Pressure-temperature Phase Diagram of Polycrystalline UCoGe Studied by Resistivity Measurement

Recently, coexistence of ferromagnetism (T_Curie = 2.8K) and superconductivity (T_sc = 0.8K) has been reported in UCoGe, a compound close to a ferromagnetic instability at ambient pressure P. Here we present resistivity measurements under pressure on a UCoGe polycrystal. The phase diagram obtained from resistivity measurements on a polycrystalline sample is found to be qualitatively different to those of all other ferromagnetic superconductors. By applying high pressure, ferromagnetism is suppressed at a rate of 1.4 K/GPa. No indication of ferromagnetic order has been observed above P ~ 1GPa. The resistive superconducting transition is, however, quite stable in temperature and persists up to the highest measured pressure of about 2.4GPa. Superconductivity would therefore appear also in the paramagnetic phase. However, the appearance of superconductivity seems to change at a characteristic pressure P* ~ 0.8GPa. Close to a ferromagnetic instability, the homogeneity of the sample can influence strongly the electronic and magnetic properties and therefore bulk phase transitions may differ from the determination by resistivity measurements.Comment: 4 pages, 4 figures, submitted to J. Phys. Soc. Jp

Extremely Large and Anisotropic Upper Critical Field and the Ferromagnetic Instability in UCoGe

Magnetoresistivity measurements with fine tuning of the field direction on high quality single crystals of the ferromagnetic superconductor UCoGe show anomalous anisotropy of the upper critical field H_c2. H_c2 for H // b-axis (H_c2^b) in the orthorhombic crystal structure is strongly enhanced with decreasing temperature with an S-shape and reaches nearly 20 T at 0 K. The temperature dependence of H_c2^a shows upward curvature with a low temperature value exceeding 30 T, while H_c2^c at 0 K is very small (~ 0.6 T). Contrary to conventional ferromagnets, the decrease of the Curie temperature with increasing field for H // b-axis marked by an enhancement of the effective mass of the conduction electrons appears to be the origin of the S-shaped H_c2^b curve. These results indicate that the field-induced ferromagnetic instability or magnetic quantum criticality reinforces superconductivity.Comment: 5 pages, 4 figures, accepted for publication in J. Phys. Soc. Jp

Pressure-temperature phase diagram of ferromagnetic superconductors

The symmetry approach to the description of the (P,T) phase diagram of ferromagnet superconductors with triplet pairing is developed. Taking into account the recent experimental observations made on UCoGe it is considered the case of a crystal with orthorhombic structure and strong spin-orbital coupling. It is shown that formation of ferromagnet superconducting state from a superconducting state is inevitably accompanied by the first order type transition.Comment: 4 pages, 1 figur

Microscopic Coexistence of Ferromagnetism and Superconductivity in Single-Crystal UCoGe

Unambiguous evidence for the microscopic coexistence of ferromagnetism and superconductivity in UCoGe ($T_{\rm Curie} \sim 2.5$ K and $T_{\rm SC}$ $\sim$ 0.6 K) is reported from $^{59}$Co nuclear quadrupole resonance (NQR). The $^{59}$Co-NQR signal below 1 K indicates ferromagnetism throughout the sample volume, while nuclear spin-lattice relaxation rate $1/T_1$ in the ferromagnetic (FM) phase decreases below $T_{\rm SC}$ due to the opening of the superconducting(SC) gap. The SC state was found to be inhomogeneous, suggestive of a self-induced vortex state, potentially realizable in a FM superconductor. In addition, the $^{59}$Co-NQR spectrum around $T_{\rm Curie}$ show that the FM transition in UCoGe possesses a first-order character, which is consistent with the theoretical prediction that the low-temperature FM transition in itinerant magnets is generically of first-order.Comment: 5 pages, 5 figure

