Noncollinear spin-fluctuation theory of transition-metal magnetism: Role of transverse spin fluctuations in Fe

Abstract

A local electronic theory of transition-metal magnetism at finite temperatures is presented, which takes into account longitudinal and transverse spin fluctuations on the same footing. The magnetic properties are determined in the framework of a rotational-invariant $d$-band model Hamiltonian by applying a four-field Hubbard-Stratonovich functional-integral method in the static approximation. The role of transverse spin excitations on the temperature-dependent magnetic properties is investigated by performing alloy averages in the single-site virtual crystal approximation. Bulk Fe is considered as the representative example for the applications. Results are given for the average magnetization $M$, for the spin-excitation energies, and for the transverse and longitudinal contributions to the local magnetic moments ${\ensuremath{\mu}}_{l}$ at atom $l$. The importance of noncollinear spin excitations is quantified by comparison with the corresponding collinear calculations. An important reduction of about 33% of the calculated Curie temperature ${T}_{\mathrm{C}}$ is obtained, which now amounts to 1250 K and is thus relatively close to the experimental value. The longitudinal (transverse) components of ${\ensuremath{\mu}}_{l}$ are found to decrease (increase) as a function of temperature until the full rotational symmetry is reached at ${T}_{C}$. This reflects the increasing importance of the transverse spin fluctuations. The origin of the temperature dependence of $M$ and ${\ensuremath{\mu}}_{l}$ is analyzed in terms of the local spin-fluctuation energies.