Abstract
The source of spin-wave resonance (SWR) in thin films of the ferromagnetic semiconductor (Ga,Mn)As is still under debate: does SWR stem from the surface anisotropy (in which case the surface inhomogeneity (SI) model would apply), or does it originate in the bulk inhomogeneity of the magnetic structure of the sample (and thus requires the use of the volume inhomogeneity (VI) model)? This paper outlines the ground on which the controversy arose and shows why in different conditions a resonance sample may meet the assumptions of either the SI or the VI model.
Highlights
In the analysis presented in this paper, we refer to our earlier quantum theory of SWR33–42, in which we have introduced the concept of surface spin pinning parameter, a quantity that measures the degree of pinning of the surface spins and reveals explicitly different surface magnetic anisotropies present in thin films
The boundary conditions to be fulfilled by the precession of the surface spins can be expressed by the surface pinning parameter, defined: A~1{
In the equations [24]–(26) we have indicated in advance what will follow from the confrontation of these formulas with the experimental data: that only the term a12ðhMÞ is configuration-dependent
Summary
This condition is the counterpart of the condition [10] obtained in the macroscopic approach (for kH ? 0). Note that the adoption of the formula [19] implies taking into account only two mechanisms of surface spin pinning: the isotropic pinning component a0, the influence of which on the freedom of the spins is independent of their configuration with respect to the surface of the film, and the uniaxial factor a2(hM) representing the contribution of the uniaxial symmetry, with the surface normal as the symmetry axis, to the surface pinning Already at this stage interesting conclusions regarding the properties of the surface pinning can be drawn from the equation [19]. The following equations apply to these special angles: AÀhcM The latter equation provides a simple formula for the determination of the isotropic component a0 of the surface pinning, only necessitating the value of the surface parameter in the external field configuration corresponding to the uniaxial pinning annihilation angle huM. With a0 known, the configuration dependence of the uniaxial factor a2(hM) can be determined by the measurement of the surface parameter A(hM) vs. hM (see the equation [19]). (We shall refer in this regard to the paper by Liu et al. providing measurement data which will allow us to plot the experimental A(hM) dependence; see Section below.) On the other hand, theoretical considerations within the model used for describing the surface anisotropy in (Ga,Mn)As samples will lead us to an equation, formulated in which a2(hM) is expressed by magnetic characteristics of the (Ga,Mn)As thin film; very interesting conclusions regarding the interrelation between the ranges of the exchange interaction on the surface and in the bulk of (Ga,Mn)As thin films will be drawn from the confrontation of the theory with the experiment
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