Ordered magnetic charge created by Dirac multipoles that are magnetic and polar is examined. It has previously been revealed in the pseudo-gap phase of high-Tc materials by use of the Kerr effect and magnetic neutron Bragg diffraction. There are several forms of the polar operator for magnetic neutron scattering built from spin and electric dipole operators of unpaired electrons. 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. Most reported expressions and results have universal value, because they are not specific to ceramic superconductors. To illustrate this aspect of our work we simulate neutron diffraction from a magnetically ordered iridate (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 publi…
A recent polarized neutron diffraction experiment on the 5d2 rhenium double perovskite Ba2YReO6 held at a low temperature uncovered weak magnetic diffraction peaks. Data analysis inferred a significantly reduced Re dipole moment, and long-range order compatible with an antiferromagnet, non-collinear motif. To interpret the experimental findings, we present a model wavefunction for Re ions derived from the crystal field potential, Coulomb interaction, and spin-orbit coupling that fully respects the symmetry of the low-temperature ordered state. It is used to calculate in analytic form all multi…
Compulsory Dirac multipoles in the bilayer perovskite Ca3Ru2O7 are absent in published analyses of experimental data. In a first step at correcting knowledge of the magnetic structure, we have analysed existing Bragg diffraction patterns gathered on samples held well below the Néel temperature at which A-type antiferromagnetic order of axial dipoles spontaneously develops. Patterns were gathered with neutrons, and linearly polarized x-rays tuned in energy to a ruthenium atomic resonance. Neutron diffraction data contains solid evidence of Dirac dipoles (anapoles or toroidal moments). No such c…
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 crystal 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 e…
Nonlinear optics, and particularly second harmonic generation (SHG), is increasingly used in many modern disciplines from material characterization in physical sciences to bio-imaging in medicine and optical signal processing in information technology. We present a theoretical analysis providing a strong estimate for the energy-integrated SHG response. Requirements of symmetry in time and space are fully respected in the calculation, and estimates of natural and magnetic circular dichroic signals are superior to previous ones. Like symmetry requirements are traced in the amplitude for magnetic…
Cerium electronic multipoles in trigonal symmetry viewed in magnetic neutron diffraction are investigated. Analytic expressions for all the magnetic multipoles, and radial integrals calculated with an established atomic code, are used to scrutinize a recent claim to have observed an octupole-ice configuration in a powder sample of pyrochlore Ce2Sn2O7. Three equally plausible suites of multipoles belonging to uncorrelated cerium ions give equally satisfactory accounts of the available diffraction pattern. Our multipoles are suitable for future experiments using Bragg diffraction from a compound…
A theory of neutron scattering by magnetic materials is reviewed with emphasis on the use of electronic multipoles that have universal appeal, because they are amenable to calculation and appear in theories of many other experimental techniques. The conventional theory of magnetic neutron scattering, which dates back to Schwinger (1937) and Trammell (1953), yields an approximation for the scattering amplitude in terms of magnetic dipoles formed with the spin (S) and orbital angular momentum (L) of valence electrons. The so-called dipole-approximation has been widely adopted by researchers duri…
Structural and magnetic transitions in a double perovskite hosting 5d1 Re ions are discussed on the basis of recently published high-resolution x-ray diffraction patterns [D. Hirai, et al., Phys. Rev. Res. 2, 022063(R) (2020)]. A reported structural transition below room temperature, from cubic to tetragonal symmetry, appears not to be driven by T2g-type quadrupoles, as suggested. A magnetic motif at lower temperature is shown to be composed of two order parameters, associated with propagation vectors k = (0, 0, 1) and k = (0, 0, 0). Findings from our studies, for structural and magnetic prope…
An ancient Hamiltonian of electrons with entangled spin and orbital degrees of freedom is re-examined as a model of magneto-electric multipoles. 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 magneto-electric multipoles almost perfectly accord with those inferred from an analysis of magnetic neutron diffraction data on a ceramic superconductor (YBCO) in the pseudo-gap phase. Nigh on perfection between Stone's model and inferred magneto-electric multipoles is achieved by addition to the origina…
The sesquioxide, Ce$_{2}$O$_{3}$, has been a material of intense interest in recent years due to reports of an anomalous giant magnetodielectric effect and emergent mixed crystal field-phonon (vibronic) excitations below a putative antiferromagnetic transition at T$_{N}$ = 6.2 K. The claim of long-range magnetic order in this material is based on heat capacity and temperature-dependent susceptibility measurements; however, multiple neutron diffraction studies have been unable to distinguish any magnetic Bragg peaks. In this article, we present the results of a comprehensive investigation of th…
Magnetic diffraction of polarized neutrons by the cubic Laves compound UAl2 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 a…
The Bragg diffraction of neutrons and x-rays are well-suited to the task of determining the distribution of magnetization in crystals. Applications of the two techniques proceed by contrasting observed intensities with intensities calculated with a specific model, and changing the model as need be to achieve satisfactory agreement. An all-in-all-out (AIAO) magnetic configuration of magnetic dipoles on a cubic face-centred lattice with networks of corner-sharing tetrahedra is often mentioned in the context of pyrochlore oxides, for example, but the corresponding neutron and x-ray diffraction pa…
