X-Ray Resonant Scattering Study of the Quadrupolar Order inUPd3

Abstract

Quadrupolar ordering in a 5f electron system has been observed directly for the first time, using x-ray scattering techniques. In UPd (3) at low temperatures satellite peaks appear at (1,0,l) (orthorhombic notation) with l odd and even. Both sets of peaks show a resonant enhancement of the scattering at the M(IV) edge of U. At resonance, the dominant scattering of the l odd peaks occurs in the unrotated polarization channel, whereas for l even a significant rotated component is found. These results are discussed in terms of possible structures of the antiferroquadrupolar phases.

5fdelocalization-induced suppression of quadrupolar order in U(Pd1−xPtx)Walker1, Le2, McEwen3 et al. 2011Phys. Rev. BSelf Cite7020View full textAdd to dashboardCite

“…The narrow temperature range between T +1 and T −1 and difficulty in stabilizing a displex cryostat within this interval means that it has not been possible to perform azimuthal measurements in this phase. However, in temperature dependent measurements, we observed the emergence of a (104) superlattice reflection only below the T −1 transition 13 . In combination with the small change in the magnetic entropy, as obtained from heat capacity measurements, this is consistent with the onset at T +1 of a Q yz component to the quadrupolar order, with an anti-phase stacking along the c -axis.…”

“…5) at this temperature, although this is close to the base temperature limit attainable for the cryostat, and it is possible that due to heating by the beam we might not have reached sufficiently low temperatures to enter this phase. Alternatively, it may be that due to insufficient data density we are unable to identify any anomaly, which has previously been found to be very weak at the T 2 transition in the temperature dependence of UPd 3 as measured by X-ray resonant scattering 13 . In UPd 3 the sharp change in entropy at the T −1 transition is associated with the onset of an in-phase component of the quadrupole stacking along the c-axis described by the Q xy order parameter in addition to a Q zx anti-phase ordering.…”

“…Bulk measurements (ultrasound 7 , heat capacity 8-10 , magnetic susceptibility 9,11 , thermal expansion and magnetostriction 12 ) reveal that UPd 3 undergoes four successive phase transitions below 8 K, which have been identified through X-ray resonant scattering studies as relating to the antiferroquadrupolar order of the 5f 2 electrons on the quasi-cubic uranium sites 4,10,13,14 . The four transitions: T 0 = 7.8 K, T +1 = 6.9 K, T −1 = 6.7 K and T 2 = 4.4 K can be explained by a crystal field model requiring a doublet ground state on the quasi-cubic sites 15 .…”

Resonant elastic X-ray scattering from 5f systems

“…These experiments (at BNL) showed that a dead layer was formed at the surface of the crystal, probably due to a change in the stoichiometry, and that the first-order nature of the transition (AF to para) became 2 nd order at the surface, as expected from theory. (4) The detection of higher-order multipoles in 5f systems was first reported in UPd 3 [11,12]. The case of NpO 2 is extraordinary, as there is no dipole moment, but the quadrupolar moment is induced [13] as a consequence of the ordering of the trikontadipole (rank 5) [14].…”

Mean-field model for the quadrupolar phases ofUPd3

“…X-ray resonant scattering (XRS) measurements 13 showed that this transition arises from the ordering of the electric quadrupole moment of the 5 f 2 electrons. In addition to this phase transition at T 0 = 7.8 K, there are three further transitions to different antiferroquadrupolar (AFQ) ordered states at T +1 = 6.9 K, T −1 = 6.7 K and T 2 = 4.4 K. Below T 0 a superlattice peak at ( 1 2 0l) where l is odd is observed, whilst below T −1 there are additional peaks at ( 1 2 0l) where l is even.…”