A theory of the electric quadrupole contribution to resonant x-ray scattering: Application to multipole ordering phases in Ce_{1-x}La_{x}B_{6}

We study the electric quadrupole (E2) contribution to resonant x-ray scattering (RXS). Under the assumption that the rotational invariance is preserved in the Hamiltonian describing the intermediate state of scattering, we derive a useful expression for the RXS amplitude. One of the advantages the derived expression possesses is the full information of the energy dependence, lacking in all the previous studies using the fast collision approximation. The expression is also helpful to classify the spectra into multipole order parameters which are brought about. The expression is suitable to investigate the RXS spectra in the localized f electron systems. We demonstrate the usefulness of the formula by calculating the RXS spectra at the Ce L_{2,3} edges in Ce_{1-x}La_{x}B_{6} on the basis of the formula. We obtain the spectra as a function of energy in agreement with the experiment of Ce_{0.7}La_{0.3}B_{6}. Analyzing the azimuthal angle dependence, we find the sixfold symmetry in the \sigma-\sigma' channel and the threefold onein the \sigma-\pi' channel not only in the antiferrooctupole (AFO) ordering phase but also in the antiferroquadrupole (AFQ) ordering phase, which behavior depends strongly on the domain distribution. The sixfold symmetry in the AFQ phase arises from the simultaneously induced hexadecapole order. Although the AFO order is plausible for phase IV in Ce_{1-x}La_{x}B_{6}, the possibility of the AFQ order may not be ruled out on the basis of azimuthal angle dependence alone.Comment: 12 pages, 6 figure

Superconductivity induced by spark erosion in ZrZn2

We show that the superconductivity observed recently in the weak itinerant ferromagnet ZrZn2 [C. Pfleiderer et al., Nature (London) 412, 58 (2001)] is due to remnants of a superconducting layer induced by spark erosion. Results of resistivity, susceptibility, specific heat and surface analysis measurements on high-quality ZrZn2 crystals show that cutting by spark erosion leaves a superconducting surface layer. The resistive superconducting transition is destroyed by chemically etching a layer of 5 microns from the sample. No signature of superconductivity is observed in rho(T) of etched samples at the lowest current density measured, J=675 Am-2, and at T < 45 mK. EDX analysis shows that spark-eroded surfaces are strongly Zn depleted. The simplest explanation of our results is that the superconductivity results from an alloy with higher Zr content than ZrZn2.Comment: Final published versio

Pressure Induced Changes in the Antiferromagnetic Superconductor YbPd2Sn

Low temperature ac magnetic susceptibility measurements of the coexistent antiferromagnetic superconductor YbPd2Sn have been made in hydrostatic pressures < 74 kbar in moissanite anvil cells. The superconducting transition temperature is forced to T(SC) = 0 K at a pressure of 58 kbar. The initial suppression of the superconducting transition temperature is corroborated by lower hydrostatic pressure (p < 16 kbar) four point resisitivity measurements, made in a piston cylinder pressure cell. At ambient pressure, in a modest magnetic field of ~ 500 G, this compound displays reentrant superconducting behaviour. This reentrant superconductivity is suppressed to lower temperature and lower magnetic field as pressure is increased. The antiferromagnetic ordering temperature, which was measured at T(N) = 0.12 K at ambient pressure is enhanced, to reach T(N) = 0.58 K at p = 74 kbar. The reasons for the coexistence of superconductivity and antiferromagnetism is discussed in the light of these and previous findings. Also considered is why superconductivity on the border of long range magnetic order is so much rarer in Yb compounds than in Ce compounds. The presence of a new transition visible by ac magnetic susceptibility under pressure and in magnetic fields greater than 1.5 kG is suggested.Comment: 5 pages, 6 figure

The dual nature of 5f electrons and origin of heavy fermions in U compounds

We develop a theory for the electronic excitations in UPt$_3$ which is based on the localization of two of the $5f$ electrons. The remaining $f$ electron is delocalized and acquires a large effective mass by inducing intra-atomic excitations of the localized ones. The measured deHaas-vanAlphen frequencies of the heavy quasiparticles are explained as well as their anisotropic heavy mass. A model calculation for a small cluster reveals why only the largest of the different $5f$ hopping matrix elements is operative causing the electrons in other orbitals to localize.Comment: 6 pages, 3 figure

