Spin wave

In condensed matter physics, a spin wave is a propagating disturbance in the ordering of a magnetic material.

As temperature is increased, the thermal excitation of spin waves reduces a ferromagnet's spontaneous magnetization.

can be verified by rewriting it in terms of the spin-raising and spin-lowering operators given by: resulting in where z has been taken as the direction of the magnetic field.

The exchange energy penalty associated with changing the orientation of one spin is reduced by spreading the disturbance over a long wavelength.

The propagation of spin waves is described by the Landau-Lifshitz equation of motion: where γ is the gyromagnetic ratio and λ is the damping constant.

The cross-products in this forbidding-looking equation show that the propagation of spin waves is governed by the torques generated by internal and external fields.

In metals the damping forces described by the constant λ are in many cases dominated by the eddy currents.

The dispersion relation for phonons is to first order linear in wavevector k, namely ώ = ck, where ω is frequency, and c is the velocity of sound.

The underlying reason for the difference in dispersion relation is that the order parameter (magnetization) for the ground-state in ferromagnets violates time-reversal symmetry.

Two adjacent spins in a solid with lattice constant a that participate in a mode with wavevector k have an angle between them equal to ka.

When magnetoelectronic devices are operated at high frequencies, the generation of spin waves can be an important energy loss mechanism.

Spin wave generation limits the linewidths and therefore the quality factors Q of ferrite components used in microwave devices.