The “in-plane” angular spin distribution in layered systems as obtained by 57Fe Mössbauer spectroscopy
Introduction
The most comprehensive theory about the evaluation of the spin texture by Mössbauer spectroscopy with both polarised and unpolarised source radiation was given by Pfannes and Fischer in 1977 [1]. The texture was described by a two-variable density probability function, D(θm,ϕm), where θm and ϕm are the polar angles of the quantisation axis for the analysed nucleus in the laboratory fixed system. They showed that the maximum information obtainable from Mössbauer measurements for the magnetic dipolar radiation of 57Fe is a set of nine expansion spherical harmonics coefficients of the texture distribution D(θm,ϕm). In the case of unpolarised dipole radiation, only five independent variables are required in order to construct a minimum texture function, Dmin(θm,ϕm), which can properly approximate the real texture of the system. Subsequently, Greneche and Varret [2] have shown that by using a convenient rotation of the reference axes, a texture with a D2h symmetry can be described by only three coefficients and three angular parameters, respectively. Further developments in the case of amorphous ribbons presenting spin-canting phenomena have been done by Pankhurst and Gibbs [3].
However, in spite of these important achievements, the practical determination of the angular spin distribution from the intensity ratio of the Mössbauer spectra is rather complicated. In many practical situations, there is an apriori knowledge of the texture symmetry which could simplify drastically the general procedures. Most often, metallic low dimensional systems such as thin films and multilayers present spins distributed predominantly in the sample plane. The peculiar magnetic properties of these systems depend strongly on the surface and/or interface spin distribution that could be intimately studied in connection with the microstructural behaviour by suitable Mössbauer techniques.
In this work we propose a simplified procedure for extracting the in-plane angular spin distribution from Mössbauer spectra acquired on two-dimensional magnetic systems in non-perpendicular geometry. Spin distributions with a small out-of-plane component and with mirror symmetry can be also treated within the assumption that the out-of-plane component can be derived independently in a perpendicular geometry. The procedure was experimentally verified on four samples of advanced double-coated metal particle tapes, and the results have been compared with easy axis distributions (EADs) obtained by using bulk vector vibrating sample magnetometry techniques.
Section snippets
Theory
Let us assume a spin distribution in the sample plane defined by the Oxy rectangular axes. The laboratory-fixed orthogonal system, Oxyz, has the z-axis normal to the sample plane (Fig. 1). The γ-beam is incident on the sample in the Oxz-plane under an angle φ relative to the Ox-axis. The orientation of the magnetic hyperfine field, Bhf, of an 57Fe nucleus (anti-parallel to the Fe magnetic moment) is fully determined either by the angle ϕ made with the Ox-axis or by the angle ψ made with the
Unidirectional distribution
This is the simplest model assuming all Fe spins in the xy-plane and pointing to only one direction, e.g. described by ϕ0. In this case we deal with a Dirac type probability distribution, P(ϕ)=δ(ϕ−ϕ0) and relation (6) may be expressed asThe spin orientation described by ϕ0 may be deduced by only one experimental spectrum taken at an incidence angle φ. Theoretical dependencies of the R23 ratio versus ϕ0 for different
Experimental results
The above-presented procedures will be used in order to find the magnetic EAD in four samples of advanced double-coated metal particle tapes. The analysed double-coated metal particle tapes present a magnetic layer and a non-magnetic under-layer. The magnetic layer contains ellipsoidal particles of metallic iron (doped with a very small amount of Co) embedded in a polymer matrix, whereas the non-magnetic under-layer is based on antiferromagnetic α-Fe2O3 particles. The metallic ellipsoids have
Conclusions
Simple procedures for deducing in-plane angular spin distributions by Mössbauer spectroscopy are described. A convenient type of distribution is initially proposed. Theoretical R23 intensity ratios in Mössbauer patterns are expressed in terms of the distribution parameters. Experimental R23 ratios fix subsequently the proper values of the parameters in the analysed distributions. The procedure was applied in order to derive the angular magnetic moment distributions of metallic nano-particles in
Acknowledgements
Financial support by the Alexander-von-Humboldt Stiftung is highly acknowledged by one of the authors (V. Kuncser). The authors wish to thank U. von Hörsten for valuable technical assistance. Work partially supported by the Deutsche Forschungsgemeinschaft (SFB 491).
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