Electronic and magnetic properties of orthorhombic iron selenide (FeSe)

Iron orbitals in orthorhombic iron selenide (FeSe) can produce charge-like multipoles that are polar (parity-odd). Orbitals in question include Fe(3d), Fe(4p) and p-type ligands that participate in transport properties and bonding. The polar multipoles may contribute weak, space-group forbidden Bragg spots to diffraction patterns collected with x-rays tuned in energy to a Fe atomic resonance (Templeton & Templeton scattering). Ordering of conventional, axial magnetic dipoles does not accompany the tetragonal-orthorhombic structural phase transition in FeSe, unlike other known iron-based superconductors. We initiate a new line of inquiry for this puzzling property of orthorhombic FeSe, using a hidden magnetic-order that belongs to the m'm'm' magnetic crystal-class. It is epitomized by the absence of ferromagnetism and axial magnetic dipoles, and the appearance of magnetic monopoles and magneto-electric quadrupoles. A similar magnetic order occurs in cuprate superconductors, YBCO & Hg1201, where it was unveiled with the Kerr effect and in Bragg diffraction patterns revealed by polarized neutrons. PACS number 75.25.-

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 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

Anapole Correlations in Sr2IrO4 Defy the jeff = 1/2 Model

Zel'dovich (spin) anapole correlations in Sr2IrO4 unveiled by magnetic neutron diffraction contravene the spin-orbit coupled ground state used by the jeff = 1/2 (pseudo-spin) model. Specifically, spin and space know inextricable knots which bind each to the other in the iridate. The diffraction property studied in the Letter is enforced by strict requirements from quantum mechanics and magnetic symmetry. It has not been exploited in the past, whereas neutron diffraction by anapole moments is established. Entanglement of the electronic degrees of freedom is captured by binary correlations of the anapole and position operators, and hallmarked in the diffraction amplitude by axial atomic multipoles with an even rank

High-order Dy multipole motifs observed in DyB2C2 with resonant soft x-ray Bragg diffraction

Resonant soft x-ray Bragg diffraction at the Dy M4,5 edges has been exploited to study Dy multipole motifs in DyB2C2. Our results are explained introducing the intra-atomic quadrupolar interaction between the core 3d and valence 4f shell. This allows us to determine for the first time higher order multipole moments of dysprosium $4f$ electrons and to draw their precise charge density. The Dy hexadecapole and hexacontatetrapole moment have been estimated at -20% and +30% of the quadrupolar moment, respectively. No evidence for the lock-in of the orbitals at T_N has been observed, in contrast to earlier suggestions. The multipolar interaction and the structural transition cooperate along c but they compete in the basal plane explaining the canted structure along [110].Comment: 4 pages, 3 figure

Comment on "Case for a U(1)pi Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore Ce2Zr2O7" by E. M. Smith et al., Phys. Rev. X 12, 021015 (2022)

All interpretations of extensive magnetic neutron scattering data in the cited paper are at fault [Phys. Rev. X 12, 021015]. For, the expressions for scattered intensities therein do not contain the cerium multipole whose likely contribution to the magnetic state of the pyrochlore is a principal goal of the published investigation. The Comment includes a brief look at essential corrections to the theory

Antiferromagnetic iron based magnetoelectric compounds

The Landau free-energy of a compound that benefits from a linear coupling of an electric field and a magnetic field includes a product of the two fields, one polar and time-even and one axial and time-odd. In ME compounds, expectation values of some atomic magnetic tensors are invariant with respect to anti-inversion. An invariance shared by the Dirac monopole (an element of charge allowed in Maxwell's equations that has not been observed) and a Zeldovich anapole, also known as a Dirac dipole. From the science of materials perspective, it has been established that Dirac multipoles contribute to the diffraction of x-rays and neutrons. We identify Dirac monopoles in bulk magnetic properties of iron tellurate (Fe2TeO6) and a spin ladder (SrFe2S2O). Both cited compounds present a simple antiferromagnetic configuration of axial dipoles, and their different magnetic crystal classes allow a linear ME effect. However, the Kerr effect is symmetry allowed in the spin ladder and forbidden in iron tellurate. Anapoles are forbidden in iron tellurate and allowed in the spin ladder compound, a difference evident in diffraction patterns fully informed by symmetry. More generally, we identify a raft of Dirac multipoles, and axial multipoles beyond dipoles, visible in future experiments using standard techniques with beams of neutrons or x-rays tuned in energy to an iron atomic resonance. ME invariance imposes a phase relationship between nuclear (charge) and magnetic contributions to neutron (x-ray) diffraction amplitudes. In consequence, intensities of Bragg spots in an x-ray pattern do not change when helicity in the primary beam is reversed. A like effect occurs in the magnetic diffraction of polarized neutrons