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Related Concept Videos

Diamagnetism01:26

Diamagnetism

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.
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.
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...
Paramagnetism01:30

Paramagnetism

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...
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

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 energy to a nearby...
Magnetic Susceptibility and Permeability01:31

Magnetic Susceptibility and Permeability

In linear magnetic materials, like paramagnets and diamagnets, magnetization is proportional to the magnetic field intensity. The constant of proportionality, a dimensionless number, is called magnetic susceptibility. The value of the susceptibility depends on the type of material.
When diamagnetic materials are placed under an external magnetic field, the moments opposite to the field are induced. Hence, the susceptibility for diamagnets has a minimal negative value of 10-5–10-6. Since...
Ferromagnetism01:31

Ferromagnetism

Materials like iron, nickel, and cobalt consist of magnetic domains, within which the magnetic dipoles are arranged parallel to each other. The magnetic dipoles are rigidly aligned in the same direction within a domain by quantum mechanical coupling among the atoms. This coupling is so strong that even thermal agitation at room temperature cannot break it. The result is that each domain has a net dipole moment. However, some materials have weaker coupling, and are ferromagnetic at lower...

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Updated: May 31, 2026

Paramagnetic Relaxation Enhancement for Detecting and Characterizing Self-Associations of Intrinsically Disordered Proteins
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Paramagnetic Relaxation Enhancement for Detecting and Characterizing Self-Associations of Intrinsically Disordered Proteins

Published on: September 23, 2021

Relaxation properties in classical diamagnetism.

A Carati1, F Benfenati, L Galgani

  • 1Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, I-20133 Milano, Italy.

Chaos (Woodbury, N.Y.)
|July 5, 2011
PubMed
Summary
This summary is machine-generated.

Classical statistical mechanics predicts no magnetization at equilibrium. This study numerically investigates electron systems in magnetic fields, finding relaxation to equilibrium is not always guaranteed, with potential for metastable diamagnetic states.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Classical statistical mechanics dictates no equilibrium magnetization in static magnetic fields.
  • Magnetization arises in non-equilibrium states, such as those induced by Foucault currents.
  • Bohr hypothesized rapid relaxation back to equilibrium after non-equilibrium states are established.

Purpose of the Study:

  • To numerically investigate the relaxation dynamics of electron systems in a modified Bohr model.
  • To determine if equilibrium is always attained within typical microscopic timescales.
  • To explore the conditions leading to equilibrium versus metastable states.

Main Methods:

  • Numerical simulation of a modified Bohr model.
  • Mathematical equivalence to a billiard system with obstacles in an adiabatically switched magnetic field.
  • Analysis of relaxation processes under varying parameter values.

Main Results:

  • Equilibrium is not always reached within typical microscopic timescales.
  • System relaxation depends on parameter values.
  • Two distinct relaxation pathways observed: return to equilibrium or stabilization in a diamagnetic state.

Conclusions:

  • The assumption of rapid relaxation to equilibrium in magnetic fields is not universally valid.
  • Metastable diamagnetic states can persist in modified Bohr models.
  • The study highlights complex relaxation behaviors analogous to the Fermi Pasta Ulam problem.