X-ray scattering study of the order parameters in multiferroicTbMnO3

Abstract

We report on an extensive investigation of the multiferroic compound TbMnO 3 using x-ray scattering techniques. Nonresonant x-ray magnetic scattering ͑NRXMS͒ 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 L 3 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 experiments͒ 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 L 3 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 L 3 edge only. In addition to a dominant E1-E1 component in the -Ј channel, a weaker component is found in the preedge with -Ј 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 -Ј component of the Tb L 3 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.

Long-range antiferromagnetic order of formally nonmagneticEu3+Van Vleck ions observed in multiferroicEu1−xSkaugen1, Schierle2, Laan3 et al. 2015Phys. Rev. B

“…This means that the exchange field from the A and G type Mn order, both being antiferromagnetically ordered along c, would cancel out at the Eu site, and A and G type order of the 7 F 1 moments can in theory not be induced. However, similar observations have also been made in earlier studies on TbMnO 3 , where the Tb moments mirror the A type Mn magnetic structure in the collinear phase [34,35]. Possible explanations, already discussed in the above-mentioned references, are either a nonmagnetic origin of these reflections, or ionic displacements of the Eu ions from their ideal positions which could either lift the strict extinction rules for the A and G type reflections or even break the crystal symmetry such that A and G type order can be induced at the Eu sites.…”

Coherent diffractive imaging using randomly coded masks

“…This is promising for future optical and X-ray applications, particularly in cases of samples that offer weak contrast mechanisms such as in medical applications using near-field THz imaging, 30 or ferroelectric domains using resonant x-rays diffraction. 31 The technique offers similar advantages over classic CDI to those obtained using ptychography. Specifically, there is no need for use of an object-space phase constraint or a support constraint.…”

Resonant X-Ray Scattering and Absorption

“…V 2 O 3 is certainly the most well known case [38] but in this instance the reflection structure factor allows an E2E2 term (the magnetic octupole) to occur together with the E1E2 terms [36]. More recently, a possible E1E2 signal has been reported in the ferroelectric phase of TbMnO 3 [39]. Here, both the E1E2 and the E1E1 contributions are symmetry allowed, but occur at different energies.…”