Finite temperature magnetic properties of small Fe chains and clusters on Pt(111)

Abstract

The magnetic properties of Fe chains and clusters on Pt(111) are investigated in the framework of a functional-integral theory of itinerant magnetism. The considered nanostructures show a ferromagnetic (FM) ground state with nearly saturated Fe local magnetic moments ${\ensuremath{\mu}}_{\text{Fe}}^{0}\ensuremath{\simeq}3.15{\ensuremath{\mu}}_{\text{B}}$. In addition, small moments ${\ensuremath{\mu}}_{\text{Pt}}^{0}\ensuremath{\simeq}0.1--0.3{\ensuremath{\mu}}_{\text{B}}$ are induced at the Pt substrate, which depend sensitively on the number of Fe atoms in their nearest-neighbor (NN) shell. The spin-fluctuation (SF) energies $\mathrm{\ensuremath{\Delta}}{F}_{l}(\ensuremath{\xi})$ at the different atoms $l$ are calculated as a function of the local exchange fields ${\ensuremath{\xi}}_{l}$, by using a real-space recursive expansion of the local Green's functions. Results for the temperature dependence of the average magnetization per atom ${\overline{\ensuremath{\mu}}}_{N}$, local magnetic moments ${\ensuremath{\mu}}_{l}$, and spin correlation functions ${\ensuremath{\gamma}}_{lk}$ are derived. At the Fe atoms the dominant magnetic excitations are fluctuations of the local-moment orientations. The spin-flip energies $\mathrm{\ensuremath{\Delta}}{F}_{l}(\ensuremath{\xi})$ in the deposited Fe clusters are found to be about $50%$ smaller than in free-standing clusters of comparable size. This results in flatter SF-energy landscapes and in a weaker stability of the FM order at $Tg0$. The effective exchange interactions between the Fe local moments, which are derived from the electronic calculations, reveal competing FM and antiferromagnetic couplings at different distances. In contrast to Fe, the main spin excitations at the Pt atoms are fluctuations of the size of the induced local magnetic moments. The interplay between the different types of spin excitations and their effect on the temperature-dependent magnetic properties is discussed.