Summary

The aim of this research project was to study the magnetic properties of Laves phase multilayer and alloy films, grown by Molecular Beam Epitaxy on top of a (110) Nb (11 0) sapphire substrate structure.
The epitaxial structures which are single-crystal in nature, possess directions of easy magnetization which differ from their respective bulk compounds. In particular, because the RE-Fe₂ compounds are characterized by giant magnetostriction, strains built into the Laves phase structure during the crystal growth procedure, profoundly modify the direction of easy magnetization. Magnetic measurements on epitaxial films of the highly magnetostrictive materials DyFe₂ and TbFe₂ showed that the epitaxial strain influences the direction of easy magnetization. The MBE films exhibit a re-orientation of their easy axis which is temperature dependent. This magnetic feature is associated with the different thermal evolution of the magneto crystalline anisotropy constants and the magneto elastic coupling coefficient.
At low temperature, the easy axis of the epitaxial DyFe₂ film for example is found to be the same than the easy axis of the bulk i.e. [001]. However, at room temperature, the magnetostriction term which favors [-110] as easy axis [1], becomes significant and determines the axis of easy magnetisation. Similar effects were observed for TbFe2 films. In contrast, for the YFe2 Laves phase compound, which is unsensitive to stress, the easy axis remains temperature independent.
Another example of the significant effect of the epitaxial strain upon the magnetic properties of the materials can be clearly observed in the magnetic characterization of the strongly magnetostrictive Dy_(1-x) Tb_x Fe₂ epitaxial alloy. Indeed, it has been found by A. E. Clark et al. that Dy_(1-x) Tb_x Fe₂ alloy bulk showed a minimum of coercivity for x = 0.3 [2]. In contrast, the epitaxial film shows a linear dependence of the coercivity B_C with the relative concentration x. The maximum of coercivity is displayed by the TbFe2 film and the minimum by the DyFe₂ film. The magnetisation reversal mechanism can be successfully described by Stoner and Wohlfarth model, which is based on the principle of coherent rotation of the magnetisation [3]. Adjusting the model to multilayer composites, BC can be successfully predicted by: (9.01) where the parameters possess their usual meaning, and the indices refer to the different components of the film.
The DyFe₂ – YFe₂ superlattices are layered magnetic systems consisting of two single crystalline Laves phase compounds, with very close crystal structures, but with different magnetic behaviour. In DyFe₂, the Dysprosium and Iron moments are aligned anti-parallel. It is a hard magnetic material characterised by large anisotropy and saturation magnetisation. By contrast, YFe₂ is a typical soft phase with negligible anisotropy and relatively small magnetisation. The exchange coupling at the interface between the two compounds arises via positive exchange between Iron moments. Thus, the system is a kind of giant ferrimagnet where the net magnetisation in the DyFe₂ and YFe₂ compounds is anti-parallel.
If the soft layer is sufficiently thin, the net magnetisation remains rigidly coupled to that of the hard layer and the composite film reverses as a coherent unit at a coercive field B_C. For such composites, the prediction of the Stoner and Wohlfarth model is in reasonable agreement with experiments. Consequently, by adjusting ratio and thickness of the layers accordingly, it is possible to tailor the coercivity B_C of the MBE grown DyFe₂ YFe₂ multilayer films. However, it should be noted that while the coherent rotation model allows prediction of B_C to be made, the temperature dependence of the coercivity suggests that the magnetisation reversal occurs via domain walls, as expected. In particular, it was shown that the coercivity is affected by strong domain wall pinning (SDWP) [4].
When the thickness of the magnetically soft layers is increased, magnetic exchange springs can be created. Here, the Fe spins at the hard/soft phase interface are pinned by the magnetically hard DyFe₂ layers, while the Fe spins in the magnetic exchange springs rotate towards the direction of the applied magnetic field. The anti ferromagnetically coupled DyFe₂ / YFe₂ layered structure provides a realization of the ideal nanostructure of symmetric exchange-springs magnets. The exchange springs profoundly modifies the properties of the magnetic loops. In particular, it gives rise to an additional magnetic moment in the high field region, which is fully reversible, a classic signature of a magnetic exchange springs. The magnetisation behaviour of an exchange springs film can be characterised by two fields, known as the bending field BB and the irreversible field Birr. For
• B_app < B_irr, the soft layer remains anti-parallel to the hard layer
• B_app > B_irr, the magnetic reversal proceeds via an irreversible switches of the magnetisation in the hard layer and the simultaneous creation of the magnetic exchange springs.
• B_app > B_B, the applied field creates a sufficiently large torque on the Fe moments so that the gain in Zeeman energy from rotation of Fe magnetic spins in the YFe₂ blocks outweights the concomitant loss in magnetic exchange energy.
