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Tham khảo tài liệu 'neutron scattering from magnetic materials part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Magnetic excitations 267 Fig. 9. Double logarithm plot of the linewidth FWHM of the spin wave excitations in EuS versus wave vector at T 14.1 K. The solid line is a guide to the eye. The straight parts of the curve indicate a slope proportional to q3 or q4. The change in slope occurs near q 0.7 Ả-1 where htó k T from Bohn et al. 19 . Fig. 10. Linewidth FWHM at T Tc of EuS as a function of q in a double logarithmic scale. The straight line represents the best fit of the data giving a dynamical scaling exponent of z 2.09 0.06 from Bohn et al. 19 . 268 T. Chatterji Fig. 11. Double logarithm plot of the linewidth versus q of EuO at Tc. The prediction of the dynamical scaling theory straight line is obeyed in d decades in energy from Boni et al. 23 . 3.4. Spin waves in Heisenberg antiferromagnets We already noted that there are only a few insulating Heisenberg ferromagnets. But there exist several insulating ionic antiferromagnets that are well described by a Heisenberg Hamiltonian with the addition of some single-ion anisotropy terms. It is convenient to start with a more general Hamiltonian that can describe ferrimagnets and as well as antiferro- Magnetic excitations 269 magnets H J r Sm Sm r J r Sn Sn r J1 R Sm Sm R J2 R Sn Sn R - gi B H Ha i Sm - g2 B H - Ha 2 SZ 48 where m and n are lattice vectors connecting the sites of the two interpenetrating sublattices the up sublattice lattice vector m and the down sublattice lattice vector n . R connects sites on the same sublattice and r connects sites on the opposite sublattices. The spins on the m sublattice have magnitude S1 and those on n magnitude S2 . J1 and J2 are exchange parameters within each sublattice. An uniaxial anisotropy is incorporated by the effective magnetic fields HA 1 and HA 2 and g1 and g2 are the gyromagnetic ratios of the two types of ions. Following a similar procedure as indicated in the case of the spin waves in Heisenberg ferromagnets one arrives at the spin wave dispersion equations 2h q 0 a1