EMaP: Explainable AI with Manifold-based Perturbations

In the last few years, many explanation methods based on the perturbations of input data have been introduced to improve our understanding of decisions made by black-box models. The goal of this work is to introduce a novel perturbation scheme so that more faithful and robust explanations can be obtained. Our study focuses on the impact of perturbing directions on the data topology. We show that perturbing along the orthogonal directions of the input manifold better preserves the data topology, both in the worst-case analysis of the discrete Gromov-Hausdorff distance and in the average-case analysis via persistent homology. From those results, we introduce EMaP algorithm, realizing the orthogonal perturbation scheme. Our experiments show that EMaP not only improves the explainers' performance but also helps them overcome a recently-developed attack against perturbation-based methods.Comment: 29 page

Absence of Meissner State and Robust Ferromagnetism in the Superconducting State of UCoGe: Possible Evidence of Spontaneous Vortex State

We report ac magnetic susceptibility and dc magnetization measurements on the superconducting ferromagnet UCoGe (with superconducting and Curie temperatures of $T_{{\rm SC}} \sim 0.5$~K and $T_{{\rm Curie}} \sim 2.5$~K, respectively). In the normal, ferromagnetic state ($T_{{\rm SC}} < T < T_{{\rm Curie}}$), the magnetization curve exhibits a hysteresis loop similar to that of a regular itinerant ferromagnet. Upon lowering the temperature below $T_{{\rm SC}}$, the spontaneous magnetization is unchanged, but the hysteresis is markedly enhanced. Even deeply inside the superconducting state, ferromagnetism is not completely shielded, and there is no Meissner region, a magnetic field region of $H < H_{\rm c1}$ (a lower critical field). From these results, we suggest that UCoGe is the first material in which ferromagnetism robustly survives in the superconducting state and a spontaneous vortex state without the Meissner state is realized.Comment: 5 pages, 4 figures, to be published in J. Phys. Soc. Jp

Upper critical field in superconductors near ferromagnetic quantum critical points; UCoGe

We study the strong-coupling superconductivity near ferromagnetic quantum critical points, mainly focusing on the upper critical fields $H_{c2}$. Based on our simple model calculations, we discuss experimentally observed unusual behaviors of $H_{c2}$ in a recently discovered ferromagnetic superconductor UCoGe. Especially, the large anisotropy between $H_{c2}\parallel a$-axis and $H_{c2}\parallel c$-axis, and the strong-coupling behaviors in $H_{c2}^{\parallel a}$ are investigated. We also examine effects of non-analytic corrections in the spin susceptibility on the superconductivity, which can arise from effective long range interactions due to particle-hole excitations.Comment: Proceedings of ICHE2010, Toky

Ferromagnetic Quantum Critical Fluctuations and Anomalous Coexistence of Ferromagnetism and Superconductivity in UCoGe Revealed by Co-NMR and NQR Studies

Co nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) studies were performed in the recently discovered UCoGe, in which the ferromagnetic and superconducting (SC) transitions were reported to occur at $T_{\rm Curie} \sim 3$ K and $T_S \sim 0.8$ K (N. T. Huy {\it et al.}, Phys. Rev. Lett. {\bf 99} (2007) 067006), in order to investigate the coexistence of ferromagnetism and superconductivity as well as the normal-state and SC properties from a microscopic point of view. From the nuclear spin-lattice relaxation rate $1/T_1$ and Knight-shift measurements, we confirmed that ferromagnetic fluctuations which possess a quantum critical character are present above $T_{\rm Curie}$ and the occurrence of ferromagnetic transition at 2.5 K in our polycrystalline sample. The magnetic fluctuations in the normal state show that UCoGe is an itinerant ferromagnet similar to ZrZn$_2$ and YCo$_2$. The onset SC transition was identified at $T_S \sim 0.7$ K, below which $1/T_1$ of 30 % of the volume fraction starts to decrease due to the opening of the SC gap. This component of $1/T_1$, which follows a $T^3$ dependence in the temperature range of $0.3 - 0.1$ K, coexists with the magnetic components of $1/T_1$ showing a $\sqrt{T}$ dependence below $T_S$. From the NQR measurements in the SC state, we suggest that the self-induced vortex state is realized in UCoGe.Comment: 5 pages, 7 figures. submitted to J. Phys. Soc. Jpn. To appear in J. Phys. Soc. Jp