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X-ray Resonant Scattering Study of the Order Parameters in Multiferroic TbMnO
We report on an extensive investigation of the multiferroic compound
TbMnO. Non-resonant x-ray magnetic scattering (NRXMS) revealed a dominant
-type domain. The temperature dependence of the intensity and wavevector
associated with the incommensurate magnetic order was found to be in good
agreement with neutron scattering data. XRS experiments were performed in the
vicinity of the Mn and Tb edges in the high-temperature collinear
phase, the intermediate temperature cycloidal/ferroelectric phase, and the
low-temperature phase. In the collinear phase resonant satellites were
found at the Mn edge associated with -type but also -type peaks. The
azimuthal dependence of the -type satellites (and their absence in the NRXMS
experiments) indicates that they are most likely non-magnetic in origin. We
suggest instead that they may be associated with an induced charge multipole.
At the Tb edge resonant - and -type satellites () were
observed in the collinear phase. These we attribute to a polarisation of the Tb
5 states by the ordering of the Mn sublattice. In the
cycloidal/ferroelectric phase a new set of resonant satellites appear
corresponding to -type order. These appear at the Tb edge only. In
addition to a dominant component in the channel, a
weaker component is found in the pre-edge with
polarization. Calculations of the XRS were performed using the code
showing that the unrotated component of the Tb
-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.Comment: Phys. Rev. B (In press