A spin-rotational-invariant approach to the spin-fluctuation theory of itinerant-electron magnetism is proposed and evaluated in the framework of a $d$-band model Hamiltonian including intra-atomic exchange interactions $J$ and the coupling to a local magnetic field $B$. Using a vector-field Hubbard-Stratonovich transformation, we obtain a static approximation to the density matrix operator from which the equilibrium properties are directly derived. The method is applied to a single-site model taking Fe as a representative example. Exact and approximate analytical results are given for the local magnetic moments, their longitudinal and transversal components, the field-induced magnetizations, entropy, and heat capacity. Goals and limitations of various approximations are discussed as a function of $J,B$, and temperature. The quantum-mechanical origin of some important drawbacks found in previous vector-field static approaches is identified. The significant improvements achieved with the static density operator are demonstrated.

• Received 3 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.214435