Probing the mutual interactions between superconductor and ferromagnet in hybrid systems with nanoscale magnetic modulation.

An important aspect in the fast developing field of nanotechnology is the understanding of how properties evolve when reducing the dimensions to the nanoscale. Spatial confinement of phonons in nanostructures can strongly affect the phonon density of states and related properties. Despite the importance of understanding the vibrational behaviour at the nanoscale, lattice vibrations in nanostructures have been less explored due to the difficulty of experimentally obtaining the phonon density of states.
In this work we have selected Sn as a model system for studying the phonon properties at the nanoscale and their intimate relation to superconductivity and to structural phase transitions in nanosystems.

In the first part of this work we present the results of the study on the coexistence of superconductivity and ferromagnetism in Sn-Co nanocomposites. This work illustrates the intimate interplay between morphology, composition, superconductivity and magnetism in complex nanocomposites. Nanoscale morphology and composition can have a strong influence on the hybrid interfaces and on the electronic coupling between the superconducting (S) and ferromagnetic (F) constituents. By tuning these parameters, a coexistence between S and F up to high F content can be realized where S and F interact mainly via magnetic fields.

In order to gain a deeper understanding of how superconductivity changes at the nanoscale, we have in particular focussed on the role of lattice vibrations in Sn nanosystems. A first major challenge was to address experimentally the phonon density of states of nanoscale Sn systems by nuclear inelastic x-ray scattering experiments.

From the phonon behaviour of Sn nano islands, cluster-assembled films and nanoparticles embedded in a matrix, it was concluded that atoms with a reduced coordination cause an enhancement of low-energy phonon modes because of their reduced symmetry and coordination compared to bulk Sn atoms. It was found that the phonon damping (indicated by a lowering of the value of the quality factor) increases with decreasing average size of the Sn nanostructures. The phonon damping was quantified by the damped harmonic oscillator model. From the phonon density of states of the nanoscale Sn structures several thermodynamic properties were extracted. In general, it was found that the increase in the mean square atomic displacement, accompanied by a decrease of the mean force constant, scales with the fraction of grain boundary or surface atoms in the nanostructure.

After tackling the challenge of probing and gaining deeper understanding of the vibrational behaviour in Sn nanostructures, the aim was to correlate the changes in the phonon density of states to changes in the superconducting behaviour of nanoscale Sn and to quantify the role of phonons in the observed increase in the superconducting transition temperature in Sn nanosystems. Probing the phonon density of states of nanoscale Sn enables the disentanglement of electron and phonon confinement effects that emerge when reducing the system's dimensions.

Tc was calculated based on the phonon density of states of the Sn nano islands and cluster-assembled films. These calculated values for Tc were compared to the experimentally obtained values for Tc, from which a good agreement was found. It was concluded that phonon confinement effects play a dominating role, while electron confinement effects only play a minor role in the observed enhancement of Tc.

The final aim was to unravel the role of phonons in the alpha-Sn to beta-Sn phase transformation in thin Sn films. By numerical integration of the calculated and experimentally determined phonon spectra, the free energy as a function of temperature was obtained in the alpha-Sn and beta-Sn phase. From the free energy curves of bulk Sn, it was observed that the phase transition from the alpha-Sn to the beta-Sn phase is entropy-driven and hence occurs due to stronger increase of the vibrational entropy per atom for the beta-Sn phase than for the alpha-Sn phase as a function of temperature. It was concluded that phonons indeed play an essential role in the phase transformation in Sn.

Sn layers in the alpha-Sn phase were stabilized by the InSb substrate and the thickness of the layer determines the energy difference between a strained alpha-Sn layer and the introduction of a misfit dislocation which leads to the beta-Sn phase. So the alpha- to beta-Sn phase transition in thin layers grown on a substrate is a consequence of the interplay between the vibrational behaviour on the one hand and the stabilizing influence of the substrate on the other hand. It was concluded that while the vibrational entropy per atom (determined by the phonon behaviour) makes the phase transition happen, it is the thickness of the a-Sn layer which determines at what temperature the phase transition will happen.