Local spins coupled to superconductors give rise to several emerging phenomena directly linked to the competition between Cooper pair formation and magnetic exchange. These effects are generally scrutinized using a spectroscopic approach which relies on detecting the in-gap bound modes arising from Cooper pair breaking, the so-called Yu-Shiba-Rusinov (YSR) states. However, the impact of local magnetic impurities on the superconducting order parameter remains largely unexplored. Here, we use scanning Josephson spectroscopy to directly visualize the effect of magnetic perturbations on Cooper pair tunneling between superconducting electrodes at the atomic scale. By increasing the magnetic impurity orbital occupation by adding one electron at a time, we reveal the existence of a direct correlation between Josephson supercurrent suppression and YSR states. Moreover, in the metallic regime, we detect zero bias anomalies which break the existing framework based on competing Kondo and Cooper pair singlet formation mechanisms. Based on first-principle calculations, these results are rationalized in terms of unconventional spin-excitations induced by the finite magnetic anisotropy energy. Our findings have far reaching implications for phenomena that rely on the interplay between quantum spins and superconductivity.

The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the trianglewell and the ramp potentials is worked out. In contrast to previous studies, where the radial distribution function g(r) was obtained numerically from the structure factor by Fourier inversion, we provide a fully analytic representation of g(r) up to any desired distance. The solution is employed to perform an extensive study of the equation of state, the excess internal energy per particle, the residual multiparticle entropy, the structure factor, the radial distribution function, and the direct correlation function. In addition, scatter plots of the bridge function versus the indirect correlation function are used to gauge the reliability of the hypernetted-chain, Percus-Yevick, and Martynov-Sarkisov closures. Finally, the Fisher-Widom and Widom lines are obtained in the case of the triangle-well model.

A method of the hydrothermal synthesis of Fe3+-doped titanate nanotubes (TNT) is reported in which the ultra-small Fe3O4 nanoparticles are used as the sources of Fe3+ ions. The magnetic nanoparticles with a diameter of about 2 nm are added during the washing stage of the hydrothermal procedure. During washing, they gradually degrade and at the same time, the titanate product is transformed into nanotubes. The obtained nanotubes were characterized by structural and magnetic measurements. It was found that, depending on the value of the external magnetic field, they may show the property of room temperature ferromagnetism, paramagnetism or they may be diamagnetic. It was also shown that the modified TNTs have greater photocatalytic activity compared to unmodified TNTs.