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Related Concept Videos

Potential Due to a Magnetized Object01:24

Potential Due to a Magnetized Object

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.
The vector...
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...
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.
Magnetic Moment of an Electron01:23

Magnetic Moment of an Electron

Electrons revolving around a nucleus are analogous to a circular current carrying loop. This current produces a magnetic dipole moment proportional to the electron's orbital angular momentum. Since the orbital angular momentum is quantized in terms of the reduced Planck's constant, the dipole moment is quantized in the Bohr Magneton. The value of the Bohr magneton is 9.27 x 10-24 Am2. Electrons also have an intrinsic spin angular momentum, and the associated spin magnetic moment is...
Atomic Nuclei: Nuclear Magnetic Moment00:59

Atomic Nuclei: Nuclear Magnetic Moment

All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
Atomic Nuclei: Magnetic Resonance01:05

Atomic Nuclei: Magnetic Resonance

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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Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures
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Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Published on: November 21, 2019

Orbital magnetization as a local property.

Raffaello Bianco1, Raffaele Resta

  • 1Dipartimento di Fisica, Università di Trieste, 34127 Trieste, Italy.

Physical Review Letters
|March 12, 2013
PubMed
Summary
This summary is machine-generated.

Orbital magnetization, a bulk property of insulators, can now be calculated in real space. This new method is independent of boundary conditions and works even for complex topological materials.

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Area of Science:

  • Condensed matter physics
  • Solid-state physics
  • Materials science

Background:

  • Current theoretical frameworks express polarization and orbital magnetization using k-space integrals.
  • A true bulk property should be definable in real space, independent of boundary conditions, and sensitive only to the local electronic structure.

Purpose of the Study:

  • To derive a real-space expression for orbital magnetization in insulators.
  • To demonstrate that orbital magnetization is a genuine bulk property, unlike electric polarization.
  • To provide a method applicable to insulators with or without non-zero Chern invariants.

Main Methods:

  • Derivation of real-space formulas for orbital magnetization.
  • Utilizing the concept of 'nearsightedness' of electronic properties in insulators.
  • Validation through numerical simulations on a model Hamiltonian.

Main Results:

  • A novel real-space expression for orbital magnetization (M) has been successfully derived.
  • The derived expression is shown to be a genuine bulk property, independent of boundary conditions.
  • The method is applicable to all insulators, including those with non-zero Chern invariants.

Conclusions:

  • Orbital magnetization is confirmed as a true bulk property expressible in real space.
  • The new real-space formulation offers a more robust and fundamental way to calculate orbital magnetization.
  • This work provides a valuable theoretical tool for understanding and predicting the magnetic properties of insulating materials.