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Register a new userX-ray resonant magnetic scattering from structurally and magnetically rough interfaces in multilayered systems II. Diffuse scattering
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The theoretical formulation of x-ray resonant magnetic scattering from rough surfaces and interfaces is given for the diffuse (off-specular) scattering, and general expressions are derived in both the Born approximation (BA) and the distorted-wave Born approximation (DWBA) for both single and multiple interfaces. We also give in the BA the expression for off-specular magnetic scattering from magnetic domains. For this purpose, structural and magnetic interfaces are defined in terms of roughness parameters related to their height-height correlation functions and the correlations between them. The results are generalized to the case of multiple interfaces, as in the case of thin films or multilayers. Theoretical calculations for each of the cases are illustrated as numerical examples and compared with experimental data of mangetic diffuse scattering from a Gd/Fe multilayer.
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The theoretical formulation of x-ray resonant magnetic scattering from rough surfaces and interfaces is given for specular reflectivity. A general expression is derived for both structurally and magnetically rough interfaces in the distorted-wave Born approximation (DWBA) as the framework of the theory. For this purpose, we have defined a ``structural and a ``magnetic interface to represent the actual interfaces. A generalization of the well-known Nevot-Croce formula for specular reflectivity is obtained for the case of a single rough magnetic interface using the self-consistent method. Finally, the results are generalized to the case of multiple interfaces, as in the case of thin films or multilayers. Theoretical calculations for each of the cases are illustrated with numerical examples and compared with experimental results of magnetic reflectivity from a Gd/Fe multilayer.
Resonant x-ray scattering is performed near the Mn K-absorption edge for an epitaxial thin film of BiMnO3. The azimuthal angle dependence of the resonant (003) peak (in monoclinic indices) is measured with different photon polarizations; for the $sigmatopi$ channel a 3-fold symmetric oscillation is observed in the intensity variation, while the $sigmatosigma$ scattering intensity remains constant. These features are accounted for in terms of the peculiar ordering of the manganese 3d orbitals in BiMnO3. It is demonstrated that the resonant peak persists up to 770 K with an anomaly around 440 K; these high and low temperatures coincide with the structural transition temperatures, seen in bulk, with and without a symmetry change, respectively. A possible relationship of the orbital order with the ferroelectricity of the system is discussed.
Motivated by the recent synthesis of Ba$_2$CuO$_{3+delta}$ (BCO), a high temperature superconducting cuprate with putative $d_{3z^2-r^2}$ ground state symmetry, we investigated its electronic structure by means of Cu $L_3$ x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) at the Cu $L_3$ edge on a polycrystalline sample. We show that the XAS profile of BCO is characterised by two peaks associated to inequivalent Cu sites, and that its RIXS response features a single, sharp peak associated to crystal-field excitations. We argue that these observations are only partially compatible with the previously proposed crystal structure of BCO. Based on our spectroscopic results and on previously published powder diffraction measurements, we propose a crystalline structure characterized by two inequivalent Cu sites located at alternated planes along the $c$ axis: nominally trivalent Cu(1) belonging to very short Cu-O chains, and divalent Cu(2) in the oxygen deficient CuO$_ {1.5}$ planes. We also analyze the low-energy region of the RIXS spectra to estimate the magnitude of the magnetic interactions in BCO and find that in-plane nearest neighbor superexchange exceeds 120~meV, similarly to that of other layered cuprates. Although these results do not support the pure $d_{3z^2-r^2}$ ground state scenario, they hint at a significant departure from the common quasi-2D electronic structure of superconducting cuprates of pure $d_{x^2-y^2}$ symmetry.
We have investigated the magnetic correlations in the candidate Weyl semimetals EuCd$_2Pn_2$, ($Pn$=As, Sb) by resonant elastic X-ray scattering (REXS) at the Eu$^{2+}$ $M_5$ edge. The temperature and field dependence of the diffuse scattering of EuCd$_2$As$_2$ provide direct evidence that the Eu moments exhibit slow ferromagnetic correlations well above the N{e}el temperature. By contrast, the diffuse scattering in the paramagnetic phase of isostructural EuCd$_2$Sb$_2$ is at least an order of magnitude weaker. The FM correlations present in the paramagnetic phase of EuCd$_2$As$_2$ could create short-lived Weyl nodes.
We report the study of the skyrmion state near the surface of Cu$_2$OSeO$_3$ using soft resonant elastic x-ray scattering (REXS) at the Cu $L_3$ edge. Within the lateral sampling area of $200 times 200$ $mu$m$^2$, we found a long-range-ordered skyrmion lattice phase as well as the formation of skyrmion domains via the multiple splitting of the diffraction spots. In a recent REXS study of the skyrmion phase of Cu$_2$OSeO$_3$ [Phys. Rev. Lett. 112, 167202 (2014)], Langner et al. reported the observation of the unexpected existence of two distinct skyrmion sublattices that arise from inequivalent Cu sites, and that the rotation and superposition of the two periodic structures leads to a moir{e} pattern. However, we find no energy splitting of the Cu peak in x-ray absorption measurements and, instead, discuss alternative origins of the peak splitting. In particular, we find that for magnetic field directions deviating from the major cubic axes, a multidomain skyrmion lattice state is obtained, which consistently explains the splitting of the magnetic spots into two - and more - peaks.
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