High-order Dy multipole motifs observed in DyB₂C₂with resonant soft x-ray Bragg diffraction

Abstract

Resonant soft x-ray Bragg diffraction at the Dy M4,5 edges has been exploited to study Dy multipole motifs in DyB2C2. Our results are explained introducing the intra-atomic quadrupolar interaction between the core 3d and valence 4f shell. This allows us to determine for the first time higher order multipole moments of dysprosium 4f electrons and to draw their precise charge density. The Dy hexadecapole and hexacontatetrapole moment have been estimated at −20% and +30% of the quadrupolar moment, respectively. No evidence for the lock-in of the orbitals at TN has been observed, in contrast to earlier suggestions. The multipolar interaction and the structural transition cooperate along c but they compete in the basal plane explaining the canted structure along [110].

Manipulating4fquadrupolar pair-interactions inTbB2C2using a magnetic field

“…21 From resonant scattering, it has been suggested that the buckling of the B and C sheets accompanying the orbital order and assisting the AFQ along c actually opposes the AFQ interaction in the plane, giving rise to the quasi-onedimensional behavior. 19 Our findings suggest that the AFQ interaction in the plane dominates in TbB 2 C 2 because the angle of Tb orbital misalignment in the plane equals 4°com-pared to 1°for out of plane ͑15 K, zero field͒.…”

“…The energy profile recorded in an applied magnetic field is similar to that recorded for the ͑ 00 1 2 ͒ reflection in DyB 2 C 2 in the AFQ phase. 19 There, the energy spectra with its interference like shape has been theoretically described due to an intra-atomic quadrupole interaction, which splits the core state. With such an ansatz, information on higher multipole moments were extracted.…”

Crystal symmetry lowering in chiral multiferroic Ba3TaFe3Si2O14 observed by x-ray magnetic scattering

“…As for case (iii), the splitting of core-levels leading to the hyperfine structure of spectral lines is a well-known phenomenon in atomic physics and core-level spectroscopies. In the context of RXD, effects of such a splitting have been discussed for the case of M 4,5 edges of 4f atoms 39,40 . In BTFS, due to the non-collinear spin structure, the axis of relativistic spin quantization varies from one atom to the next.…”

Resonant X-ray Scattering Experiments on the Ordering of Electronic Degrees of Freedom

“…[82][83][84][85][86][87][88][89][90] In the AFQ state, only the quadrupole moments are ordered, whereas the magnetic degree of freedom remains paramagnetic. DyB 2 C 2 is a tetragonal compound exhibiting two successive phase transitions at T Q ¼ 25 and T N ¼ 15 K. 91) Since the AFM order is observed only below T N , the intermediate phase between T N and T Q was ascribed to an AFQ-ordered phase.…”

“…90,97,98) The advantage of M-edge RXS is that the f orbital is directly probed by the fundamental E1 resonance. Furthermore, resonance enhancement is much larger than that in L-edge RXS because the overlap between the 3d and 4f orbitals is much larger than that between the 2p and 5d orbitals.…”