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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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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...
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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 Constant: Overview01:08

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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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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.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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Unconventional Discontinuous Transitions in Isospin Systems.

Zachary M Raines1, Leonid I Glazman2, Andrey V Chubukov1

  • 1School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, <a href="https://ror.org/017zqws13">University of Minnesota</a>, Minneapolis, Minnesota 55455, USA.

Physical Review Letters
|October 18, 2024
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Summary
This summary is machine-generated.

Two-dimensional fermions with specific energy-momentum dispersions exhibit a first-order Stoner transition to a spin-polarized state. Further analysis reveals instabilities leading to fractional-metal states in related systems.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Materials science

Background:

  • Two-dimensional (2D) electron systems are crucial for understanding novel quantum phenomena.
  • The Stoner transition describes the onset of ferromagnetism in metals due to spin-polarization.
  • Electron band structure and dispersion relations significantly influence electronic properties.

Purpose of the Study:

  • To investigate the nature of the Stoner transition in 2D fermions with specific dispersion relations (k^2, k^4).
  • To explore instabilities and potential fractional-metal states in generalized 2D systems (k^{2α}) with spin and valley isospin.
  • To analyze the behavior of spin susceptibility near critical points and transitions.

Main Methods:

  • Theoretical analysis of two-dimensional fermion systems.
  • Calculation of electronic band structures and dispersion relations.
  • Investigation of spin susceptibility and phase transitions.

Main Results:

  • First-order Stoner transitions to fully spin-polarized states were identified for dispersions k^2 and k^4, even with diverging spin susceptibility.
  • A cascade of instabilities into fractional-metal states, characterized by depleted electron bands, was found for generalized dispersions k^{2α}.
  • Narrow intermediate ranges with partially depleted bands exist for specific values of α (α<1 or α>2).
  • Spin susceptibility increases significantly near these transitions.

Conclusions:

  • The Stoner transition can be first-order in 2D systems, contrary to some expectations based on diverging susceptibility.
  • Fractional-metal states are a likely outcome in tunable 2D electronic systems with specific band structures.
  • These findings have implications for understanding and designing materials like biased bi- and trilayer graphene and moiré systems.