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This contributes an amount VHo to the frequency of the wave. Typically one has VHo~4n),Ms, so that the contribution from the Zeeman and magnetic dipole fields are comparable. 32 D. L. Mills The short range interactions between the spins are the exchange interactions of quantum mechanical origin, w r i t t e n - J12S1 "$2 between two neighboring spins. If a spin wave is excited, and 012 is the angle between spins 1 and 2, excitation of the spin wave increases the exchange energy over that in the fully aligned ground state by J12 $2 022/2 at long wavelengths, where 012 ,~ 1.

Mills The short range interactions between the spins are the exchange interactions of quantum mechanical origin, w r i t t e n - J12S1 "$2 between two neighboring spins. If a spin wave is excited, and 012 is the angle between spins 1 and 2, excitation of the spin wave increases the exchange energy over that in the fully aligned ground state by J12 $2 022/2 at long wavelengths, where 012 ,~ 1. We have 012 ,,,ka o, with a 0 being the lattice constant and k the wave vector of the wave. Exchange couplings contribute a term proportional to k 2 to the spin wave frequency in the long wavelength limit.

Iii) Light scattering spectrometers are extremely simple, inexpensive, and ecologically safe when compared with a neutron reactor spectrometer. 7, 8]. 9J. Thus, they can be used for the characterization of semiconducting materials under industrial production conditions. 10-12]. Optical phonon branches are usually very flat at k_-__0 (quadratic dispersion). Hence, no dispersion is seen in Raman scattering in bulk crystals and the phonon frequency for k - 0 is obtained even if k differs somewhat from zero.

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