A theory of the spin-crossover phenomena in the rare earth perovskite LaCoOinduced by temperature or a magnetic field.

Published magnetic data for LaCoOare successfully analyzed with coexistingand low-spin (LS) cobalt states. Energy levels of the two states are derived in analytic forms. To this end, fictitious orbital angular momentumof magnitude one defines the Γ() state.

Polar magnetism and chemical bond in-RuCl.

The micaceous black allotrope of ruthenium trichloride is the subject of many recent experimental and theoretical studies. Even so, its structural and magnetic properties remain undecided; monoclinic, trigonal and rhombohedral space groups for the crystal structure have been proposed on the basis of various types of experiments. The magnetic structure is often discussed in the context of the Kitaev state, but inevitably they are inconclusive discussions in the absence of structural and magnetic space groups.

Ligand-metal bonding effects in resonance enhanced x-ray Bragg diffraction.

Chlorine covalently bonded to an open shell metal is present in many materials with desirable or intriguing physical properties. Materials include highly luminescent nontoxic alternatives to lead halide perovskites for optoelectronic applications KCuCland RbCuCl, enantiomorphic CsCuClthat presents magneto-chiral dichroism at a low temperature, and cubic KRuClthat possesses a singlet ground state generated by antiparallel spin and orbital angular momenta. Structural chirality of CsCuClhas been confirmed by resonant x-ray Bragg diffraction.

Electric field control of chirality.

Polar textures have attracted substantial attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second-harmonic generation–based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field.

Direct Observation of Anapoles by Neutron Diffraction.

The scope of magnetic neutron scattering has been expanded by the observation of electronic Dirac dipoles (anapoles) that are polar (parity odd) and magnetic (time odd). A zero-magnetization ferromagnet Sm_{0.976}Gd_{0.

A unified formulation of dichroic signals using the Borrmann effect and twisted photon beams.

Dichroic X-ray signals derived from the Borrmann effect and a twisted photon beam with topological charge l = 1 are formulated with an effective wavevector. The unification applies for non-magnetic and magnetic materials. Electronic degrees of freedom associated with an ion are encapsulated in multipoles previously used to interpret conventional dichroism and Bragg diffraction enhanced by an atomic resonance.

Electronic and magnetic properties of multiferroic ScFeO available from diffraction experiments.

Electronic and magnetic properties of ferric ions (3d ) in multiferroic ScFeO are puzzling, in part because they are different from the only other multiferroic known to possess the same polar chemical structure, BiFeO. Open questions about ScFeO can be addressed by confronting observations with results for G-type antiferromagnetism allowed by the lithium niobate (LiNbO)-like parent R3c structure. Calculated structure factors for resonant x-ray diffraction include all charge-like quadrupoles allowed by symmetry, and if experimental results for ScFeO subsequently imply they are different from zero then ferric ions cannot be in the high-spin S state.

Neutron scattering by Dirac multipoles.

Scattering by magnetic charge formed by Dirac multipoles that are magnetic and polar is examined in the context of materials with properties that challenge conventional concepts. An order parameter composed of Dirac quadrupoles has been revealed in the pseudo-gap phase of ceramic, high-T superconductors on the basis of Kerr effect and magnetic neutron Bragg diffraction measurements. Construction of Dirac quadrupoles that emerge from centrosymmetric sites used by Cu ions in the ceramic superconductor Hg1201 is illustrated, together with selection rules for excitations that will feature in neutron inelastic scattering, and RIXS experiments.

Ordered state of magnetic charge in the pseudo-gap phase of a cuprate superconductor (HgBa2CuO(4+δ)).

A symmetry-based interpretation of published experimental results demonstrates that the pseudo-gap phase of underdoped HgBa2CuO(4+δ) (Hg1201) possesses an ordered state of magnetic charge epitomized by Cu magnetic monopoles. Magnetic properties of one-layer Hg1201 and two-layer YBa2Cu3O(6+x) (YBCO) cuprates have much in common, because their pseudo-gap phases possess the same magnetic space-group, e.g.

Ferro-type order of magneto-electric quadrupoles as an order-parameter for the pseudo-gap phase of a cuprate superconductor.

There is general agreement within the community of researchers that investigate high-Tc materials that it is most important to understand the pseudo-gap phase. To this end, many experiments on various cuprates have been reported. Two prominent investigations-Kerr effect and neutron Bragg diffraction-imply that underdoped YBCO samples possess long-range magnetic order of an unusual kind.

A model of magneto-electric multipoles.

A long-known Hamiltonian of electrons with entangled spin and orbital degrees of freedom is re-examined as a model of magneto-electric multipoles (MEs). In the model, a magnetic charge and simple quantum rotator are tightly locked in action, some might say they are enslaved entities. It is shown that MEs almost perfectly accord with those inferred from an analysis of magnetic neutron diffraction data on a ceramic superconductor (YBCO) in the pseudo-gap phase.

Magneto-electric operators in neutron scattering from electrons.

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 (toroidal) analogue, in addition to familiar parity-even operators like the magnetic moment. 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.

