Muon spin rotation and relaxation in the superconducting ferromagnet UCoGe

We report zero-field muon spin rotation and relaxation measurements on the superconducting ferromagnet UCoGe. Weak itinerant ferromagnetic order is detected by a spontaneous muon spin precession frequency below the Curie temperature $T_C = 3$ K. The $\mu^+$ precession frequency persists below the bulk superconducting transition temperature $T_{sc} = 0.5$ K, where it measures a local magnetic field $B_{loc} = 0.015$ T. The amplitude of the $\mu$SR signal provides unambiguous proof for ferromagnetism present in the whole sample volume. We conclude ferromagnetism coexists with superconductivity on the microscopic scale.Comment: 4 pages, 3 figures, accepted for publication in PR

Stratifying multiparameter persistent homology

A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter family of spaces obtained from the data. In applications data often depend on several parameters, and in this case one is interested in studying the persistent homology of a multiparameter family of spaces associated to the data. While the theory of persistent homology for one-parameter families is well-understood, the situation for multiparameter families is more delicate. Following Carlsson and Zomorodian we recast the problem in the setting of multigraded algebra, and we propose multigraded Hilbert series, multigraded associated primes and local cohomology as invariants for studying multiparameter persistent homology. Multigraded associated primes provide a stratification of the region where a multigraded module does not vanish, while multigraded Hilbert series and local cohomology give a measure of the size of components of the module supported on different strata. These invariants generalize in a suitable sense the invariant for the one-parameter case.Comment: Minor improvements throughout. In particular: we extended the introduction, added Table 1, which gives a dictionary between terms used in PH and commutative algebra; we streamlined Section 3; we added Proposition 4.49 about the information captured by the cp-rank; we moved the code from the appendix to github. Final version, to appear in SIAG

Possible Quantum Diffusion of Polaronic Muons in Dy2_2Ti2_2O7_7 Spin Ice

We interpret recent measurements of the zero field muon relaxation rate in the frustrated magnetic pyrochlore Dy$_2$Ti$_2$O$_7$ as resulting from the quantum diffusion of muons in the substance. In this scenario, the plateau observed at low temperature ($<7$ K) in the relaxation rate is due to coherent tunneling of the muons through a spatially disordered spin state and not to any magnetic fluctuations persisting at low temperature. Two further regimes either side of a maximum relaxation rate at $T^* = 50$ K correspond to a crossover between tunnelling and incoherent activated hopping motion of the muon. Our fit of the experimental data is compared with the case of muonium diffusion in KCl.Comment: 15 pages, 2 figure

Weak magnetism phenomena in heavy-fermion superconductors: selected μ\muSR studies

The behavior of the so-called weak moment antiferromagnetic states, observed in the heavy-fermion superconductors UPt$_3$ and URu$_2$Si$_2$, is discussed in view of recent $\mu$SR results obtained as function of control parameters like chemical substitution and external pressure. In UPt$_3$, the Pd substitution for Pt reveals the dynamical character of the weak moment order. On the other hand, $\mu$SR measurements performed on samples in which Th substitutes U suggest that crystallographic disorder on the magnetic sites deeply affects the fluctuation timescale. In URu$_2$Si$_2$, a phase separation between the so-called hidden order state, present at ambient pressure, and an antiferromagnetic state, occurring under pressure, is observed. In view of the pressure-temperature phase diagram obtained by $\mu$SR, it is deduced that the respective order parameters have different symmetries.Comment: To appear in: J. Phys.: Cond. Matte

Spin dynamics in rare earth single molecule magnets from muSR and NMR in [TbPc2_{2}]0^{0} and [DyPc2_{2}]0^{0}

The spin dynamics in [TbPc$_{2}$]$^{0}$ and [DyPc$_{2}$]$^{0}$ single molecule magnets have been investigated by means of muon and nuclear spin-lattice relaxation rate measurements. The correlation time for the spin fluctuations was found to be close to 0.1 ms already at 50 K, about two orders of magnitude larger than the one previously found in other lanthanide based single molecule magnets. In [TbPc$_{2}$]$^{0}$ two different regimes for the spin fluctuations have been evidenced: a high temperature activated one involving spin fluctuations across a barrier $\Delta\simeq 880 K$ separating the ground and first excited states and a low temperature regime involving quantum fluctuations within the twofold degenerate ground-state. In [DyPc$_{2}$]$^{0}$ a high temperature activated spin dynamics is also evidenced which, however, cannot be explained in terms of a single spin-phonon coupling constant.Comment: 4 pages, 4 figure

