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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A quantum of a spin wave; an elementary excitation of a magnetic system which is usually long-range-ordered, such as a ferromagnet. See also 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, S_z, is reduced by one unit of ℏ = h/2π, 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 ω. 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 S_z, labeled Δ, is only ℏ/N, whereas the z component of the atomic spin in the fully aligned state is typically 1–10 times ℏ. 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 2ℏ/N, the state is a two-magnon state, and so forth. The integer values of NΔ/ℏ correspond to the possible changes in S_z being integral multiples of ℏ. See also Electron spin; Wave motion.

Spin wave in a linear ferromagnetic array of precessing atomic spins of equal magnitude, represented as arrows (vectors) in perspective. The axis of precession is along the vertical direction of the total magnetization, M.

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 also Electromagnetic wave; Phonon; Photon; Quantum mechanics.

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There is a place named Magnon in Gabon.

A magnon is a collective excitation of the electrons' spin structure in a crystal lattice. In contrast, a phonon is a collective excitation of the crystal lattice atoms or ions. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. As a quasiparticle, a magnon carries a fixed amount of energy and lattice momentum. It also possesses a spin of $\hbar$ (where $\hbar$ is Planck's constant divided by 2π).

Brief history

The concept of a magnon was introduced in 1930 by Felix Bloch in order to explain the reduction of the spontaneous magnetization in a ferromagnet. At absolute zero temperature, a ferromagnet reaches the state of lowest energy, in which all of the atomic spins (and hence magnetic moments) point in the same direction. As the temperature increases, more and more spins deviate randomly from the common direction, thus increasing the internal energy and reducing the net magnetization. If one views the perfectly magnetized state at zero temperature as the vacuum state of the ferromagnet, the low-temperature state with a few spins out of alignment can be viewed as a gas of quasiparticles, in this case magnons. Each magnon reduces the total spin along the direction of magnetization by one unit of $\hbar$ and the magnetization itself by $g \hbar$ , where $g$ is the gyromagnetic ratio.

The quantitative theory of quantized spin waves, or magnons, was developed further by Theodore Holstein and Henry Primakoff (1940) and Freeman Dyson (1956). By using the formalism of second quantization they showed that the magnons behave as weakly interacting quasiparticles obeying the Bose-Einstein statistics (the bosons).

For a brief outline of the theory see spin wave. A comprehensive treatment can be found in Kittel's textbook or in the article by Van Kranendonk and Van Vleck.

A direct experimental detection of magnons by means of inelastic neutron scattering in ferrite was achieved in 1957 by Bertram Brockhouse. Since then magnons have been detected in ferromagnets, ferrimagnets, and antiferromagnets.

The Bose-Einstein statistics of magnons was proven recently (1999) by demonstrating the effect of Bose-Einstein condensation of magnons in an antiferromagnet. See the news report by Schewe and Stein and the scientific article by Nikuni et al. for more details.

References

C. Kittel, Introduction to Solid State Physics, 7th edition (Wiley, 1995). ISBN 0-471-11181-3.
F. Bloch, Z. Physik 61, 206 (1930).
T. Holstein and H. Primakoff, Phys. Rev. 58, 1098 (1940). online
F. J. Dyson, Phys. Rev. 102, 1217 (1956). online
B. N. Brockhouse, Phys. Rev. 106, 859 (1957). online
J. Van Kranendonk and J. H. Van Vleck, Rev. Mod. Phys. 30, 1 (1958). online
T. Nikuni, M. Oshikawa, A. Oosawa, and H. Tanaka, Phys. Rev. Lett. 84, 5868 (1999). online
P. Schewe and B. Stein, Physics News Update 746, 2 (2005). online
A.V. Kimel, A. Kirilyuk and T.H. Rasing, Laser & Photon Rev. 1, No. 3, 275-287 (2007). online

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Hypothetical composite particles	Exotic hadrons: Exotic baryons: Dibaryon · Pentaquark • Exotic mesons: Glueball · Tetraquark Other: Mesonic molecule · Pomeron

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