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# Magnon

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 Ted 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