Concept

Spin wave

Summary
In condensed matter physics, a spin wave is a propagating disturbance in the ordering of a magnetic material. These low-lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as magnons, which are bosonic modes of the spin lattice that correspond roughly to the phonon excitations of the nuclear lattice. As temperature is increased, the thermal excitation of spin waves reduces a ferromagnet's spontaneous magnetization. The energies of spin waves are typically only μeV in keeping with typical Curie points at room temperature and below. Theory The simplest way of understanding spin waves is to consider the Hamiltonian \mathcal{H} for the Heisenberg ferromagnet: :\mathcal{H} = -\frac{1}{2} J \sum_{i,j} \mathbf{S}_i \cdot \mathbf{S}j - g \mu{\rm B} \sum_i \mathbf{H} \cdot \mathbf{S}_i where J is the exchange energy, the operators S
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