Strange magnetic multipoles and neutron diffraction by an iridate perovskite (Sr2IrO4).

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 tensors, are absent from the so-called j(eff) = 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 Sr(2)IrO(4).

Effects of dispersion and absorption in resonant Bragg diffraction of x-rays.

Resonant diffraction of x-rays by crystals with anisotropic optical properties is investigated theoretically, to assess how the intensity of a Bragg spot is influenced by effects related to dispersion (birefringence) and absorption (dichroism). Starting from an exact but opaque expression, simple analytic results are found to expose how intensity depends on dispersion and absorption in the primary and secondary beams and, also, the azimuthal angle (rotation of the crystal about the Bragg wavevector). If not the full story for a given application, our results are more than adequate to explore consequences of dispersion and absorption in the intensity of a Bragg spot.

Symmetry-protected hidden order and magnetic neutron Bragg diffraction by URu2Si2.

We investigate how the order parameter of a continuous phase transition can be protected from view by symmetry in a magnetic crystal. The symmetry in question forbids atomic displacements and formation of magnetic dipoles, rendering the order parameter invisible in standard x-ray and magnetic neutron Bragg diffraction. Analysis of the allowed magnetic space-groups reveals exact properties of the hidden order parameter.

Melting of chiral order in terbium manganate (TbMnO3) observed with resonant x-ray Bragg diffraction.

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 cycloid, 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 differs in the two harmonics.

Magnetic symmetries in neutron and resonant x-ray Bragg diffraction patterns of four iridium oxides.

The magnetic properties of Sr(2)IrO(4), Na(2)IrO(3), Sr(3)Ir(2)O(7) and CaIrO(3) are discussed, principally in the light of experimental data in recent literature for Bragg intensities measured in x-ray diffraction with enhancement at iridium L-absorption edges. The electronic structure factors we report, which incorporate parity-even and acentric entities, serve the immediate purpose of making full use of crystal and magnetic symmetry to refine our knowledge of the magnetic properties of the four iridates from resonant x-ray diffraction data. They also offer a platform on which to interpret future investigations, using dichroic signals, resonant x-ray diffraction and neutron diffraction, for example, as well as ab initio calculations of electronic structure.

Magnetic correlations in a layered iridate, Na2IrO3.

Analysis of published data gathered on a sample of Na(2)IrO(3), held deep inside the antiferromagnetic phase at 1.58 K, shows that iridium magnetic dipole moments, measured in resonant x-ray Bragg diffraction, lie in the a-c plane of the monoclinic crystal and enclose an angle ≈118° with the c-axis. These findings, together with bulk measurements, are united in a plausible magnetic ground state for an iridium ion constructed from a Kramers doublet.

Neptunium multipoles and resonant x-ray Bragg diffraction by neptunium dioxide (NpO2).

The low-temperature ordered state of neptunium dioxide (NpO(2)) remains enigmatic. After decades of experimental and theoretical efforts, long-range order of a time-odd (magnetic) high-order atomic multipole moment is now generally considered to be the fundamental order parameter, the most likely candidate being a magnetic triakontadipole (rank 5). To date, however, direct experimental observation of the primary order parameter remains outstanding.

Acentric magnetic and optical properties of chalcopyrite (CuFeS2).

The absence of spatial inversion symmetry at both local (point group 4) and global (crystal class (4)2m) levels greatly influences the electronic properties of chalcopyrite (CuFeS(2)). The predicted dichroic signals (natural circular, non-reciprocal and magneto-chiral) and resonant, parity-odd Bragg diffraction patterns at space-group forbidden reflections portray the uncommon, acentric symmetry. Despite extensive experimental investigations over several decades, by mineralogists, chemists and physicists, there is no consensus view about the electrical and magnetic properties of chalcopyrite.

Triakontadipole and high-order dysprosium multipoles in the antiferromagnetic phase of DyB2C2.

Resonant soft x-ray Bragg diffraction at the Dy M(4,5) edges has been used to study Dy multipoles in the combined magnetic and orbitally ordered phase of DyB(2)C(2). The analysis incorporates both the intra-atomic magnetic and quadrupolar interactions between the 3d core and 4f valence shells. Additionally, we introduce to the formalism the interference of magnetic and nonmagnetic oscillators.

Observation of orbital currents in CuO.

Orbital currents are proposed to be the order parameter of the pseudo-gap phase of cuprate high-temperature superconductors. We used resonant x-ray diffraction to observe orbital currents in a copper-oxygen plaquette, the basic building block of cuprate superconductors. The confirmation of the existence of orbital currents is an important step toward the understanding of the cuprates as well as materials lacking inversion symmetry, such as magnetically induced multiferroics.

Determination of the absolute chirality of tellurium using resonant diffraction with circularly polarized x-rays.

Many proteins, sugars and pharmaceuticals crystallize into two forms that are mirror images of each other (enantiomers) like our right and left hands. Tellurium is one enantiomer having a space group pair, P3(1)21 (right-handed screw) and P3(2)21 (left-handed screw). X-ray diffraction with dispersion correction terms has been playing an important role in determining the handedness of enantiomers for a long time.