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Atomic Nuclei: Nuclear Magnetic Moment00:59

Atomic Nuclei: Nuclear Magnetic Moment

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All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
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Consider two charges of equal magnitude but opposite signs. If they cannot be separated by an external electric field, the system is called a permanent dipole. For example, the water molecule is a dipole, making it a good solvent.
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The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Atomic Nuclei: Nuclear Spin State Overview01:03

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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Studying Soft-matter and Biological Systems over a Wide Length-scale from Nanometer and Micrometer Sizes at the Small-angle Neutron Diffractometer KWS-2
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Neutron scattering by Dirac multipoles.

S W Lovesey1,2, D D Khalyavin1

  • 1ISIS Facility, STFC, Chilton, Oxfordshire OX11 0QX, United Kingdom.

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This study reveals Dirac quadrupoles in high-temperature superconductors using magnetic neutron diffraction. These findings offer universal insights into magnetic scattering by polar multipoles in exotic materials.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Magnetism

Background:

  • Conventional concepts of material properties are challenged by exotic magnetic phenomena.
  • High-temperature superconductors exhibit complex electronic phases, such as the pseudo-gap phase.

Purpose of the Study:

  • To examine scattering by magnetic charges formed by Dirac multipoles (magnetic and polar).
  • To reveal the order parameter in the pseudo-gap phase of ceramic, high-temperature superconductors.
  • To establish universal magnetic scattering amplitudes for polar multipoles.

Main Methods:

  • Kerr effect measurements.
  • Magnetic neutron Bragg diffraction.
  • Analysis of neutron inelastic scattering and RIXS (Resonant Inelastic X-ray Scattering) experiments.

Main Results:

  • An order parameter composed of Dirac quadrupoles was identified in the pseudo-gap phase of ceramic, high-temperature superconductors.
  • Construction of Dirac quadrupoles from Cu ions in Hg1201 was illustrated.
  • Universal magnetic scattering amplitudes for polar multipoles were reported, applicable beyond ceramic superconductors.

Conclusions:

  • Dirac quadrupoles represent a significant order parameter in high-temperature superconductors.
  • The study provides a universal framework for understanding magnetic scattering by polar multipoles.
  • Re-evaluation of published diffraction data for materials like Sr2IrO4 is suggested.