We investigate transport properties of junctions between two spin-split superconductors linked by a spin-polarized tunneling barrier. The spin-splitting fields in the superconductors (S) are induced by adjacent ferromagnetic insulating (FI) layers with arbitrary magnetization. The aim of this study is twofold. On the one hand, we present a theoretical framework based on the quasiclassical Green's functions to calculate the Josephson and quasiparticle current through the junctions in terms of the different parameters characterizing it. Our theory predicts qualitative new results for the tunneling differential conductance, $dI/dV$, when the spin-splitting fields of the two superconductors are noncollinear. We also discuss how junctions based on FI/S can be used to realize anomalous Josephson junctions with a constant geometric phase shift in the current-phase relation. As a result, they may exhibit spontaneous triplet supercurrents in the absence of a phase difference between the S electrodes. On the other hand, we show results of planar tunneling spectroscopy of a $\mathrm{EuS}/\mathrm{Al}/{\mathrm{AlO}}_x/\mathrm{EuS}/\mathrm{Al}$ junction and use our theoretical model to reproduce the obtained $dI/dV$ curves. Comparison between theory and experiment reveals information about the intrinsic parameters of the junction, such as the size of the superconducting order parameter, spin-splitting fields and spin relaxation, and also about properties of the two EuS films, such as their morphology, domain structure, and magnetic anisotropy.

We study theoretically the spectral and transport properties of a superconducting wire with a magnetic defect. We start by modeling the system as a one-dimensional magnetic Josephson junction and derive the equation determining the full subgap spectrum in terms of the normal-state transfer matrix for arbitrary length and exchange field of the magnetic region. We demonstrate that the quantum phase transition predicted for a short-range magnetic impurity, and associated with a change of the total spin of the system, also occurs in junctions of finite length. Specifically, we find that the total spin changes discontinuously by integer jumps when bound states cross the Fermi level. The spin can be calculated by using a generalization of the Friedel sum rule for the superconducting state, which we also derive. With these tools, we analyze the subgap spectrum of a junction with the length of the magnetic region smaller than the superconducting coherence length and demonstrate how phase transitions also manifest as a change of sign of the supercurrent.

Ni-Cr-Si-Fe-B self-fluxing alloys are commonly used in hardfacing applications; in addition, they are subjected to conditions of wear, corrosion, and high temperatures, but are not used in casting applications. In this work, gravity casting is presented as a potential manufacturing route for these alloys. Three alloys with different chemical compositions were investigated with a focus on microstructure characterization, solidification path, and strengthening mechanisms. Phases and precipitates were characterized using a field emission scanning electron microscope employing energy-dispersive X-ray spectroscopy, wavelength dispersive spectroscopy, and electron backscatter diffraction. Nano- and microhardness indentations were performed at different phases to understand their contribution to the overall hardness of the studied alloys. Hardness measurements were performed at room temperature and high temperature (650 °C). The borides and carbides were the hardest phases in the microstructure, thus contributing significantly to the overall hardness of the alloys. Additional hardening was provided by the presence of hard Ni₃B eutectics; however, there was also a small contribution from the solid solution hardening of the γ-Ni dendrites in the high-alloy-grade sample. The amount and size of the different phases and precipitates depended mainly on the contents of the Cr, C, and B of the alloy.

We study a periodic arrangement of magnetic regions in a quasi-one-dimensional superconducting wire. Due to the local exchange field, each region supports Andreev bound states that hybridize, forming Bloch bands in the subgap spectrum of what we call the Andreev crystal (AC). As an illustration, ACs with ferromagnetic and antiferromagnetic alignment of the magnetic regions are considered. We relate the spectral asymmetry index of a spin-resolved Hamiltonian to the spin polarization and identify it as the observable that quantifies the closing and reopening of the excitation gap. In particular, antiferromagnetic ACs exhibit a sequence of gapped phases separated by gapless Dirac phase boundaries. Heterojunctions between antiferromagnetic ACs in neighboring phases support spin-polarized bound states at the interface. In close analogy to the charge fractionalization in Dirac systems with a mass inversion, we find a fractionalization of the interface spin.

We present an exhaustive study of Andreev crystals (ACs)—quasi-one-dimensional superconducting wires with a periodic distribution of magnetic regions. The exchange field in these regions is assumed to be much smaller than the Fermi energy. Hence, the transport through the magnetic region can be described within the quasiclassical approximation. In the first part of the paper, by assuming that the separation between the magnetic regions is larger than the coherence length, we derive the effective nearest-neighbor tight-binding equations for ACs with a helical magnetic configuration. The spectrum within the gap of the host superconductor shows a pair of energy-symmetric bands. By increasing the strength of the magnetic impurities in ferromagnetic ACs, these bands cross without interacting. However, in any other helical configuration, there is a value of the magnetic strength at which the bands touch each other, forming a Dirac point. Further increase of the magnetic strength leads to a system with an inverted gap. We study junctions between ACs with inverted spectrum and show that junctions between (anti)ferromagnetic ACs (always) never exhibit bound states at the interface. In the second part, we extend our analysis beyond the nearest-neighbor approximation by solving the Eilenberger equation for infinite ACs and junctions between semi-infinite ACs with collinear magnetization. From the obtained quasiclassical Green functions, we compute the local density of states and the local spin polarization in anti- and ferromagnetic ACs. We show that these junctions may exhibit bound states at the interface and fractionalization of the surface spin polarization.