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Analysis of azimuthal-angle scans in resonant x-ray Bragg diffraction and parity even and odd atomic multipoles in the multiferroic modification of the terbium manganate TbMnO 3

2009; American Physical Society; Volume: 79; Issue: 3 Linguagem: Inglês

10.1103/physrevb.79.035111

1550-235X

Valerio Scagnoli, S W Lovesey,

Advanced Condensed Matter Physics

We present a theoretical analysis of resonant x-ray Bragg diffraction data from multiferroic ${\text{TbMnO}}_{3}$ presented by Mannix et al. [Phys. Rev. B 76, 184420 (2007)] and Voigt et al. [Phys. Rev. B 76, 104431 (2007)]. We have chosen an approach that does not rely on knowledge of the low-temperature phase space group of the sample, which is not precisely known. Results show that the low-temperature satellite reflections originate from dipole-dipole (E1-E1) and dipole-quadrupole (E1-E2) events. Presence on quadrupole-quadrupole (E2-E2) events can be excluded. The physical origin of the data is discussed in terms of atomic multipoles (expectation value of an operator equivalent) that represent magnetization, lattice distortions, and magnetoelectric properties of the Tb and Mn ions. A handed (chiral) cycloid of atomic multipoles, traced out in the $b\text{\ensuremath{-}}c$ plane, is shown to be a plausible model of the Tb electron structure within a multiferroic modification that exists in the temperature interval $7\text{ }\text{K}<T<28\text{ }\text{K}$. Appendixes A--F record universal expressions for unit-cell structure factors appropriate to all four polarization channels $({\ensuremath{\sigma}}^{\ensuremath{'}}\text{\ensuremath{-}}\ensuremath{\sigma},{\ensuremath{\sigma}}^{\ensuremath{'}}\text{\ensuremath{-}}\ensuremath{\pi},{\ensuremath{\pi}}^{\ensuremath{'}}\text{\ensuremath{-}}\ensuremath{\sigma},{\ensuremath{\pi}}^{\ensuremath{'}}\text{\ensuremath{-}}\ensuremath{\pi})$ of E1-E1, E1-E2, and E2-E2 resonance events.