X-ray scattering study of the order parameters in multiferroic TbMn O3
Physical Review B - Condensed Matter and Materials Physics 76:18 (2007)
Authors:
D Mannix, DF McMorrow, RA Ewings, AT Boothroyd, D Prabhakaran, Y Joly, B Janousova, C Mazzoli, L Paolasini, SB Wilkins
Abstract:
We report on an extensive investigation of the multiferroic compound TbMn O3 using x-ray scattering techniques. Nonresonant x-ray magnetic scattering (NRXMS) was used to characterize the domain population of the single crystal used in our experiments. This revealed that the dominant domain is overwhelmingly A type. The temperature dependence of the intensity and wave vector associated with the incommensurate magnetic order was found to be in good agreement with neutron scattering data. X-ray resonant scattering experiments were performed in the vicinity of the Mn K and Tb L3 edges in the high-temperature collinear phase, the intermediate temperature cycloidal and ferroelectric phase, and the low-temperature phase. In the collinear phase, where according to neutron diffraction only the Mn sublattice is ordered, resonant E1-E1 satellites were found at the Mn K edge associated with A -type but also F -type peaks. Detailed measurements of the azimuthal dependence of the F -type satellites (and their absence in the NRXMS experiments) leads us to conclude that they are most likely nonmagnetic in origin. We suggest instead that they may be associated with an induced charge multipole. At the Tb L3 edge, resonant A - and F -type satellites were observed in the collinear phase again associated with E1-E1 events. We attribute these to a polarization of the Tb 5d states by the ordering of the Mn sublattice. On cooling into the cycloidal and ferroelectric phase, a new set of resonant satellites appear corresponding to C -type order. These appear at the Tb L3 edge only. In addition to a dominant E1-E1 component in the σ- π′ channel, a weaker component is found in the preedge with σ- σ′ polarization and displaced by -7 eV with respect to the E1-E1 component. Comprehensive calculations of the x-ray scattering cross section were performed using the FDMNES code. These calculations show that the unrotated σ- σ′ component of the Tb L3 C -type peaks appearing in the ferroelectric phase contains a contribution from a multipole that is odd with respect to both space and time, known in various contexts as the anapole. Our experiments thus provide tentative evidence for the existence of a type of anapolar order parameter in the rare-earth manganite class of mulitferroic compounds. © 2007 The American Physical Society.
