A magnon is a quasiparticle, a collective excitation of the spin structure of an electron 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 Crystal momentum, and are spin-1, indicating they obey boson behavior.
History
Felix Bloch introduced the concept of a magnon in 1930
to explain the reduction of the spontaneous magnetization in a
ferromagnet. At
absolute zero temperature (0 K), a Heisenberg ferromagnet reaches the state of lowest energy (so-called
ground state), in which all of the atomic spins (and hence
) point in the same direction. As the temperature increases, more and more spins deviate randomly from the alignment, increasing the internal energy and reducing the net magnetization. Viewing the perfectly magnetized state at zero temperature as the
vacuum state of the ferromagnet, shows the low-temperature state with a few misaligned spins as a gas of quasiparticles, in this case magnons. Each magnon reduces the total spin along the direction of magnetization by one unit of
(the reduced Planck constant) and the magnetization by
, where
is the gyromagnetic ratio. This leads to Bloch's law for the temperature dependence of spontaneous magnetization:
where
is the (material dependent) critical temperature, and
is the magnitude of the spontaneous magnetization.
Theodore Holstein and Henry Primakoff,[C. Kittel, Introduction to Solid State Physics, 7th edition (Wiley, 1995). ]
Bertram Brockhouse achieved direct experimental detection of magnons by inelastic neutron scattering in ferrite in 1957.
The fact that magnons obey Bose–Einstein statistics was confirmed by light-scattering experiments done during the 1960s through the 1980s. Classical theory predicts equal intensity of Stokes shift. However, the scattering showed that if the magnon energy is comparable to or smaller than the thermal energy, or , then the Stokes line becomes more intense, as follows from Bose–Einstein statistics. Bose–Einstein condensation of magnons was proven in an antiferromagnet at low temperatures by Nikuni et al.
Paramagnons
Paramagnons are magnons in magnetic materials which are in their high temperature, disordered (
Paramagnetism) phase. For low enough temperatures, the local atomic
(spins) in
Ferromagnetism or anti-ferromagnetic compounds become ordered. Small oscillations of the moments around their natural direction propagate as
(magnons). At temperatures higher than the critical temperature, long range order is lost, but spins align locally (in patches), allowing for spin waves to propagate for short distances. These waves are known as a paramagnon, and undergo
Diffusion (instead of ballistic or long range) transport.
The concept was proposed based on the spin fluctuations in , by Berk and Schrieffer
Properties
Spin wave can be studied with a variety of scattering techniques. Magnons behave as a Bose gas with no chemical potential. Microwave pumping can be used to excite spin waves and create additional non-equilibrium magnons which thermalize into
. At a critical density, a condensate is formed, which appears as the emission of monochromatic microwaves. This microwave source can be tuned with an applied magnetic field.
See also
-
Magnonics
-
Holstein–Primakoff transformation
-
Surface magnon polariton
Further reading
