# Magnon

A magnon is a collective excitation of the electrons' spin structure in a crystal lattice.

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 ħ (where ħ is the reduced Planck constant).

In contrast, a phonon is a collective excitation of the crystal lattice atoms or ions.

## 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 ħ and the magnetization itself by γħ, where γ 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 fact that magnons obey the Bose-Einstein statistics was confirmed at latest by the light scattering experiments from magnons in 1960s–1980s. According to the classical theory the intensity of the Stokes and anti-Stokes lines in the light scattering spectrum should be the same. However, experimentally it was shown that if the energy of magnon ħω is comparable or smaller than the thermal energy $k_B T$, the Stokes line becomes more intensive as it is followed from the Bose-Einstein statistics. The effect of Bose-Einstein condensation of magnons was proven recently in an antiferromagnet at low temperatures by Nikuni et al. and in a ferrimagnet by Demokritov et al. at room temperature. See the news report by Schewe and Stein and the scientific articles by Nikuni et al. and Demokritov et al. for more details.