Show Abstract ▼

Abstract: The ferrimagnet Mn 3 Si 2 Te 6 attracts attention because of a recently discovered colossal magnetoresistance (CMR) with unique magnetic field properties. An improved magnetic structure for the material has emerged from a neutron diffraction study linked to understanding the CMR. A deeper theoretical investigation of the magnetic structure has now revealed anapole, chiral, and orbital states of manganese ions not previously mentioned. Moreover, it is shown that existence of these states in the low temperature form of Mn 3 Si 2 Te 6 , with a magnetic field applied, can be tested by neutron and resonant x-ray diffraction.

Open Access

Show Abstract ▼

Abstract: 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. Evidently, the coefficient of the product of fields is unchanged by a simultaneous change in the directions of space and time, a symmetry operation labeled anti-inversion. Invariance with respect to anti-inversion is the defining symmetry of the linear magnetoelectric (ME) effect included in 58 of 122 magnetic crystal classes, 19 of which prohibit higher-order (nonlinear) contributions to the free energy. 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 Zel'dovich anapole, is 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 ( Fe 2 Te O 6 ) and a spin ladder ( Sr Fe 2 S 2 O ). They are visible in the diffraction of light using an iron electric dipole–magnetic dipole absorption event. 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.

Open Access

Show Abstract ▼

Abstract: The nature and origin of electronic nematicity remains a significant challenge in our understanding of the iron-based superconductors. This is particularly evident in the iron chalcogenide, FeSe, where it is currently unclear how the experimentally determined Fermi surface near the M point evolves from having two electron pockets in the tetragonal state, to exhibiting just a single electron pocket in the nematic state. This has posed a major theoretical challenge, which has become known as the missing electron pocket problem of FeSe, and is of central importance if we wish to uncover the secrets behind nematicity and superconductivity in the wider iron-based superconductors. Here, we review the recent experimental work uncovering this nematic Fermi surface of FeSe from both ARPES and STM measurements, as well as current theoretical attempts to explain this missing electron pocket of FeSe, with a particular focus on the emerging importance of incorporating the dxy orbital into theoretical descriptions of the nematic state. Furthermore, we will discuss the consequence this missing electron pocket has on the theoretical understanding of superconductivity in this system and present several remaining open questions and avenues for future research.

Open Access

Show Abstract ▼

Abstract: A threefold symmetric kagome lattice that has negative spin chirality can give a nonzero x-ray magnetic circular dichroism (XMCD) signal, despite the total spin moment amounting to zero. In order to explain this, I present here a rule for the rotational symmetry invariance of the XMCD signal. A necessary condition is the existence of an anisotropic XMCD signal for the local magnetic atom, which can arise from a spin anisotropy either in the ground state or the final state. The angular dependence of the XMCD as a function of the beam direction has an unusual behavior. The maximum dichroism is not aligned along the spin direction, but depends on the relative orientation of the spin with respect to the atomic orientation. Therefore, different geometries can result in the same angular dependence, and the spin direction can only be determined if the atomic orientation is known. The consequences for the x-ray magneto-optical sum rules are given. The integrated XMCD signals are proportional to the anisotropy in the orbital moment and the magnetic dipole term, where the isotropic spin moment drops out.

Show Abstract ▼

Abstract: Nonlinear optics, and particularly second harmonic generation (SHG), is increasingly used in many modern disciplines from material characterization in physical sciences to bioimaging in medicine and optical signal processing in information technology. We present a theoretical analysis yielding a strong estimate of the energy integrated SHG response. Compact spherical multipoles are provided for the corresponding natural and magnetic circular dichroic signals. Like symmetry requirements in time and space are traced in the amplitude for magnetic neutron scattering, which includes all axial and polar (Dirac) contributions. Our method of working in terms of,now standard, electronic multipoles and Racah algebra, with full implementation of discrete symmetries, could be of use in a variety of other probes of matter.