Magnetization without spin: Effective Lagrangian of itinerant electrons

In this paper, an effective Lagrangian of an itinerant electron system of finite density at a finite magnetic field is obtained. It includes a Chern-Simons term of electromagnetic potentials of lower-scale dimensions compared to those studied before. This term has an origin in the many-body wave function and a unique topological property that is independent of a spin degree of freedom. The coupling strength is proportional to $\frac{\rho }{eB}$, which is singular at $B=0$ for a constant charge density. The effective Lagrangian at a finite B represents the physical effects at $B\ne 0$ properly. A universal shift of the magnetic field known as the Slater-Pauling curve is obtained from the effective Lagrangian.