Quadrupolar Coefficients Research Articles

LARGE-SCALE DISTRIBUTION OF ARRIVAL DIRECTIONS OF COSMIC RAYS DETECTED ABOVE 1018 eV AT THE PIERRE AUGER OBSERVATORY

ABSTRACT A thorough search for large-scale anisotropies in the distribution of arrival directions of cosmic rays detected above 1018 eV at the Pierre Auger Observatory is presented. This search is performed as a function of both declination and right ascension in several energy ranges above 1018 eV, and reported in terms of dipolar and quadrupolar coefficients. Within the systematic uncertainties, no significant deviation from isotropy is revealed. Assuming that any cosmic-ray anisotropy is dominated by dipole and quadrupole moments in this energy range, upper limits on their amplitudes are derived. These upper limits allow us to test the origin of cosmic rays above 1018 eV from stationary Galactic sources densely distributed in the Galactic disk and predominantly emitting light particles in all directions.

The interplay of the crystalline electric field and quadrupolarinteractions in the spontaneous magnetic phases of DyIn3

DyIn3orders at TN = 20 Kand undergoes a second spontaneous magnetic transition at16.5 K. From bulk magnetization measurements, performed on asingle crystal along the three main axes of the cubic AuCu3-typestructure, the magnetic phase diagrams have been established. The crystallineelectric field (CEF) scheme, in the paramagnetic phase, and the magneticstructures of the spontaneous and low field-induced phases have been probed byneutron techniques. All the magnetic phases studied are found to be multipleq withqbelonging to the ⟨1/2, 1/2, 0⟩star. In the low temperature phase (T < 16.5 K) the structureis double qwith moments along twofold axes, whereas above 16.5 K it becomes tripleqwith moments along threefold axes. The analysis of the experimentalresults within the periodic molecular field model leads to a coherentinterpretation of the spontaneous magnetic transitions, mainly drivenby bilinear exchange and CEF interactions. Though the existence ofquadrupolar interactions is definitively proved by the stabilization of multipleqmagnetic structures, quadrupolar coefficients are found to be one orderof magnitude smaller than those previously reported for NdIn3 andTbIn3.

Anomalies in thermal expansion of DyVO4 induced by quadrupolar ordering

The thermal expansion of the DyVO4 crystal has been experimentally and theoretically investigated in the range of the Jahn-Teller structural phase transition. The manifestation of totally symmetric magnetoelastic interactions upon this transition has been studied for the first time. It is found that the temperature dependences of the unit-cell and thermal expansion parameters along the nonactive Jahn-Teller direction in the basal plane for the DyVO4 crystal exhibit characteristic magnetoelastic anomalies at T<Tc due to the ordering of quadrupole moments of Dy3+ ions. The magnetoelastic contributions of the totally symmetric eα1 and eα2 and symmetry-lowering eγ modes to the thermal expansion are calculated within the general crystal-field formalism. The total quadrupolar coefficient Gγ and magnetoelastic coefficient Bγ are determined from the spectroscopic and spontaneous deformation data. It is demonstrated that the thermal expansion of the DyVO4 crystal in the tetragonal and orthorhombic phases is well described in the framework of the unified model using a common set of interaction parameters for both phases.