We submit that the magnetic space-group Cac (#9.41) is consistent with the established magnetic structure of BaFe2Se3, with magnetic dipole moments in a motif that uses two ladders [Caron J M et al 2011 Phys. Rev. B 84 180409(R)]. The corresponding c
rystal class m1 allows axial and polar dipoles and forbids bulk ferromagnetism. The compound supports magneto-electric multipoles, including a magnetic charge (monopole) and an anapole (magnetic toroidal dipole) visible in the Bragg diffraction of x-rays and neutrons. Our comprehensive simulation of neutron Bragg diffraction by BaFe2Se3 exploits expressions of a general nature that can be of use with other magnetic materials. Electric toroidal moments are also allowed in BaFe2Se3. A discussion of our findings for resonant x-ray Bragg diffraction illustrates the benefit of a common platform for neutron and x-ray diffraction.
Magneto-structural phase transitions in Ba1-xAxFe2As2 (A = K, Na) materials are discussed for both magnetically and orbitally driven mechanisms, using a symmetry analysis formulated within the Landau theory of phase transitions. Both mechanisms predi
ct identical orthorhombic space-group symmetries for the nematic and magnetic phases observed over much of the phase diagram, but they predict different tetragonal space-group symmetries for the newly discovered re-entrant tetragonal phase in Ba1-xNaxFe2As2 (x ~ 0.24-0.28). In a magnetic scenario, magnetic order with moments along the c-axis, as found experimentally, does not allow any type of orbital order, but in an orbital scenario, we have determined two possible orbital patterns, specified by P4/mnc1 and I4221 space groups, which do not require atomic displacements relative to the parent I4/mmm1 symmetry and, in consequence, are indistinguishable in conventional diffraction experiments. We demonstrate that the three possible space groups are however, distinct in resonant X-ray Bragg diffraction patterns created by Templeton & Templeton scattering. This provides an experimental method of distinguishing between magnetic and orbital models.
A theoretical investigation of a plausible construct for electronic structure in iridate perovskites demonstrates the existence of magnetic multipoles hitherto not identified. The strange multipoles, which are parity-even, time-odd and even rank tens
ors, are absent from the so-called jeff = 1/2 model. We prove that the strange multipoles contribute to magnetic neutron diffraction, and we estimate their contribution to intensities of Bragg spots for Sr2IrO4. The construct encompasses the jeff = 1/2 model, and it is consistent with the known magnetic structure, ordered magnetic moment, and published resonant x-ray Bragg diffraction data. Over and above time-odd quadrupoles and hexadecapoles, whose contribution changes neutron Bragg intensities by an order of magnitude, according to our estimates, are relatively small triakontadipoles recently proposed as the primary magnetic order-parameter of Sr2IrO4.
We succeed in deriving an exact expression for the magnetic interaction of neutrons and electrons including magneto-electric operators, allowed in the absence of a centre of inversion symmetry. Central characters are a spin anapole and an orbital (to
roidal) analogue, in addition to familiar parity-even operators. A simulation of neutron diffraction by antiferromagnetic copper oxide makes full use of information inferred from a thorough investigation with resonant x-ray Bragg diffraction.
Magnetic charges, or magnetic monopoles, may form in the electronic structure of magnetic materials where ions are deprived of symmetry with respect to spatial inversion. Predicted in 2009, the strange magnetic, pseudoscalars have recently been found
different from zero in simulations of electronic structures of some magnetically ordered, orthorhombic, lithium orthophosphates (LiMPO4). We prove that magnetic charges in lithium orthophosphates diffract x-rays tuned in energy to an atomic resonance, and to guide future experiments we calculate appropriate unit-cell structure factors for monoclinic LiCoPO4 and orthorhombic LiNiPO4.
Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a c
ycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence is different in the two harmonics. Our direct observation of melting is supported by a solid foundation of evidence, derived from extensive studies of the azimuthal-angle dependence of intensities with both linear and circular polarization.
Chiral properties of the two phases - collinear motif (below Morin transition temperature, TM=250 K) and canted motif (above TM) - of magnetically ordered hematite ({alpha}-Fe2O3) have been identified in single crystal resonant x-ray Bragg diffractio
n, using circular polarized incident x-rays tuned near the iron K-edge. Magneto-electric multipoles, including an anapole, fully characterize the high-temperature canted phase, whereas the low-temperature collinear phase supports both parity-odd and parity-even multipoles that are time-odd. Orbital angular momentum accompanies the collinear motif, while it is conspicuously absent with the canted motif. Intensities have been successfully confronted with analytic expressions derived from an atomic model fully compliant with chemical and magnetic structures. Values of Fe atomic multipoles previously derived from independent experimental data, are shown to be completely trustworthy.
Collinear and canted magnetic motifs in haematite were investigated by Kokubun et al. (2008) using x-ray Bragg diffraction magnified at the iron K-edge, and analyses of observations led to various potentially interesting conclusions. We demonstrate t
hat the reported analyses for both non-resonant and resonant magnetic diffraction at low energies near the absorption K-edge are not appropriate. In its place, we apply a radically different formulation, thoroughly tried and tested, that incorporates all magnetic contributions to resonant x-ray diffraction allowed by the established chemical and magnetic structures. Essential to a correct formulation of diffraction by a magnetic crystal with resonant ions at sites that are not centres of inversion symmetry are parity-odd atomic multipoles, time-even (polar) and time-odd (magneto-electric), that arise from enhancement by the electric-dipole (E1) - electric-quadrupole (E2) event. Analyses of azimuthal-angle scans on two space-group forbidden reflections, hexagonal (0, 0, 3)h and (0, 0, 9)h, collected by Kokubun et al. above and below the Morin temperature (TM = 250K), allow us to obtain good estimates of contributing polar and magneto-electric multipoles, including the iron anapole. We show, beyond reasonable doubt, that available data are inconsistent with parity-even events only (E1-E1 and E2- E2). For future experiments, we show that chiral states of haematite couple to circular polarization and differentiate E1-E2 and E2-E2 events, while the collinear motif supports magnetic charges.
