Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

Magnetic properties of iron oxide nanoparticles with spinel structure are strictly related to a complex interplay between cationic distribution and the presence of a non-collinear spin structure (spin canting). With the aim to gain better insight into the effect of the magnetic structure on magnetic properties, in this paper we investigated a family of small crystalline ferrite nanoparticles of the formula Co_xNi_1−xFe₂O₄ (0 ≤ x ≤ 1) having equal size (≈4.5 nm) and spherical-like shape. The field dependence of magnetization at low temperatures indicated a clear increase of magnetocrystalline anisotropy and saturation magnetization (higher than the bulk value for CoFe₂O₄: ∼130 A m² kg⁻¹) with the increase of cobalt content. The magnetic structure of nanoparticles has been investigated by Mössbauer spectroscopy under an intense magnetic field (8 T) at a low temperature (10 K). The magnetic properties have been explained in terms of an evolution of the magnetic structure with the increase of cobalt content. In addition a direct correlation between cationic distribution and spin canting has been proposed, explaining the presence of a noncollinear spin structure in terms of superexchange interaction energy produced by the average cationic distribution and vacancies in the spinel structure.

This paper aims to analyze the competition of single particle anisotropy and interparticle interactions in nanoparticle ensembles using a random anisotropy model. The model is first applied to ideal systems of non-interacting and strongly dipolar interacting ensembles of maghemite nanoparticles. The investigation is then extended to more complex systems of pure cobalt ferrite CoFe₂O₄ (CFO) and mixed cobalt–nickel ferrite (Co,Ni)Fe₂O₄ (CNFO) nanoparticles. Both samples were synthetized by the polyol process and exhibit the same particle size (D_TEM ≈ 5 nm), but with different interparticle interaction strengths and single particle anisotropy. The implementation of the random anisotropy model allows investigation of the influence of single particle anisotropy and interparticle interactions, and sheds light on their complex interplay as well as on their individual contribution. This analysis is of fundamental importance in order to understand the physics of these systems and to develop technological applications based on concentrated magnetic nanoparticles, where single and collective behaviors coexist.