Magnetic and electrical properties of ferromagnetic alloys near the critical concentration

A simple molecular field theory is developed to explain at least qualitatively the behaviour of weakly ferromagnetic and strongly paramagnetic alloys near their critical concentration c F . The free energy of a weakly ferromagnetic alloy can be expanded in powers of magnetization ζ and a modified Landau theory is used to calculate the concentration dependence of the magnetization, specific heat and the susceptibility near c F . It is believed that such a theory can work better in this case than does the usual Landau theory as fluctuations in ζ are relatively small for low temperatures. A change in low temperature resistivity around c _F is also expected as a result of ciritcal scattering of conduction electrons. This change was first calculated by Rice (1967) for strongly paramagnetic alloys giving a large T ² term. However, this calculation is not applicable for c very close to c _F . It is shown that for c → c _F the paramagnetic resistivity remains finite and has a maximum for c ═ c _F , ρ ^Para _c ═ c F ∝ T ^5/3 . It is also found that the ferromagnetic resistivity ρ ^ferro has a similar dependence on concentration and temperature as ρ ^Para and ρ ^ferro c ═ c _F ═ ρ ^Para c ═ c _F , i.e. the resisitivity is symmetrical around c _F .