Field-induced magnetic charge in a cubic Laves compound UAl₂

Abstract

Magnetic diffraction of polarized neutrons by the cubic Laves compound UAl 2 in a magnetic field has unveiled weak Bragg spots that are nominally forbidden. On the one hand, they can be viewed as magnetic analogues of the basis-forbidden (2, 2, 2) reflection in diamond-type structures that has been painstakingly and frequently investigated over almost a century. Alternatively, the pattern of weak intensities can be assigned to Dirac multipoles imbedded in field-induced magnetic charge. To this end, a published diffraction pattern is successfully confronted with intensities calculated from the appropriate magnetic spacegroup (Imm′a′) that includes Dirac dipoles (anapoles) to describe the basis-forbidden magnetic reflections (H o + K o + L o = 4n + 2), and conventional (axial) dipole and octupole multipoles to describe basis-allowed magnetic reflections.

Multipole orders and Bragg diffraction patterns for the chain ferrate Na2FeSe2

“…Rakhecha et al [30] reported weak basis-forbidden intensities 134425-6 and confirmed their origin as magnetic by use of neutron polarization analysis. A successful interpretation of the entire diffraction pattern with a correct magnetic space group followed almost four decades later, and it showed that (2, 2, 2)-type reflections are due to anapoles beyond reasonable doubt [31].…”

Electronic multipoles in second harmonic generation and neutron scattering

“…The scalar operator does not contribute to Q⊥, i.e., the electronic Dirac monopole is not visible in neutron scattering, although it is visible in resonance enhance x-ray scattering [41]. Next in line, the spin anapole contribution {κβ εαβγ (s × n)γ} = [κ κ κ κ × (s × n)]α has been unambiguously detected in diffraction by two compounds with the C15 cubic Laves structure [36,37]. Lastly, the traceless Dirac quadrupole accounts for Bragg diffraction patterns collected on pseudo-gap phases of Hg1201 and YBCO [38].…”

“…A direct observation of neutron diffraction by anapoles (Dirac dipoles) [34,35] and compelling evidence from neutron Bragg diffraction patterns that ceramic superconductors support Dirac (magnetoelectric) quadrupoles [36] are reasons enough to revisit theories of neutron scattering. The onset of magnetic Bragg diffraction in ceramic superconductors occurs at temperatures associated with the appearance of the pseudogap state as determined by probes such as angle-resolved photoemission spectroscopy, NMR, and optical conductivity [37].…”