Radial integrals for the magnetic form factor of 5dtransition elements

The Magnetism of Nonstoichiometric Sr2Cr1+xRe1-xO6 (0 < x < 0.5) Double Perovskites

The effect of nonstoichiometry on the cation distribution, crystal structure, and magnetic properties of a series of Cr-rich Sr2Cr1+xRe1-xO6 samples has been investigated. The double perovskite structure is maintained over a wide solid solution range that extends from x = 0 to approximately x = 0.5. For most of the solid solution range, the Cr-rich octahedral site maintains a nearly constant occupancy, 87% Cr and 13% Re, that is comparable to prior studies of Sr2CrReO6, while Cr steadily replaces Re on the other octahedral site. As x approaches 0.5, long-range Cr/Re ordering drops precipitously. Analysis of X-ray powder diffraction peak shapes reveals antiphase boundaries, associated with Cr/Re ordering, the concentration of which increases steadily with increasing x. Neutron powder diffraction studies confirm antiferromagnetic coupling between antisite Cr3+ ions and Cr3+ ions that occupy the normal sites, leading to site-dependent ferrimagnetic ordering. Density functional theory calculations indicate that chromium maintains a +3 oxidation state across the series, while the oxidation state of rhenium increases with increasing x. Calculations are also used to explore the energies of competing magnetic ground states. Except for the most chromium-rich compositions (x ≈ 0.5), site-dependent ferrimagnetism is retained with only a modest reduction in TC. The saturation magnetization steadily decreases as the chromium content increases due to a combination of Cr/Re antisite disorder and antiphase boundaries.

Polar magnetism and chemical bond inα-RuCl3

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. Johnsonet alinfer a candidate for the magnetic structure (C_c2/m) from results gathered in an extensive set of experiments on an untwined sample ofα-RuCl₃(Johnsonet al2015Phys. Rev.B92235119). The proposed zigzag antiferromagnetic ground state of Ru ions does not respond to bulk magnetic probes, with optical rotation and all forms of dichroism prohibited by symmetry. Experimental techniques exploited by Johnsonet alincluded x-ray and magnetic neutron diffraction. Properties of the candidate magnetic structure not previously explored include polar magnetism that supports Ru Dirac multipoles, e.g. a ruthenium anapole that is also known as a toroidal dipole. In a general case, Dirac dipoles are capable of generating interactions between magnetic ions, as in an electrical Dzyaloshinskii-Moryia interaction (Kaplan and Mahanti 2011Phys. Rev.B83174432; Zhaoet al2021Nat. Mater.20341). Notably, the existence of Dirac quadrupoles in the pseudo-gap phases of cuprate superconductors YBCO and Hg1201 account for observed magnetic Bragg diffraction patterns. Dirac multipoles contribute to the diffraction of both x-rays and neutrons, and a stringent test of the magnetic structure C_c2/m awaits future experiments. From symmetry-informed calculations we show that, the magnetic candidate permits Bragg spots that arise solely from Dirac multipoles. Stringent tests of C_c2/m can also be accomplished by performing resonant x-ray diffraction with signal enhancement from the chlorineK-edge. X-ray absorption spectra published forα-RuCl₃possess a significant low-energy feature (Plumbet al2014Phys. Rev.B90041112(R)). Many experimental studies of other Cl-metal compounds concluded that identical features hallmark the chemical bond. Using a monoclinic C_c2/m structure, we predict the contribution to Bragg diffraction at the ClK-edge absorption. Specifically, the variation of intensity of Bragg spots with rotation of the sample about the reflection vector. The two principal topics of our studies, polar magnetism and the chemical bond in the black allotrope of ruthenium trichloride, are brought together in a minimal model of magnetic Ru ions in C_c2/m.

Ferro-octupolar Order and Low-Energy Excitations in d^{2} Double Perovskites of Osmium

Conflicting interpretations of experimental data preclude the understanding of the quantum magnetic state of spin-orbit coupled d^{2} double perovskites. Whether the ground state is a Janh-Teller-distorted order of quadrupoles or the hitherto elusive octupolar order remains debated. We resolve this uncertainty through direct calculations of all-rank intersite exchange interactions and inelastic neutron scattering cross section for the d^{2} double perovskite series Ba_{2}MOsO_{6} (M=Ca, Mg, Zn). Using advanced many-body first-principles methods, we show that the ground state is formed by ferro-ordered octupoles coupled by superexchange interactions within the ground-state E_{g} doublet. Computed ordering temperature of the single second-order phase transition is consistent with experimentally observed material-dependent trends. Minuscule distortions of the parent cubic structure are shown to qualitatively modify the structure of gaped magnetic excitations.