Ruthenium trichloride is the subject of many recent experimental and theoretical studies. Johnson et al. infer a candidate for the magnetic structure (Cc2/m) from results gathered in an extensive set of experiments on an untwined sample of alpha-RuCl3 [R. D. Johnson et al., Phys. Rev. B 92, 235119 (2015)]. The proposed zigzag antiferromagnetic ground state of Ru ions does not respond to bulk magnetic probes. Properties of the candidate magnetic structure not previously explored include polar magnetism that supports Ru Dirac multipoles, e.g., a ruthenium anapole. In a general case, Dirac dipole…
The magnetization-density distribution in the metallic ferromagnet SrRuO$_3$ was studied by means of polarized neutron diffraction. The analyzes by multipole refinements and by the maximum entropy method consistently reveal a strong polarization of all oxygen sites carrying 30\% of the total magnetization. The spin-density distribution on the Ru site exhibits a nearly cubic shape in agreement with an almost equal occupation of $t_{2g}$ orbitals and $pd$ hybridization. The experimental analysis is well reproduced by density functional calculations. There is no qualitative change in the magnetiz…
Real-space manifestation of ferroic multipoles in altermagnetic MnF$_2$
European Spallation Source, ERIC（欧洲散裂源）；Laboratoire Léon Brillouin, CEA, CNRS（勒内·布朗利实验室）；Institut Laue-Langevin（朗之万研究所）；Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay（巴黎综合理工学院固体物理实验室）；Quantum Innovation Centre (Q.InC), (A*STAR)（量子创新中心）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Physics, University of Windsor（温莎大学物理系）
Magnetic ordering phenomena in CexPr1-xB6 solid solutions have been studied using both powder and single-crystal neutron diffraction. A variety of magnetic structures are observed depending on temperature and Ce concentration. Over a broad composition range (x $\le$ 0.7), Pr-Pr interactions play a dominant role, giving rise to incommensurate structures with wave vectors of the form k{IC1}=(1/4-delta, 1/4, 1/2) or k{IC2}=(1/4-delta, 1/4-delta, 1/2). The crossover to a CeB6-like regime takes place near x = 0.7-0.8. For the latter composition, the antiferroquadrupolar phase transition observed in…
Soft resonant x-ray Bragg diffraction (SRXD) at the Ho M$_{4,5}$ edges has been used to study Ho $4f$ multipoles in the combined magnetic and orbitally ordered phase of HoB$_2$C$_2$. A full description of the energy dependence for both $σ$ and $π$ incident x-rays at two different azimuthal angles, as well as the ratio $I_σ/I_π$ as a function of azimuthal angle for a selection of energies, allows a determination of the higher order multipole moments of rank 1 (dipole) to 6 (hexacontatetrapole). The Ho 4f multipole moments have been estimated, indicating a dominant hexadecapole (rank 4) order wi…
Mag2Pol is a graphical user interface program which is devoted to the analysis of data from polarized neutron diffractometers with spherical polarization analysis. Nuclear and magnetic structure models can be introduced using space group symbols and individual symmetry operators, respectively, and viewed in an OpenGL widget. The program calculates nuclear/magnetic structure factors, flipping ratios and polarization matrices for magnetic Bragg reflections taking into account structural twins and magnetic domains. Spherical neutron polarimetry data can be analyzed by refining a magnetic structur…
KV3Sb5 has recently attracted a considerable attention, due to its low temperature superconducting properties, which are heralded by a charge density wave. The apparent presence of a very weak magnetism does not result in long range ordering. We propose a model compatible with a detectable internal magnetic field with no evidence of magnetic long-range order. It invokes higher order terms in the vanadium magnetization density compatible with the presence of a "hidden order" of Dirac (polar) multipoles. The Dirac dipole, known as an anapole or toroidal dipole, is one of a family of electronic m…
We have performed a single crystal neutron scattering experiment on Ce0.7La0.3B6 to investigate the order parameter of phase IV microscopically. Below the phase transition temperature 1.5 K of phase IV, weak but distinct superlattice reflections at the scattering vector (h/2,h/2,l/2) (h, l = odd number) have been observed by neutron scattering for the first time. The intensity of the superlattice reflections is stronger for high scattering vectors, which is quite different from the usual magnetic form factor of magnetic dipoles. This result directly evidences that the order parameter of phase …
Field-dependent magnetic structure of a layered Dirac material EuMnBi$_2$ was investigated in detail by the single crystal neutron diffraction and the resonant x-ray magnetic diffraction techniques. On the basis of the reflection conditions in the antiferromagnetic phase at zero field, the Eu moments were found to be ordered ferromagnetically within the $ab$ plane and stacked antiferromagnetically along the $c$ axis in the sequence of up-up-down-down. Upon the spin-flop transition under the magnetic field parallel to the $c$ axis, the Eu moments are reoriented from the $c$ to the $a$ or $b$ di…
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 Sm0.976Gd0.024Al2 with a diamond-type structure presents Dirac multipoles at basis-forbidden reflections that include the standard (2, 2, 2) reflection. Magnetic amplitudes measured at four such reflections are in full accord with a structure factor calculated from the appropriate magnetic space group.
The coexistence of the strongly correlated 3$d$ transition metal (TM) atom and the strong spin-orbit coupling (SOC) of 5$d$ TM atom is potential to host exotic physical phenomena. In the present work, we have studied the magnetism resulting from such a coexistence in La$_2$CoIrO$_6$ (LCIO), a representative of bulk 3$d$-5$d$ double perovskites. In order to gain further insight into the effect of Co-$d$ states on the Ir-$d$ states, comparisons are carried out with the isostructural La$_2$ZnIrO$_6$, where nonmagnetic Zn atom replaces the Co atom. An in-depth analysis of the magnetic states in th…
