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Inertia Tensor01:24

Inertia Tensor

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The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
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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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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.
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Atomic Nuclei: Magnetic Resonance01:05

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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...
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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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NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

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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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Engineering spin-wave spectrum via the magnetization inertia tensor.

Subhadip Ghosh1, Darpa Narayan Narayan Basu1, Ritwik Mondal1

  • 1Department of Physics, Indian Institute of Technology (Indian School of Mines) Dhanbad, IN-826004 Dhanbad, India.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|December 9, 2025
PubMed
Summary
This summary is machine-generated.

Magnetic inertia in ferromagnets creates unique spin-wave bands. This research reveals how magnetic inertia controls magnonic band structures and enables nonreciprocal magnon transport for spintronics.

Keywords:
inertial magnetization dynamicsmagnonsnonreciprocal transportspin torques

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Area of Science:

  • Condensed Matter Physics
  • Spintronics
  • Magnonics

Background:

  • Magnetic inertial dynamics observed in two-sublattice ferromagnets.
  • Previous studies focused on limited aspects of magnetic inertia.

Purpose of the Study:

  • Investigate spin-wave spectrum incorporating the complete magnetic inertia tensor.
  • Analyze contributions of magnetic inertia to magnonic band structures.
  • Explore nonreciprocal magnon transport mechanisms.

Main Methods:

  • Decomposition of the magnetic inertia tensor into symmetric and antisymmetric components.
  • Application of linear spin-wave theory.
  • Analysis of magnonic band structures and nonreciprocity.

Main Results:

  • Identified isotropic, anisotropic, and chiral contributions to magnetic inertia.
  • Spin-wave spectrum comprises two precessional and two inertial magnon bands.
  • Upper precessional and lower inertial bands intersect within the Brillouin zone.
  • Chiral and cross-sublattice inertia components tune magnonic bands.
  • Inertial spin-wave spectrum exhibits nonreciprocity, even without Dzyaloshinskii-Moriya interaction.

Conclusions:

  • Magnetic inertia is a crucial factor in determining magnonic band structures.
  • Magnetic inertia offers a novel route for engineering nonreciprocal magnon transport.
  • This work paves the way for ultrafast spintronic device functionalities.