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Ferromagnetism01:31

Ferromagnetism

3.0K
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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Paramagnetism01:30

Paramagnetism

3.0K
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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Diamagnetism01:26

Diamagnetism

2.9K
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....
2.9K
Magnetic Susceptibility and Permeability01:31

Magnetic Susceptibility and Permeability

2.3K
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...
2.3K
Colors and Magnetism03:02

Colors and Magnetism

14.0K
Color in Coordination Complexes
When atoms or molecules absorb light at the proper frequency, their electrons are excited to higher-energy orbitals. For many main group atoms and molecules, the absorbed photons are in the ultraviolet range of the electromagnetic spectrum, which cannot be detected by the human eye. For coordination compounds, the energy difference between the d orbitals often allows photons in the visible range to be absorbed and emitted, which is seen as colors by the human...
14.0K
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

1.2K
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.
1.2K

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Updated: Jan 18, 2026

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Energy minima and ordering in ferromagnets with static randomness.

Dmitry A Garanin1

  • 1Physics Department, Herbert H. Lehman College and Graduate School, The City University of New York, 250 Bedford Park Boulevard West, Bronx, NY 10468-1589, United States of America.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|September 10, 2025
PubMed
Summary

Simulations reveal that 3D random-anisotropy (RA) models magnetically order with decreasing temperature, challenging the Imry-Ma argument. However, 3D random-field (RF) models freeze into a spin-glass state, preventing magnetic ordering due to pinned singularities.

Keywords:
2D3DImry–Madisorderingorderingrandom anisotropyrandom field

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Computational physics

Background:

  • The Imry-Ma argument predicts that random-field (RF) and random-anisotropy (RA) systems should not exhibit long-range magnetic order at finite dimensions.
  • Understanding the magnetic ordering behavior of disordered systems is crucial for materials science and condensed matter physics.

Purpose of the Study:

  • To investigate the magnetic ordering of 2D and 3D random-field and random-anisotropy models.
  • To challenge or confirm theoretical predictions, specifically the Imry-Ma argument, through large-scale simulations.

Main Methods:

  • Energy minimization at T=0 Kelvin.
  • Monte Carlo simulations at temperatures above 0 Kelvin.
  • Modeling of up to 150 million classical spins in 2D and 3D lattices.

Main Results:

  • 3D RA models exhibit magnetic ordering upon cooling, contradicting the Imry-Ma argument.
  • In 3D RA models, if anisotropy exceeds exchange interactions, magnetization is reduced, and a spin-glass component emerges.
  • 3D RF systems do not magnetically order but freeze into a correlated spin-glass state due to pinned singularities.

Conclusions:

  • The Imry-Ma argument's predictions for magnetic ordering in 3D RA models are challenged by simulation results.
  • Singularities play a critical role in preventing magnetic ordering in 3D RF systems.
  • The behavior of magnetic systems with competing interactions (exchange, random field, anisotropy) is complex and depends on their relative strengths.