Magnon dispersion of the dipolar ferromagnet EuS near the zone center

The dispersion of the spin waves in EuS has been investigated by means of neutron scattering. In zero field and at small momentum transfer q, the energy Latin small letter h with strokeωq of the spin waves is proportional to q in agreement with the predictions of spin-wave theory that includes demagnetization effects. By application of a magnetic field Hq, the spin waves attain a finite mass, i.e., a gap is induced and Latin small letter h with strokeωq becomes proportional to q2. Using polarization analysis we show that the degeneracy between spin waves at 0.87Tc polarized along and transverse to q is lifted due to the depolarizing fields. The transverse spin-wave modes are the Goldstone modes and diverge at Tc, whereas the longitudinal spin waves do not diverge. This situation resembles the lifting of the degeneracy between the longitudinal and transverse fluctuations in the paramagnetic phase. Both the dynamics and the statics are in agreement with linear spin-wave theory.