The present work is devoted to the derivation of an effective magnon–paramagnon
theory starting from a microscopic single-band lattice model of ferromagnetic
metals. For some values of the microscopic parameters it reproduces the
Heisenberg theory of localized spins. For small magnetization the effective model
describes the physics of weak ferromagnets. It allows us to account for the
magnon–magnon and magnon–paramagnon interactions going beyond
Moriya's theory. The effective theory is written in a way which keeps
O(3)
symmetry manifest, and describes both the ordered and disordered phases of the
system.
To derive the effective model a Schwinger-bosons–slave-fermions representation of
the operators is used. Within this approach the local Coulomb repulsion is treated
exactly, and as a result, the constants in the effective theory are finite and well
defined for all values of the magnetization.
An equation for the Curie temperature, which takes the magnon
fluctuations into account exactly, is obtained. For weak ferromagnets, in the
spin-wave approximation, the critical temperature scales like Tc ∼ m5/3.
It is well below the Stoner critical temperature Tc ∼ m
and the critical temperature obtained within Moriya's theory Tc ∼ m3/2.