Spin wave excitations

The magnitude of the spontaneous magnetization M in ordered magnets is temperature dependent due to spin wave excitations. Spin wave frequencies are so fast (THz) that they are fully motional-narrowed in jxSR. All one will observe is the expectation value of the internal field which is coupled (but not necessarily directly proportional) to the expectation value of M T). For this reason one calls the of an ordered magnet a quasistatic field. The spontaneous precession vanishes at a second-order magnetic transition point and reaches a saturation value for T —> 0. An example is shown in fig. 27. 

Thermally Excited Spin Waves In Ultrathin Ferromagnetic Films... 

It would be important to figure out the low energy excitation modes (Nambu-Goldstone modes) built on the ferromagnetic phase. The spin waves are well known in the Heisenberg model [10]. Then, how about our case [32] ... 

The arrangement of moments in a typical antiferromagnetic is shown in Fig. 3.1. Moments on adjacent atoms are, in the simplest cases such as MnO or NiO, coupled so that they are antiparallel. Then at low temperatures the susceptibility depends on whether the field is parallel or perpendicular to the moments. If it is parallel, the susceptibility X goes to zero as T->0. This is because the coupling prevents any spins from turning over, and no spin waves are excited. On the other hand, if the field is perpendicular to the moments, they will be oriented by the field as shown in Fig. 3.2 and x is independent of temperature. The susceptibilities in the two directions are shown in Fig. 3.3. In practice, a macroscopic sample will usually contain numerous domains, and then the average susceptibility is... 

Such a low-lying excitation is shown on the right. These elementary excitations are called spin waves. The spin vectors precess on cones and successive spins have a constant angle of phase shift. This is shown in the lower part of the figure showing one wavelength of a spin wave in a chain of spins (a) in perspective projection and (b) viewed from above. 

Longitudinal fluctuations of a Neel-ordered state are usually strongly damped and not included in a spin-wave approximation of its excitation spectrum. Until now similar modes have been only observed in neutron scattering on spin chain systems as broadened maxima [44 46]. The present narrow linewidth is probably related to the small scattering vector involved in light scattering experiments. 

The Bloch theorem is one of the tools that helps us to mathematically deal with solids [5,6], The mathematical condition behind the Bloch theorem is the fact that the equations which governs the excitations of the crystalline structure such as lattice vibrations, electron states and spin waves are periodic. Then, to jsolve the Schrodinger equation for a crystalline solid where the potential is periodic, [V(r + R) = V(r), this theorem is applied [5,6],... 

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