# Magnon

For other uses, see Magnon (disambiguation).

A magnon is a quasiparticle, 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. Magnons carry a fixed amount of energy and lattice momentum, and are spin-1, indicating they obey boson behavior.

## 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 by γħ, where γ is the gyromagnetic ratio.

The quantitative theory of magnons, quantized spin waves, was developed further by Theodore Holstein, Henry Primakoff (1940), and Freeman Dyson (1956). Using the second quantization formalism they showed magnons behave as weakly interacting quasiparticles obeying Bose–Einstein statistics (the bosons). A comprehensive treatment can be found in Kittel's textbook or the article by Van Kranendonk and Van Vleck.

Direct experimental detection of magnons by 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 by the light scattering experiments done 1960s–1980s. Classical theory predicts equal intensity of Stokes and anti-Stokes lines. However, the scattering showed that if the magnon energy is comparable or smaller than the thermal energy: $\hbar \omega < k_B T$, the Stokes line becomes more intense, as follows from Bose–Einstein statistics. 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 articles by Nikuni et al. and Demokritov et al. for more details.