High-order Ho multipoles in HoB₂C₂observed with soft resonant x-ray diffraction

Abstract

Soft resonant x-ray Bragg diffraction (SRXD) at the Ho M4,5 edges has been used to study Ho 4f multipoles in the combined magnetic and orbitally ordered phase of HoB2C2. A full description of the energy dependence for both σ and π incident x-rays at two different azimuthal angles, as well as the ratio I(σ)/I(π) as a function of azimuthal angle for a selection of energies, allows a determination of the higher order multipole moments of rank 1 (dipole) to 6 (hexacontatetrapole). The Ho 4f multipole moments have been estimated, indicating a dominant hexadecapole (rank 4) order with an almost negligible influence from either the dipole or the octupole magnetic terms. The analysis incorporates both the intra-atomic magnetic and quadrupolar interactions between the 3d core and 4f valence shells as well as the interference of contributions to the scattering that behave differently under time reversal. Comparison of SRXD, neutron diffraction and non-resonant x-ray diffraction shows that the magnetic and quadrupolar order parameters are distinct. The (00½) component of the magnetic order exhibits a Brillouin type increase below the orbital ordering temperature T(Q), while the quadrupolar order increases more sharply. We conclude that the quadrupolar interaction is strong, but quadrupolar order only occurs when the magnetic order gives rise to a quasi-doublet ground state, which results in a lock-in of the orbitals at T(Q).

The UE46 PGM-1 beamline at BESSY II

“…Together with very stable X-ray beam conditions, this allows to perform high quality di raction experiments even from tiny crystals (< 100 µm x 100 µm) over a large angular range, as well as measurements of specular re ectivity with very high precision. The standard setup features a sample holder directly attached to a liquid He-ow-cryostat, providing sample temperatures below 4 K. Azimuthal rotation in situ is provided for azimuth-dependent measurements even at these low temperatures (Leininger et al, 2010;Princep et al, 2012). Photons are detected by an AXUV100-type photodiode with a set of changeable slits in front for adapting the resolution.…”

Resonant elastic soft x-ray scattering

“…Here, the shielding of the 4f shell by the outer 5d electrons causes a weaker coupling of the electronic degrees of freedom of the 4f electrons to the lattice and hence, allows studying orbital order mechanisms in a less complex situation. In a series of publications on orbital ordering of 4f electrons in REB 2 C 2 compounds Mulders et al could show that RSXS performed at the RE −M 4,5 resonances is not just able to observe orbital order of the 4f electrons but can in addition quantify the contributions of the different higher order multipole moments to the electronic ordering [219,220,221,222].…”

Neptunium multipoles and resonant x-ray Bragg diffraction by neptunium dioxide (NpO2)

“…The same basic atomic theory of resonant scattering of x-rays, used here to interpret diffraction data gathered on the low-temperature phase of neptunium dioxide at the Np M 4 edge (3846.9 eV), has been applied with equal success to interpretations of diffraction data gathered on rare-earth compounds with combined magnetic and orbitally ordered phases. Mulders and collaborators [13][14][15] report three studies of soft x-ray resonant Bragg diffraction at M 4,5 edges of Dy and Ho in borocarbides (DyB 2 C 2 and HoB 2 C 2 ) and extract good estimates of high-order rare-earth multipoles, e.g. the Dy triakontadipole [14].…”