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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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...
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved in...
Atomic Nuclei: Magnetic Resonance01:05

Atomic Nuclei: Magnetic Resonance

The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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. This...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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 have a...
Quantum Numbers02:43

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

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Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials
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Published on: January 21, 2016

Quantum spin Hall effect and enhanced magnetic response by spin-orbit coupling.

Shuichi Murakami1

  • 1Department of Applied Physics, University of Tokyo, Hongo, Tokyo 113-8656, Japan. murakami@appi.t.u-tokyo.ac.jp

Physical Review Letters
|February 7, 2007
PubMed
Summary

Researchers found a link between spin-Hall conductivity and magnetic susceptibility in insulators. This discovery guides the search for materials exhibiting the quantum spin-Hall effect, identifying 2D bismuth as a promising candidate.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science

Background:

  • The spin-Hall effect involves generating a transverse spin current in response to an applied electric field.
  • Understanding the spin-Hall conductivity in insulators is crucial for exploring topological electronic phases.

Purpose of the Study:

  • To establish a relationship between spin-Hall conductivity and magnetic susceptibility in insulators.
  • To utilize this relationship to identify real materials exhibiting the quantum spin-Hall effect.
  • To theoretically predict and propose experimental verification for the quantum spin-Hall effect in two-dimensional bismuth.

Main Methods:

  • Theoretical calculation of spin-Hall conductivity.
  • Analysis of magnetic susceptibility to quantify spin-orbit coupling strength.
  • Computation of helical edge states.
  • Determination of the Z2 topological invariant.

Main Results:

  • A direct relationship was established between spin-Hall conductivity and magnetic susceptibility in insulators.
  • Two-dimensional bismuth was theoretically predicted to exhibit the quantum spin-Hall effect.
  • Helical edge states and a nontrivial Z2 topological number were calculated for 2D bismuth.

Conclusions:

  • The established relationship provides a new guiding principle for discovering quantum spin-Hall materials.
  • Two-dimensional bismuth is a promising material for realizing the quantum spin-Hall effect.
  • Proposed experiments can verify the theoretical predictions for 2D bismuth.