From the theoretical point of view, a very simple relationship was established for the bending field BB, the Fe-Fe exchange field B_ex, and the number of mono-atomic layers in the YFe₂ phase N [5]. Namely: (9.02)
This result, based on (i) an essentially 1-D model and (ii) infinite pinning at the DyFe2 / YFe2 interfaces, can be used as a guide.
It is possible to tune the magnetic exchange springs in the magnetically soft YFe2 layers to produce films with: BB > BC, BB < BC, and BB ~ BC.
In addition, it is found that the magnetic exchange springs strongly influence the switching field (Birr)of the hard layer. It was shown that Birr changes linearly with the temperature, and this result suggests that magnetisation reversal occurs by motions of domain walls perturbed by weak domain wall pinning (WDWP) centers [4]. The evolution from WDWP centers, found in exchange springs multilayers, to SDWP found in strongly coupled multilayers can be explained by the competition between localized strong magneto crystalline anisotropy of the DyFe₂ and exchange interaction Fe-Fe. For increasing thickness of YFe₂ layers, the Fe-Fe exchange interactions smooth out the strong magneto-crystalline anisotropy.
However, it is worth noting that the model does not take into account influences such as next nearest neighbour interactions and the possibility that the exchange spring may extend into the DyFe₂ layers. The latter effect is particularly important because it implies that the actual thickness for the creation of the magnetic exchange springs is larger than the thickness of the YFe₂ layer and hence BB is smaller.
Using traditional magnetometry techniques it is impossible to probe the penetration of magnetic exchange springs. Static magnetisation measurement techniques only measure the average magnetic moment from the entire multilayer film. Therefore, because the magnetic profile within the DyFe2 layers should reflect the degree of spring penetration, the technique to be used must allow independent measurements of the hysteresis loops of the different component layers. C. T. Chen et al. [6] have developed such a method to determine element-specific hysteresis loops of heteromagnetic materials. By recording the absorption intensity of circular polarized soft X-Rays at each transition metal L3 absorption edge as a function of applied field, the hysteretic behaviour of each magnetic element in a compound or multilayer structure can be determined using magnetic circular dichroism (MCD) [7].
It should also be mentioned that local variations in the DyFe₂ anisotropy due to interface roughness in particular, could influence the reversal behaviour. However, it is difficult to obtain unambiguous information on the magnetic structure of surfaces and interfaces. One method of investigating surface and interface magnetism, which has proven useful in studies of ferromagnetic films, is to probe the spin-wave the magnetic moments at each site precess about their individual equilibrium directions. Since the spins are coupled with one another through exchange and dipolar interactions, spin-wave excitations are the eigen-modes of the magnetic system. Thus the frequency of a spin wave may depend quite sensitively on the exchange coupling between spins as well as other effective fields caused by, for example, anisotropies and magneto-elastic effects. These interactions will not only affect the frequency of precession but also the relative phase precession between spins at neighbouring lattice sites. In ferromagnetic systems such as Fe and Co the lowest spin-wave frequencies are typically of the order of 10 GHz. These are long wavelength excitations which can be studied using ferromagnetic resonance and Brillouin light scattering [8].
To date, most of the ‘model calculations’ of magnetic exchange springs have been carried out on the assumption that the spins remain confined to the plane of the film. However, recent measurements on the uniaxial in-plane anisotropy SmCo/Fe exchange springs films show that at high field, the magnetisation rotation created in the magnetically soft Fe layers is an out-of-plane fanning mode [9].
The DyFe2 – YFe2 structure constitutes an interesting example of how novel magnetic phases can be engineered by tuning the interfacial interaction. The present work paves the way for experiments on more magnetically complicated systems consisting of magnetostrictive multilayer materials. Indeed, combining giant magnetostrictive and high susceptibility / high moment materials is promising, as most giant magnetostrictive alloys require large fields to achieve a large magnetostriction [10]. Previous attempts to reduce the switching field have focused on reducing the anisotropy by either alloying Dy to control the Tb / Dy ratio in order to achieve compensation of fourth order anisotropy [(Tb_0.3Dy0.7)Fe2] [1]. The multilayer approach to increase the magnetostrictive susceptibility d / dBapp is based on the exchange-spring-magnet concept [11]. Using this approach, the switching field ( KS / MS) is reduced by increasing MS, a degree of freedom otherwise limited in single films [12].
Finally, the exchange springs multilayer serves as an ideal model system for studying the whole process of the nucleation, compression, decompression and propagation of an artificial in-plane domain wall. In particular, it can be used to investigate Giant Magneto-Resistance (GMR) effect due to magnetic exchange springs. In particular, Gordeev et al. [13] have shown that up to 12 % GMR due to the formation of short magnetic exchange springs in the magnetically soft YFe2 layers can be achieved. The results were explained in terms of the domain wall scattering model, developed by Levy and Zhang [14].

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