Theory of Electrical Resistivity of Ferromagnetic Metals

This paper gives a brief account of a new calculation of the electrical resistivity of ferromagnetic metals on the s‐d or s‐f exchange model. It points out that the conventional treatment of the problem taking the s‐d interaction as a small perturbation to a system of free electrons and ferromagnetically coupled spins is basically inconsistent with the indirect exchange theory. The consistent formulation of the problem is then given with the help of the Kubo method of electrical conductivity. The correlation functions involved in the Kubo formula are evaluated by the equation of motion method for many body problems. The hierarchy of equations of motion is terminated at a finite order by the decoupling approximation. The resulting equations are solved and the solutions are used to calculate the conductivity. A new result that comes out of this theory is that the low‐temperature electrical resistivity is proportional to the density of spin waves and has a $T^{\frac{3}{2}}$ dependence on the temperature T. This result is in quantitative agreement with the experimental findings of Kondorsky et al.