Magnetization Density Distribution of Sr_{2}IrO_{4}: Deviation from a Local j_{eff}=1/2 Picture

5d iridium oxides are of huge interest due to the potential for new quantum states driven by strong spin-orbit coupling. The strontium iridate Sr_{2}IrO_{4} is particularly in the spotlight because of the so-called j_{eff}=1/2 state consisting of a quantum superposition of the three local t_{2g} orbitals with, in its simplest version, nearly equal populations, which stabilizes an unconventional Mott insulating state. Here, we report an anisotropic and aspherical magnetization density distribution measured by polarized neutron diffraction in a magnetic field up to 5 T at 4 K, which strongly deviates from a local j_{eff}=1/2 picture even when distortion-induced deviations from the equal weights of the orbital populations are taken into account. Once reconstructed by the maximum entropy method and multipole expansion model refinement, the magnetization density shows four cross-shaped positive lobes along the crystallographic tetragonal axes with a large spatial extent, showing that the xy orbital contribution is dominant. The analogy to the superconducting copper oxide systems might then be weaker than commonly thought.

Octupolar versus Néel Order in Cubic 5d^{2} Double Perovskites

We report time-of-flight neutron spectroscopy and neutron and x-ray diffraction studies of the 5d^{2} double perovskite magnets, Ba_{2}MOsO_{6} (M=Zn,Mg,Ca). These materials host antiferromagnetically coupled 5d^{2} Os^{6+} ions decorating a face-centered cubic (fcc) lattice and are found to remain cubic down to the lowest temperatures. They all exhibit thermodynamic anomalies consistent with a single phase transition at a temperature T^{*}, and a gapped magnetic excitation spectrum with spectral weight concentrated at wave vectors typical of type-I antiferromagnetic orders. However, while muon spin resonance experiments show clear evidence for time-reversal symmetry breaking below T^{*}, we observe no corresponding magnetic Bragg scattering signal. These results are shown to be consistent with ferro-octupolar symmetry breaking below T^{*}, and are discussed in the context of other 5d double perovskite magnets and theories of exotic orders driven by multipolar interactions.

Spin-orbit coupling control of anisotropy, ground state and frustration in 5d(2) Sr2MgOsO6

The influence of spin-orbit coupling (SOC) on the physical properties of the 5d² system Sr₂MgOsO₆ is probed via a combination of magnetometry, specific heat measurements, elastic and inelastic neutron scattering, and density functional theory calculations. Although a significant degree of frustration is expected, we find that Sr₂MgOsO₆ orders in a type I antiferromagnetic structure at the remarkably high temperature of 108 K. The measurements presented allow for the first accurate quantification of the size of the magnetic moment in a 5d² system of 0.60(2) μ_B–a significantly reduced moment from the expected value for such a system. Furthermore, significant anisotropy is identified via a spin excitation gap, and we confirm by first principles calculations that SOC not only provides the magnetocrystalline anisotropy, but also plays a crucial role in determining both the ground state magnetic order and the size of the local moment in this compound. Through comparison to Sr₂ScOsO₆, it is demonstrated that SOC-induced anisotropy has the ability to relieve frustration in 5d² systems relative to their 5d³ counterparts, providing an explanation of the high T_N found in Sr₂MgOsO₆.

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). The construct encompasses the j(eff) = 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 Sr(2)IrO(4).

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. Unit-cell structure factors, suitable for x-ray Bragg diffraction enhanced by an electric dipole-electric dipole (E1-E1) event, reveal exactly which iridium multipoles are visible, e.g., a magnetic dipole parallel to the crystal c-axis (z-axis) and an electric quadrupole with yz-like symmetry in the specific case of CaIrO(3). Magnetic space-groups are assigned to Sr(2)IrO(4), Sr(3)Ir(2)O(7) and CaIrO(3), namely, P(I)cca, P(A)ban and Cm'cm', respectively, in the Belov-Neronova-Smirnova notation. The assignment for Sr(2)IrO(4) is possible because of our new high-resolution neutron diffraction data, gathered on a powder sample. In addition, the new data are used to show that the ordered magnetic moment of an Ir(4+) ion in Sr(2)IrO(4) does not exceed 0.29(4) μ(B). Na(2)IrO(3) has two candidate magnetic space-groups that are not resolved with currently available resonant x-ray data.