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

Studies of superconductivity in U(Pt1-xPdx)3 for x < 0.006

We report measurements of the specific heat and resistivity (T < 1 K) for high quality polycrystals of U(Pt1-xPdx)3 with x < 0.006. The Tc-x phase diagram can be constructed, and superconductivity is destroyed for x = 0.006; this is approximately the same concentration above which the onset of large-moment antiferromagnetism is observed to occur. The splitting of the double superconducting transition increases smoothly with increasing Pd content, and is large enough that for Pd concentrations 0.004 < x < 0.006 only the superconducting A-phase will be present.Comment: 8 pages total, 3 figures(proceedings SCES 98

Weighted Supermembrane Toy Model

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights. This follows from a bound for the number of negative eigenvalues of an associated matrix-valued Schr\"odinger operator.Comment: 18 pages, 2 figures; to appear in Lett. Math. Phys

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

Muon localization site in U(Pt,Pd)3

The angular and temperature (10-250 K) variation of the Knight shift of single-crystalline U(Pt0.95Pd0.05)3 has been measured in transverse field (B=0.6 T) mSR experiments. By analysing the temperature variation of the Knight shift with a modified Curie-Weiss expression the muon localization site in this hexagonal material is determined at (0,0,0).Comment: 12 pages (including 4 figures); postscript file; Proc. 8th Int. Conf. on Muon Spin Rotation, Relaxation and Resonance (Aug.30-Sept.3, Les Diablerets); 2nd version with minor correction

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

Search for a quantum phase transition in U(Pt_(1-x)Pd_x)_3

Pd in U(Pt_{1-x}Pd_x)_3 suppresses the superconducting T_c to 0 K at critical concentration x_c of 0.007 and induces a conventional AFM state for x > x_c. The resistivity below 1 K shows a deviation from Fermi liquid behavior described by a power law where the exponent ranges from 2 at x=0 to 1.6 for x = x_c. This suggests that a quantum phase transition (QPT) may exist near x_c associated with either the magnetic or superconducting transition temperature = 0 K. Transport for a sample with x = 0.004 < x_c has constant exponent of 1.77 as increasing pressure suppresses T_c to 0 K, suggesting that if a QPT exists it may be associated with the magnetic transition.Comment: 2 pages, proceedings of LT2

The Casas-Alvero conjecture for infinitely many degrees

Over a field of characteristic zero, it is clear that a polynomial of the form (X-a)^d has a non-trivial common factor with each of its d-1 first derivatives. The converse has been conjectured by Casas-Alvero. Up to now there have only been some computational verifications for small degrees d. In this paper the conjecture is proved in the case where the degree of the polynomial is a power of a prime number, or twice such a power. Moreover, for each positive characteristic p, we give an example of a polynomial of degree d which is not a dth power but which has a common factor with each of its first d-1 derivatives. This shows that the assumption of characteristic zero is essential for the converse statement to hold.Comment: 7 pages; v2: corrected some typos and references, and added section on computational aspect

Phase-field-crystal model for liquid crystals

Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits stable isotropic, nematic, smectic A, columnar, plastic crystalline and orientationally ordered crystalline phases. As far as the dynamics is concerned, the translational density is a conserved order parameter while the orientational ordering is non-conserved. The derived phase-field-crystal model can serve for efficient numerical investigations of various nonequilibrium situations in liquid crystals