Magnon

As a magnon or magnon quasiparticles is referred to a collective excitation state of a magnetic system with properties of a so-called bosonic quasiparticle. This state corresponds to excitation in solids the quantized form of a magnetic spin wave, analogous to the so-called phonons as quantized sound waves.

Basic statements

Condition for the existence of the magnon is the presence of a magnetic order, that is a coupling between the magnetic moments of the lattice atoms, which leads to the preferred orientations of the moments of each other, e.g. parallel or antiparallel with ferrous at antiferromagnet. The energy for wave-like excitations of the ordered moments is quantized as in the elastic lattice vibrations. There it is called phonons. Here, however, one chooses for obvious reasons, for the smallest possible excitation analogous to the phonon term Magnon. This Magnon is the usual semi-classical interpretation (see the figure) of a chain in a certain manner consistent rotating spins, since the energy is thus lower. In the ground state show about all the spins parallel to the top ( state while the quantum mechanical Magnonzustand that fits this ground state, at a single location - with a certain correlated probability, which corresponds to the above semiclassical picture), points downward, This is the wave vector of Magnons ( iW the reciprocal wavelength λ ). Furthermore, the position vector of the particle j, for which the spin is inverted; e is Euler's number, and i is the imaginary unit in the space of complex numbers. This corresponds to the application of a so-called magnon creation operator Mk on the ground state | ψk > = Mk | ψG >; the vector arrow over k has been omitted here for simplicity. For the nuclear spin quantum number S is assumed = 1/2.

The spin of the magnon, however, is always 1 - not only if it is ferromagnet and to atoms with half-integer spins - because the total spin of the system ( in units of Planck's constant) by the " continued worn Magnon " by NS NS -1 reduced (N is the total number of particles). The magnons are therefore Bosonenanregungen ( integer spin! ) ( One speaks also of Bose quasiparticles ).

• In ferromagnet results in the simple model of the exchange coupling of interacting spins (amount, lattice constant ) a ( for small k ) "square" dispersion relation ( relation between frequency and wavelength ) for large wavelengths (small ), namely:

The dependence of the wave number k is therefore ( here in the approximation of small k) square, as in "real" massive particles throughout the nonrelativistic region ( eg the neutrons), although magnons as bosonic quasiparticles others (such as phonons) have no mass. In general, but in any case, the dispersion relation of direction-dependent ( anisotropic).

This can be good by inelastic neutron scattering ( neutrons interact with the spins of electrons and nuclei, and thus measure the distribution of the magnetic moments of electrons) observed. First, as succeeded Brockhouse 1957, the detection of magnons. For D results, for example by Shirane et al, a value of 281 meV Å2 at iron. Also in spin wave resonance experiments in thin layers can be observed by high-frequency alternating magnetic fields magnon excitations.

Magnons were first introduced by Felix Bloch as a theoretical concept. He led a temperature dependence of the relative magnetization decays with an exponent 3/2, which was also confirmed experimentally. By thermogeneration of magnons, the magnetization is reduced.

Further theoretical treatment experienced spin waves in ferromagnets by Theodore Holstein, and Henry Primakoff and Freeman Dyson in the 1940s and 1950s, which introduced named bosons transformations for them.

• In antiferromagnetism, where magnetizations exist with opposite orientation on sublattices which penetrate each other, the magnon excitations have a very different dispersion relation as in ferromagnets: Here the energy depends as with phonons not square, but linearly on the wave number k from. This has, inter alia, concrete effects in the thermodynamics of systems (eg, by being able to abseparieren in antiferromagnets only by high magnetic fields the Magnonenbeitrag to the specific heat from the contribution of phonons). Furthermore implies this difference, that in the solid state - as indicated - the Magnonbeitrag to the specific heat of ferromagnets in proportion to T3 / 2, but that he did in antiferromagnets according to the Debye theory of the phonon contribution to the specific heat proportional to T3 (here T is the Kelvin temperature).

Since you have to do it in ferromagnets with a spontaneously broken symmetry ( the rotational symmetry is broken, because a certain magnetization direction is excellent), you can magnons than the spin state associated Goldstone (quasi ) identify particles, ie excitations with low energy or ( according to the dispersion relation ) of very large wavelength.

First Bose -Einstein condensation was observed in a solid body of magnons 1999. In 2006, Bose -Einstein condensation of magnons was detected at room temperature.