Pressure dependence of the magnetization of URu2Si2

The ground state of URu2Si2 changes from so-called hidden order (HO) to large-moment antiferromagnetism (LMAF) upon applying hydrostatic pressure in excess of 14 kbar. We report the dc-magnetization M(B,T,p) of URu2Si2 for magnetic fields B up to 12 T, temperatures T in the range 2 to 100 K, and pressure p up to 17 kbar. Remarkably, characteristic scales such as the coherence temperature T*, the transition temperature T0, and the anisotropy in the magnetization depend only weakly on the applied pressure. However, the discontinuity in dM/dT at T0, which measures the magnetocaloric effect, decreases nearly 50 % upon applying 17 kbar for M and B parallel to the tetragonal c-axis, while it increases 15-fold for the a-axis. Our findings suggest that the HO and LMAF phases have an astonishing degree of similarity in their physical properties, but a key difference is the magnetocaloric effect near T0 in the basal plane

The Fermi surface and f-valence electron count of UPt3

Combining old and new de Haas-van Alphen (dHvA) and magnetoresistance data, we arrive at a detailed picture of the Fermi surface of the heavy fermion superconductor UPt3. Our work was partially motivated by a new proposal that two 5f valence electrons per formula unit in UPt3 are localized by correlation effects -- agreement with previous dHvA measurements of the Fermi surface was invoked in its support. Comprehensive comparison with our new observations shows that this 'partially localized' model fails to predict the existence of a major sheet of the Fermi surface, and is therefore less compatible with experiment than the originally proposed 'fully itinerant' model of the electronic structure of UPt3. In support of this conclusion, we offer a more complete analysis of the fully itinerant band structure calculation, where we find a number of previously unrecognized extremal orbits on the Fermi surface.Comment: 23 pages, 12 figures, latex, iopart clas

Triple-q octupolar ordering in NpO_2

We report the results of resonant X-ray scattering experiments performed at the Np M_4,5 edges in NpO_2. Below T_0 = 25 K, the development of long-range order of Np electric quadrupoles is revealed by the growth of superlattice Bragg peaks. The electronic transition is not accompanied by any measurable crystallographic distortion, either internal or external, so the symmetry of the system remains cubic. The polarization and azimuthal dependence of the intensity of the resonant peaks is well reproduced assuming Templeton scattering from a triple-q longitudinal antiferroquadrupolar structure. Electric quadrupole order in NpO_2 could be driven by the ordering at T_0 of magnetic octupoles of Gamma_5 symmetry, splitting the Np ground state quartet and leading to a singlet ground state with zero dipole magnetic moment.Comment: 4 Pages, 3 Figures, submitted to Phys. Rev. Lett. v2: resubmitted after referee report

Superconducting transition temperatures and coherence length in non s-wave pairing materials correlated with spin-fluctuation mediated interaction

Following earlier work on electron or hole liquids flowing through assemblies with magnetic fluctuations, we have recently exposed a marked correlation of the superconducting temperature Tc, for non s-wave pairing materials, with coherence length xi and effective mass m*. The very recent study of Abanov et al. [Europhys. Lett. 54, 488 (2001)] and the prior investigation of Monthoux and Lonzarich [Phys. Rev. B 59, 14598 (1999)] have each focussed on the concept of a spin-fluctuation temperature T_sf, which again is intimately related to Tc. For the d-wave pairing via antiferromagnetic spin fluctuations in the cuprates, these studies are brought into close contact with our own work, and the result is that k_B T_sf ~ hbar^2 / m* xi^2. This demonstrates that xi is also determined by such antiferromagnetic spin-fluctuation mediated pair interaction. The coherence length in units of the lattice spacing is then essentially given in the cuprates as the square root of the ratio of two characteristic energies, namely: the kinetic energy of localization of a charge carrier of mass m* in a specified magnetic correlation length to the hopping energy. The quasi-2D ruthenate Sr_2RuO_4, with Tc ~ 1.3 K, has p-wave spin-triplet pairing and so is also briefly discussed here.Comment: Accepted for publication in Phys. Rev.

Local Moment Formation in the Periodic Anderson Model with Superconducting Correlations

We study local moment formation in the presence of superconducting correlations among the f-electrons in the periodic Anderson model. Local moments form if the Coulomb interaction U>U_cr. We find that U_cr is considerably stronger in the presence of superconducting correlations than in the non-superconducting system. Our study is done for various values of the f-level energy and electronic density. The smallest critical U_cr values occur for the case where the number of f- electrons per site is equal to one. In the presence of d-wave superconducting correlations we find that local moment formation presents a quantum phase transition as function of pressure. This quantum phase transition separates a region where local moments and d-wave superconductivity coexist from another region characterized by a superconducting ground state with no local moments. We discuss the possible relevance of these results to experimental studies of the competition between magnetic order and superconductivity in CeCu_2Si_2.Comment: 4 pages. accepted for publication in Phys. Rev.