Strong resonant enhancements of the charge-order and spin-order superstructure-diffraction intensities in La1.8Sr0.2NiO4 are observed when x-ray energies in the vicinity of the Ni L2,3 absorption edges are used. The pronounced photon-energy and polarization dependences of these diffraction intensities allow for a critical determination of the local symmetry of the ordered spin and charge carriers. We found that not only the antiferromagnetic order but also the charge-order superstructure resides within the NiO2 layers; the holes are mainly located on in-plane oxygens surrounding a Ni2+ site with the spins coupled antiparallel in close analogy to Zhang-Rice singlets in the cuprates.
We studied the stripe phase of La1.8Sr0.2NiO4 using neutron diffraction, resonant soft x-ray diffraction (RSXD) at the Ni L2,3 edges, and resonant x-ray diffraction (RXD) at the Ni K threshold. Differences in the q-space resolution of the different techniques have to be taken into account for a proper evaluation of diffraction intensities associated with the spin and charge order superstructures. We find that in the RSXD experiment the spin and charge order peaks show the same temperature dependence. In the neutron experiment by contrast, the spin and charge signals follow quite different temperature behaviors. We infer that fluctuating magnetic order contributes considerably to the magnetic RSXD signal and we suggest that this result may open an interesting experimental approach to search for fluctuating order in other systems by comparing RSXD and neutron diffraction data.
Soft resonant x-ray Bragg diffraction (SRXD) at the Ho M$_{4,5}$ edges has been used to study Ho $4f$ multipoles in the combined magnetic and orbitally ordered phase of HoB$_2$C$_2$. A full description of the energy dependence for both $sigma$ and $pi$ incident x-rays at two different azimuthal angles, as well as the ratio $I_sigma/I_pi$ 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 parameter are distinct. The $(0 0 1/2)$ 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 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$_Q$.
We investigate the order parameter dynamics of the stripe-ordered nickelate, La$_{1.75}$Sr$_{0.25}$NiO$_4$, using time-resolved resonant X-ray diffraction. In spite of distinct spin and charge energy scales, the two order parameters amplitude dynamics are found to be linked together due to strong coupling. Additionally, the vector nature of the spin sector introduces a longer re-orientation time scale which is absent in the charge sector. These findings demonstrate that the correlation linking the symmetry-broken states does not unbind during the non-equilibrium process, and the time scales are not necessarily associated with the characteristic energy scales of individual degrees of freedom.
Resonant soft X-ray scattering was used to determine the presence of more subtle orderings not detected in standard structural analyses. By tuning to specific Co absorption edges, arrangements particular to the electronic states of those elements are enhanced. We have discovered an ordering commensurate to the lattice at the ($frac{1}{4}~frac{1}{4}~frac{1}{4}$) position. Incommensurate peaks near this position were also observed. The intensity of these peaks depends on the oxygen concentration of the sample, and can be suppressed at temperatures above 320 K. Regular orderings of charge density which closely match the underlying lattice may help to explain the observed propensity for SrCoO$_{3-y}$ (0 $leq$ y $leqfrac{1}{2}$) to stabilize at particular phases.
Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a cycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence is different in the two harmonics. Our direct observation of melting is supported by a solid foundation of evidence, derived from extensive studies of the azimuthal-angle dependence of intensities with both linear and circular polarization.
C. Schuessler-Langeheine
,J. Schlappa
,A. Tanaka
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(2005)
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"Spectroscopy of stripe order in La1.8Sr0.2NiO4 using resonant soft x-ray diffraction"
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Christian Sch\\\"u{\\ss}ler-Langeheine
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