Surface anisotropy energy in terms of magnetocrystalline anisotropy fields in ferromagnetic semiconductor (Ga,Mn)As thin films

Abstract

Surface anisotropy energy density is a key quantity in the description of the dynamics of surface spins in ferromagnetic thin films and is known to result in a ferromagnetic resonance fine structure of a thin film: a multipeak spectrum is observed in an effect known as spin-wave resonance (SWR). The so-called surface pinning parameter, directly correlated with the surface anisotropy energy, plays a fundamental role in determining the character of an SWR spectrum in the theory of SWR based on the surface inhomogeneity model. Here we extend the theory of SWR by introducing a new formula representing the surface pinning parameter as a series of contributions from different anisotropies existing in (Ga,Mn)As thin films. We show how to determine the coefficients in this series by comparing the SWR theory with data obtained in a resonance experiment. The proposed procedure allows to determine the proportion with which each type of the anisotropy contributes to the total surface anisotropy of (Ga,Mn)As, and, consequently, to assess to what extent the proportions on the surface differ from those in the bulk. The presented considerations can be used for the study of any other thin-film system, since we provide also a general rule that allows to express the surface pinning parameter of a thin film, as well as its surface anisotropy energy, by the free energy of the considered thin-film system. This enables the interpretation of experimental SWR spectra in terms of the free-energy density of the thin film.

Probing dynamics of micro-magnets with multi-mode superconducting resonator

“…15,18 Once an exchange spin wave activity is excited, it completes the list of basic magnetic properties with the exchange stiffness constant and the surface anisotropy (see, for example, Refs. [19][20][21][22].…”

SWR Studies of Higher-Order Surface Anisotropy Terms in (Ga,Mn)As Thin Films

“…Now, if we use equation (2.1) of the paper [27] for expressing both the bulk and surface free energies in (2.6), we obtain the following expression for the surface pinning parameter: a r001s2 cos…”

Ferromagnetic resonance and spin-wave resonances in GaMnAsP films

“…1a) -the multi-SW spectrum collapses into a single narrow resonance line corresponding to the uniform FMR mode. 15,16 For angle θ > θ c , the multi-mode nature of the SW spectrum re-emerges, generally containing two resonances. A similar angular behavior is also observed in samples D and E. One should add that the number of SWR modes observed in the experiment increases with increasing thickness of the film, reflecting their standing wave character.…”