Temperature control of spin-wave spectra in continuously graded epitaxial Pd-Fe alloy films

In this paper, results of experimental studies and modeling of standing spin-wave spectra and their temperature evolution in graded Pd-Fe alloy thin magnetic films are presented. Studied sample series include 200-nm thick epitaxial ${\mathrm{Pd}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}$ films on MgO (001): two with the linear ($0.02\ensuremath{\cdots}0.10$ and $0.12\ensuremath{\cdots}0.18\phantom{\rule{4pt}{0ex}}x$-ranges), one with the sine and one with the cosine (both with $0.02\ensuremath{\cdots}0.10\phantom{\rule{4pt}{0ex}}x$-range) iron distribution profiles. Versatile spin-wave excitation patterns were obtained, and their pronounced evolution with temperature was observed. Importantly, temperature affects spectra not only in a trivial way via the temperature dependence of magnetization and related quantities, but also through modification of magnetic phase structure of a film due to the Curie temperature crossing by its fraction(s). Continuous at low temperatures magnetization profile becomes discontinuous or significantly altered at elevated ones. Standing spin-wave resonance spectra were modeled using a semiclassical Landau-Lifshitz approach. Based on the modeling, temperature dependences of the spin-wave stiffness $D$ and magnitudes of the interface ${\ensuremath{\alpha}}_{\mathrm{inter}}$ and surface ${\ensuremath{\alpha}}_{\mathrm{surf}}$ pinning constants were obtained. It is shown that, besides a compositional grading of magnetic thin films, the temperature variation is a powerful tool for modifying the magnetization profile and thus, for a flexile tuning of spin-wave spectra.