Multipoles, Magnetic charges and chiral properties in antiferromagnetic materials inferred from resonant X-Ray diffraction

Abstract

In the last decades, the interesting features behind the exotic orderings of materials have attracted the attention of many scientists. This new physics can be related to the magnetic and charge multipoles defined by a few electrons around the atomic core in the valence states. The uses of x-rays and neutrons techniques, due to the huge development of large facilities as synchrotrons and spallation sources, have revealed many of these behaviours. In the case of synchrotron sources, photon beams have high brightness, high tunability and good degree of polarization, which together with the development of new experimental techniques have been helpful in the characterization of new functional materials making valuable observations. Resonant Elastic x-ray Scattering (REXS), in particular using polarization analysis, has shown to be an extremely sensitive tool for determining the charge and magnetic degrees of freedom of multiferroic, superconducting or other kind of strongly correlated materials; helping whereas other techniques such as neutron probes or non-resonant x-rays scattering are not able to obtain relevant information. Conventionally, REXS experiments are performed at space group forbidden reflections, where high order contributions as Thomson scattering are not allowed. The data gathered at these weak Bragg reflections, due to space group symmetry rules, can be treated using an atomic model, which has the virtue of being used as a common platform for the analysis of x-ray and neutron diffraction experiments. In this PhD work, three different antiferromagnetic materials with magnetic ions located in threefold symmetry (3) positions have been investigated in detail by means of REXS. Neptunium Dioxide (NpO2), where an enigmatic low-temperature ordering state shows interesting physical features, similar to the one observed in UO2, that relates its crystal field, the super-exchange interactions and electron¿phonon coupling. Previous works from different groups have not been able to explain the resonant x-ray diffraction data collected at the neptunium M4-edge. But new information, related to a change in the symmetry of the neptunium sites (3 ¿m) due to the delocalization of the oxygen atoms, has helped to analyse and redefine the wave function that has successfully confirmed the reorganization of the oxygen sites and has estimated the value of hexadecapoles, which can not be observed by other techniques, confirming the antiferromagnetic ordering. Hematite (¿-Fe2O3) in its antiferromagnetic phase and above the Morin temperature, due to an anisotropic exchange interaction that force the spins of the ions to assume a canted configuration, shows a small ferromagnetic contribution also known as Dzyaloshinskii-Moriya interaction. Previous studies performed to hematite using REXS near the iron K-edge did not explain properly the behaviour under this structure for both the collinear and canted antiferromagnetic phases. The application of the formalism presented in this work, which incorporate all magnetic contributions, successful explains the behaviour by the presence of a mixture between two processes electric-dipole (E1)-electric-quadrupole (E2) and E2E2, obtaining good estimated values for the different multipoles behind these processes. A circular polarized REXS experiment was modelled, which showed the possibility of distinguishing between these two processes while doing the experiment under this kind of polarization. The collected data ratifies the coupling between this kind of polarization and the chiral properties of the compound, showing a fully characterization of the high-temperature phase by the Magnetoelectric multipoles. Bismuth Ferrite (BiFeO3), the only material from the multiferroic family that shows a magnetoelectric coupling above room temperature, is also an example of the Dzyaloshinskii-Moriya interaction. The results presented in this work supports a new chiral phase above the Néel temperature, in the ferroelectric phase, have been obtained by a REXS experiment, with the incoming x-ray beam tuned near the iron K-edge. The R3c forbidden reflection (0,0,9)H was studied as a function of the rotation of the crystal about the Bragg wave-vector in both phases, paramagnetic (700 K) and antiferromagnetic (300 K). The data gathered is consistent with a chiral structure formed by a circular cycloid propagating along (1,1,0)H. Templeton and Templeton (T&T) scattering at 700 K is attributed in part to charge-like quadrupoles absent in a standard model of a cycloid in which a material vector generates all electronic states of the resonant ion. Extensive sets of azimuthal-angle data are used to infer values of three atomic multipoles in a satisfactory minimal model of the iron electronic structure, with a quadrupole (E1E1 event) and a hexadecapole (E2E2 event) contributing T&T scattering, plus a magnetic dipole (E1E1) for the antiferromagnetic phase.