORY)

The Weiss theory of ferromagnetism explains about the molecular field but it is not possible to explain large value of internal field.

To explain the large internal field, Heisenberg gave an explanation which is based on the non-magnetic interaction called the exchange interaction between electrons. These exchange forces are caused by coulomb interaction and generally it should be larger than magnetic interaction.

Exchange force appears in the form of spin-spin interaction and the strength of the interaction depends upon the interatomic separation, it may change its sign as the separation is varied. If the interatomic distance is decreased, the electron spins are decreased and therefore the exchange force decreases and finally they favour the anti-parallel spins.

Heisenberg developed his theory on the analogy of Heitler-London model of hydrogen molecule. According to this, the exchange interaction between electrons in different quantum states lead to a lower energy, provided the spin quantum numbers of both the states are same. i.e., the spins are parallel. Therefore the exchange interaction between the electrons is represented as

E_ex=-2 J_ij S_i S_j

where J_ij is the exchange integral for the two atoms and S_i and S_j are the spin angular moments associated with the ith and th state. A plot of exchange integral value (J;;) and the interatomic distance (rab) is shown in Fig. 3.12.

Let us consider rab as the interatomic distance and ro as the orbital radius of electron. From the graph (Fig. 3.12) we can say,

(1) The value of J_ij is positive when r_ab/r_o > 3. i.e., the exchange energy is negative and hence the parallel orientation is high. Due to this the atom possess ferromagnetic properties. (Examples: Fe, Co, Ni and Gd).

 (2) The value of J_ij is negative when r_ab/r_o < 3. i.e., the exchange energy is positive and hence the atoms coming under this criteria possess anti-ferromagnetic properties. (Examples: Cr, Mn).

The ratio r_ab/r_o is  the criteria for a magnetic materials whether it is ferro(or) antiferromagnetic materials. Moreover alloys of any two materials give rise to favourable ratio value. This is a great boom in solid state for the production of new materials of any desired characteristics.