Magnetic quantum critical point and superconductivity in UPt3 doped with Pd

Transverse-field muon spin relaxation measurements have been carried out on the heavy-fermion superconductor UPt3 doped with small amounts of Pd. We find that the critical Pd concentration for the emergence of the large-moment antiferromagnetic phase is ~0.6 at.%Pd. At the same Pd content, superconductivity is completely suppressed. The existence of a magnetic quantum critical point in the phase diagram, which coincides with the critical point for superconductivity, provides evidence for ferromagnetic spin-fluctuation mediated odd-parity superconductivity, which competes with antiferromagnetic order.Comment: 4 pages (includes 3 figures); postscript fil

Magnetic quantum critical point and superconductivity in UPt3 doped with Pd

Transverse-field muon spin relaxation measurements have been carried out on the heavy-fermion superconductor UPt3 doped with small amounts of Pd. We find that the critical Pd concentration for the emergence of the large-moment antiferromagnetic phase is ~0.6 at.%Pd. At the same Pd content, superconductivity is completely suppressed. The existence of a magnetic quantum critical point in the phase diagram, which coincides with the critical point for superconductivity, provides evidence for ferromagnetic spin-fluctuation mediated odd-parity superconductivity, which competes with antiferromagnetic order.Comment: 4 pages (includes 3 figures); postscript fil

Transforming Military Justice: The 2022 and 2023 National Defense Authorization Acts

For the past decade there have been numerous and significant changes to the Uniform Code of Military Justice (UCMJ), the statutory basis for the military justice system. Although the Military Justice Act of 2016 made major changes to the UCMJ, the calls for change continued. One of the most-often heard calls for reform over the last decade has suggested removing commanders from the military justice system. Some have argued that a command-centric military justice system was outdated, and it was time to make the system look more like the federal criminal procedure system. Other critics have advocated for a military justice system that looks more like those of our allied nations. In large part, those calls for reform were driven by the seemingly intractable problem of sexual assaults in the military. While there were other proposed changes to the UCMJ, calls for reducing the role of the commander took the lead

American Military Justice: Retaining the Commander\u27s Authority to Enforce Discipline and Justice

This white paper recommends that Congress reject proposals that would remove a commander’s prosecutorial discretion and instead place it in the hands of senior armed forces lawyers. There are currently two proposed legislative provisions that would adversely affect the commander’s prosecutorial discretion and undermine the commander’s ability to enforce good order and discipline. The first proposed provision was included in Section 540F of the 2020 National Defense Authorization Act, where Congress mandated that the Department of Defense report to the congressional armed services committees on the feasibility of creating a pilot program that would remove a commander’s authority to prefer, and refer to trial, court-martial charges for serious offenses and instead place that authority in the hands of senior armed forces lawyers

Magnetism in heavy-fermion U(Pt,Pd)3 studied by mSR

We report mSR experiments carried out on a series of heavy-electron pseudobinary compounds U(Pt1-xPdx)3 (x<=0.05). For x<=0.005 the zero-field muon depolarisation is described by the Kubo-Toyabe function. However the temperature variation of the Kubo-Toyabe relaxation rate does not show any sign of the small-moment antiferromagnetic phase with TN~6 K (signalled by neutron diffraction), in contrast to previous reports. The failure to detect the small ordered moment suggests it has a fluctuating (> 10 MHz) nature, which is consistent with the interpretation of NMR data. For 0.01<=x<=0.05 the muon depolarisation in the ordered state is described by two terms of equal amplitude: an exponentially damped spontaneous oscillation and a Lorentzian Kubo-Toyabe function. These terms are associated with antiferromagnetic order with substantial moments. The Knight-shift measured in a magnetic field of 0.6 T on single-crystalline U(Pt0.95Pd0.05)3 in the paramagnetic state shows two signals for B perpendicular to c, while only one signal is observed for B||c. The observation of two signals for B perpendicular to c, while there is only one muon localisation site (0,0,0), points to the presence of two spatially distinct regions of different magnetic response.Comment: 25 pages including 12 figures (PS), J. Phys.: Condens. Matter, in prin