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Related Concept Videos

Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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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.
656
Atomic Nuclei: Magnetic Resonance01:05

Atomic Nuclei: Magnetic Resonance

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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...
661
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

958
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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NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

699
When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

303
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
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In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study.

Rustem Khasanov1, Aline Ramires2, Vadim Grinenko3,4

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Measurements of the magnetic penetration depth in Sr_{2}RuO_{4} reveal nodes in the superconducting gap. The Volovik effect and temperature dependence indicate complex gap harmonics are necessary for accurate modeling.

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Area of Science:

  • Condensed Matter Physics
  • Superconductivity Research
  • Materials Science

Background:

  • Sr_{2}RuO_{4} is a layered perovskite exhibiting unconventional superconductivity.
  • Understanding the nature of its superconducting gap is crucial for theoretical models.

Purpose of the Study:

  • To investigate the superconducting gap structure of Sr_{2}RuO_{4} through precise measurements.
  • To determine the temperature and magnetic field dependence of the magnetic penetration depth.

Main Methods:

  • Muon-spin rotation-relaxation (μSR) technique was employed.
  • Measurements were conducted on single crystals of Sr_{2}RuO_{4} down to 0.015 K.

Main Results:

  • The in-plane magnetic penetration depth (λ_{ab}) showed a linear dependence of λ_{ab}^{-2} on temperature (T≲0.7 K), suggesting gap nodes.
  • The Volovik effect was observed, further supporting the presence of nodes.
  • The experimental λ_{ab} at zero field and temperature (124(3) nm) aligns with theoretical calculations.

Conclusions:

  • The superconducting gap in Sr_{2}RuO_{4} possesses nodes.
  • A simple nodal gap model is insufficient; higher angular harmonics are required to explain the observed temperature dependence of λ_{ab}^{-2}.
  • These findings provide critical insights into the pairing symmetry of Sr_{2}RuO_{4}.