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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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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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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Spin–Spin Coupling: One-Bond Coupling01:17

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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The Pauli Exclusion Principle03:06

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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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Semiclassical magnetotransport in strongly spin-orbit coupled Rashba two-dimensional electron systems.

Cong Xiao1, Dingping Li

  • 1School of Physics, Peking University, Beijing 100871, People's Republic of China. Collaborative Innovation Center of Quantum Matter, Beijing, 100871, People's Republic of China.

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This study reveals distinct magnetotransport behaviors in spin-orbit coupled systems. Findings show unique Hall coefficients and magnetoresistance below the band crossing point, aiding experimental identification.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Phenomena

Background:

  • Investigating magnetoelectric and magnetothermoelectric transport in advanced materials.
  • Understanding electron behavior in strongly spin-orbit coupled Rashba two-dimensional electron systems.

Purpose of the Study:

  • To explore semiclassical transport phenomena in Rashba 2DECs under magnetic fields.
  • To analyze the impact of Fermi energy relative to the band crossing point on transport properties.

Main Methods:

  • Self-consistent solution of the linearized Boltzmann equation.
  • Analysis of semiclassical transport under weak magnetic fields and impurity scattering.

Main Results:

  • Observed nonmonotonic Hall coefficient dependence on electron density below the band crossing point (BCP).
  • Identified vanishing magnetoresistance (MR) and Nernst coefficient above the BCP.
  • Discovered emergence of non-zero MR and enhanced Nernst coefficient below the BCP, both nonmonotonic with Fermi energy.

Conclusions:

  • Demonstrated distinct semiclassical magnetotransport behaviors on either side of the BCP.
  • Proposed these transport differences as experimental markers for band valley regimes and Fermi surface topology changes.