# Magnon

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## Magnon

A quantum of a spin wave; an elementary excitation of a magnetic system which is usually long-range-ordered, such as a ferromagnet. See Antiferromagnetism, Ferrimagnetism, Ferromagnetism

In the lowest energy state of a simple ferromagnet, all the magnetic moments of the individual atoms are parallel (say, to the z axis). Each atomic moment derives mainly from the electron spin angular momentum of the atom. In the next-to-lowest energy state (first excited state), the total z component of spin angular momentum, Sz, is reduced by one unit of &planck; = h/2&pgr;, where h is Planck's constant. In the case of a crystalline material, this unit is shared equally by all the spins, each of which lies on a cone (see illustration), precessing at an angular rate &ohgr;. These spins form a wave, known as a spin wave, having a repeat distance or wavelength, λ. The wave amplitude (that is, the cone angle) is extremely small, because of the sharing among all the spins whose number N is very large, roughly 1023. Thus, each atom's share of the reduction in Sz, labeled Δ, is only &planck;/N, whereas the z component of the atomic spin in the fully aligned state is typically 1–10 times &planck;. It follows from simple geometry that the cone half-angle is of order 10-11 to 10-12 radian. The state with this value of the amplitude is said to be a one-magnon state with wave number k = 1/λ. If Δ is doubled to 2&planck;/N, the state is a two-magnon state, and so forth. The integer values of NΔ/&planck; correspond to the possible changes in Sz being integral multiples of &planck;. See Electron spin, Wave motion

Spin wave in a linear ferromagnetic array of precessing atomic spins of equal magnitude, represented as arrows (vectors) in perspective

While the spin waves associated with energy states, that is, stationary states, in crystals vary sinusoidally in space (see illustration), magnons can be associated, instead, with nonstationary states (wave packets) in some situations. Closely analogous to magnons are phonons and photons, quanta of mass-density waves and electromagnetic waves, respectively. See Electromagnetic wave, Phonon, Photon, Quantum mechanics

## Magnon

a quasiparticle that corresponds to an elementary excitation of a system of interacting spins. Crystals with several magnetic sublattices (such as antiferromagnets) may have several types of magnons that have different energy spectra. Magnons obey Bose-Einstein statistics. They interact with each other and with other quasiparticles. The existence of magnons has been confirmed by experiments on neutron and light scattering accompanied by the production of magnons.

### REFERENCE

Akhiezer, A. I, V. G. Bar’iakhtar, and S. V. Peletminskii. Spinovye volny. Moscow, 1967.

E. M. EPSHTEIN

## magnon

[′mag‚nän]
(solid-state physics)
A quasi-particle which is introduced to describe small departures from complete ordering of electronic spins in ferro-, ferri-, antiferro-, and helimagnetic arrays. Also known as quantized spin wave.
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