Application of quantum mechanics in physics and chemistry often entails manipulation and evaluation of sums and products of coupling coefficients for the theory of angular momentum. Challenges ...encountered in such work can be tamed by graphical techniques that provide both the insight and analytical power. The book is the first step-by-step exposition of a graphical method grounded in established work. Copious exercises recover standard results but demonstrate the power to go beyond.
The few electrons in valence states of a material participate in many of its physical properties, including both structural and transport properties. In the diffraction of X-rays, or neutrons, ...valence electrons can lead to weak Bragg reflections that are extremely sensitive signatures of their charge and magnetic degrees of freedom. In this regard, diffraction instruments supplied with X-rays from a synchrotron source are particularly useful because the brightness, tuneability and polarization of the X-rays are all helpful in making valuable observations. The data obtained from Bragg diffraction can be analyzed on the basis of an atomic model, which has the virtue that it can be used as a common platform for the analysis of X-ray and neutron diffraction and, in addition, the analysis of observations made with X-ray absorption, NMR, EPR, muon and Mössbauer spectroscopies. We present the salient features for the calculation of structure factors based on an atomic model and applied to the analysis of Bragg diffraction by non-magnetic and magnetic materials, with an emphasis on resonant X-ray Bragg diffraction. The presentation contains a new treatment of parity-odd events found in the mixed electric dipole–electric quadrupole channel of scattering. In addition we discuss the complementary observation of dichroic signals, including natural circular and magnetochiral dichroism.
The survey of available analytical tools is complemented by a series of worked examples demonstrating the application of the formalism to different materials with different crystal structures and resonant ions: dysprosium borocarbide (
DyB
2
C
2
), vanadium sesquioxide
(
V
2
O
3
)
, gadolinium tetraboride (
GdB
4
), chromium sesquioxide (
Cr
2
O
3
), haematite and perovskite-type manganites.
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 Sm_{0.976}Gd_{0.024}Al_{2} 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.
Observation of Orbital Currents in CuO Scagnoli, V.; Staub, U.; Bodenthin, Y. ...
Science (American Association for the Advancement of Science),
05/2011, Letnik:
332, Številka:
6030
Journal Article
Recenzirano
Orbital currents are proposed to be the order parameter of the pseudo-gap phase of cuprate high-temperature superconductors. We used resonant x-ray diffraction to observe orbital currents in a ...copper-oxygen plaquette, the basic building block of cuprate superconductors. The confirmation of the existence of orbital currents is an important step toward the understanding of the cuprates as well as materials lacking inversion symmetry, such as magnetically induced multiferroics. Although observed in the antiferromagnetic state of cupric oxide, we show that orbital currents can occur even in the absence of long-range magnetic moment ordering.
A theoretical study of Bragg diffraction by an enantiomorphic pair of structures should apply to patterns gathered on β-Mn using resonance-enhanced x-ray diffraction. The chiral polymorph of ...manganese, and structurally related compounds, will be more convenient than trigonal crystals of low quartz, tellurium, and berlinite used in previous structural studies of this type, because cubic symmetry removes some complications of correction for absorption and macroscopic birefringence. Intensity of a Bragg spot engaged by circular polarization in the primary beam of photons Υ (h, k, l) is proposed as a chiral signature of the illuminated material. The partial intensity requires a knowledge of scattering amplitudes in all four channels of polarization, which are reported as functions of an azimuthal angle (rotation of the crystal about the axis of the reflection vector). Unlike trigonal chiral crystals, Υ (0, 0, l) = 0 for β-Mn and it is (h, k, 0), and symmetry-related Bragg spots, that epitomize structural chirality. Specifically, reflection vectors (h, k, 0) with odd Miller indices and the chiral axis of β-Mn mesh in terms of helicity, with the corresponding Υ(h, k, 0) equal in magnitude and opposite in sign for partners in the enantiomorphic pair. Dependence of Υ(h, k, 0) on the azimuthal angle does not mirror the dyad or tetrad axes of rotation symmetry in the cubic crystal structure.
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 (pseudospin) model. Specifically, spin ...and space know inextricable knots which bind each to the other in the iridate. The diffraction property studied in the paper 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 dyadic correlations of the anapole and position operators, and hallmarked in the diffraction amplitude by axial atomic multipoles with an even rank.
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.
Cubic double perovskites that host heavy ions with total angular momentum J = 2 can exhibit a singular magnetic state epitomized by a lone octupole and bulk ferro-type magnetism. It exists in the ...Chen-Balents Hamiltonian with a quadrupole interaction and competing exchange forces between the ions. Our symmetry inspired analysis mirrors the Dzyaloshinskii-Man'ko theory of latent antiferromagnetic ordering, and a 3k collinear structure. Experimental tests for the singular state include neutron or resonant x-ray Bragg diffraction.
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