A spin wave, also known as a magn wave, is a collective excitation of the spins in a solid material, particularly in ferromagnetic and antiferromagnetic systems. It is a type of wave that propagates through a magnetic material due to the precession of the magnetic moments (spins) of the atoms or ions about their equilibrium positions.
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A spin wave is a smooth long-wavelength fluctuation of the orientation of an ordered continuous-symmetry field. In an phase it is a fluctuation of the angle governed at leading order by the Gaussian gradient energy.