Magnetic and electrical properties of ferromagnetic alloys near the critical concentration

Abstract

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 $\zeta$ 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 $\zeta$ are relatively small for low temperatures. A change in low temperature resistivity around c$_F$ is also expected as a result of critical 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$\rightarrow$ c$_F$ the paramagnetic resistivity remains finite and has a maximum for c = c$_F,\rho^{para}_{c = cF}\propto$ T$^\frac{5}{3}$. It is also found that the ferromagnetic resistivity $\rho^{ferro}$ has a similar dependence on concentration and temperature as $\rho^{para}$ and $\rho^{ferro}_{c=c_F} = \rho^{para}_{c=c_F}$, i.e. the resistivity is symmetrical around c$_F$.