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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...
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Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
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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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Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the moments opposite to the field are induced. Such materials are called diamagnets. Diamagnetism is the response of the diamagnets when placed in an external magnetic field.
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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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Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the...
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Exceptional spectrum and dynamic magnetization.

Y B Shi1, K L Zhang1, Z Song1

  • 1School of Physics, Nankai University, Tianjin 300071, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|October 3, 2022
PubMed
Summary
This summary is machine-generated.

Introducing non-Hermitian terms into many-body systems can induce macroscopic effects via exceptional points. This study demonstrates systems with unidirectional couplings exhibiting exceptional dynamics and novel macroscopic phenomena, like dynamic magnetization reversal.

Keywords:
dynamic magnetizationexceptional spectrumhigh-order exceptional pointmacroscopic quantum phenomenanon-Hermitian Hamiltonian

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Non-Hermitian Systems

Background:

  • Macroscopic phenomena in many-body systems are typically governed by Hermitian Hamiltonians.
  • Non-Hermitian terms can lead to unique spectral degeneracies known as exceptional points.
  • Exceptional points signify a breakdown of standard eigenstate behavior.

Purpose of the Study:

  • To propose and analyze a class of many-body systems exhibiting exceptional points.
  • To demonstrate that these systems support macroscopic phenomena not found in Hermitian systems.
  • To investigate the application of exceptional dynamics to control magnetization in itinerant electron systems.

Main Methods:

  • Analytical derivation of single-particle eigenstate behavior in systems with unidirectional couplings.
  • Theoretical analysis of macroscopic phenomena arising from exceptional dynamics.
  • Numerical simulations of dynamic magnetization processes in itinerant electron systems under complex fields.

Main Results:

  • Identical Hermitian sub-lattices with unidirectional couplings exhibit simultaneous pairwise eigenstate coalescence.
  • All initial states follow exceptional dynamics, leading to novel macroscopic effects.
  • Dynamic magnetization reversal of a ferromagnetic state is achieved via high-order exceptional points, a feat impossible with Hermitian terms.

Conclusions:

  • Unidirectional couplings in Hermitian sub-lattice systems are sufficient to induce exceptional points and dynamics.
  • Exceptional dynamics offer a new pathway to control macroscopic properties, such as magnetization.
  • The observed dynamic magnetization processes show universal behavior across various lattice configurations and impurity distributions.