# Spin (physics) - Magnetic Moments

Magnetic Moments

Particles with spin can possess a magnetic dipole moment, just like a rotating electrically charged body in classical electrodynamics. These magnetic moments can be experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous magnetic fields in a Stern–Gerlach experiment, or by measuring the magnetic fields generated by the particles themselves.

The intrinsic magnetic moment μ of a spin-1/2 particle with charge q, mass m, and spin angular momentum S, is

where the dimensionless quantity gs is called the spin g-factor. For exclusively orbital rotations it would be 1 (assuming that the mass and the charge occupy spheres of equal radius).

The electron, being a charged elementary particle, possesses a nonzero magnetic moment. One of the triumphs of the theory of quantum electrodynamics is its accurate prediction of the electron g-factor, which has been experimentally determined to have the value −2.0023193043622(15), with the digits in parentheses denoting measurement uncertainty in the last two digits at one standard deviation. The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of 0.002319304... arises from the electron's interaction with the surrounding electromagnetic field, including its own field. Composite particles also possess magnetic moments associated with their spin. In particular, the neutron possesses a non-zero magnetic moment despite being electrically neutral. This fact was an early indication that the neutron is not an elementary particle. In fact, it is made up of quarks, which are electrically charged particles. The magnetic moment of the neutron comes from the spins of the individual quarks and their orbital motions.

Neutrinos are both elementary and electrically neutral. The minimally extended Standard Model that takes into account non-zero neutrino masses predicts neutrino magnetic moments of:

where the μν are the neutrino magnetic moments, mν are the neutrino masses, and μB is the Bohr magneton. New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments. It can be shown in a model independent way that neutrino magnetic moments larger than about 10−14 μB are unnatural, because they would also lead to large radiative contributions to the neutrino mass. Since the neutrino masses cannot exceed about 1 eV, these radiative corrections must then be assumed to be fine tuned to cancel out to a large degree.

The measurement of neutrino magnetic moments is an active area of research. As of 2001, the latest experimental results have put the neutrino magnetic moment at less than 1.2×10−10 times the electron's magnetic moment.

In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction. Ferromagnetic materials below their Curie temperature, however, exhibit magnetic domains in which the atomic dipole moments are locally aligned, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar.

In paramagnetic materials, the magnetic dipole moments of individual atoms spontaneously align with an externally applied magnetic field. In diamagnetic materials, on the other hand, the magnetic dipole moments of individual atoms spontaneously align oppositely to any externally applied magnetic field, even if it requires energy to do so.

The study of the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. These models have many interesting properties, which have led to interesting results in the theory of phase transitions.

### Other articles related to "magnetic, magnetic moments, moments":

Spin Ices and Magnetic Monopoles
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Paramagnetism - Curie's Law
... that materials become more magnetic at lower temperatures ... is where is the resulting magnetization is the magnetic susceptibility is the auxiliary magnetic field, measured in amperes/meter is absolute temperature, measured ... For a paramagnetic ion with noninteracting magnetic moments with angular momentum J, the Curie constant is related the individual ions' magnetic moments ...
Giant Magnetoresistance - Theory - Fundamentals - Spin-dependent Scattering
... resistance is crucially affected by scattering of electrons on the magnetic sublattice of the crystal, which is formed by crystallographically equivalent atoms with nonzero nuclear magnetic moments ... Scattering depends on the relative orientations of the electron spins and magnetic moments of the atoms it is weakest when they are parallel and strongest when they are antiparallel ... is relatively strong in the paramagnetic state, in which the magnetic moments of the atoms have random orientations ...
Breit Equation - Breit Hamiltonians
... can be decomposed into the following practical energy operators for electrons in electric and magnetic fields (also called the Breit-Pauli hamiltonian), which have well-defined ... that partly accounts for retardation and can be described as the interaction between the magnetic dipole moments of the particles, which arise from the orbital motion ... classical interaction between the orbital magnetic moments (from the orbital motion of charge) and spin magnetic moments (also called spin-orbit interaction) ...

### Famous quotes containing the words moments and/or magnetic:

The moments of the past do not remain still; they retain in our memory the motion which drew them towards the future, towards a future which has itself become the past, and draw us on in their train.
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We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and Texas, it may be, have nothing important to communicate.
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