Magnons 2009-06-08 01:49:55 2009-06-08 01:56:57 Definition magnon dispersion relation two-magnon dispersion SWR FMR ferromagnetic resonance spin-wave excitations Cu $K_\alpha$ edge resonant inelastic X-ray scattering spectra RIXS neutron inelastic scattering short range antiferromagnetic fluctuations and symmetry breaking magnons magnon dispersion magnon dispersion relation two-magnon dispersion SWR FMR ferromagnetic resonance spin-wave excitations Cu $K_\alpha$ edge resonant inelastic X-ray scattering spectra RIXS neutron inelastic scattering short range antiferromagnetic fluctuations and symmetry breaking \section{Magnons} {\em Magnons} are defined as collective excitations of a magnetic lattice that possesses long range magnetic order; more specifically, magnons correspond to the change by one unit of the magnetic moment of the lattice or system. This non-local nature of magnons is the cause of the experimentally observed dispersive behavior, that is a non-constant relation between the momentum and the energy of the magnertic lattice upon its excitation. Two-magnon and mutiple-magnon dispersion phenomena have been reported and employed to explain the nonlinear dispersion behavior of both crystalline and non-crystalline systems with long range ordering compared with the atomic scale. \subsection{Experimental observation of non-linear magnon dispersion} Experimentally, magnon dispersions have been detected by resonant microwave absorption in external magnetic fields (that is, by Spin-Wave Resonance excitation (SWR) and ferromagnetic resonance (FMR)) for ferromagnetic metallic glasses at ambient temperatures. Several neutron inelastic, as well as Cu $K_\alpha$ edge resonant inelastic X-ray scattering (RIXS), spectra were also reported for crystaline materials such as the undoped antiferromagnetic cuprates below 20 K. \subsection{Applications} Such measurements and corresponding theories are of significant interest for an improved understanding of high temperature superconductivity; upon doping ( for example with Ytrium or Lanthanum, and Barium) the long-range ordering antiferromagnetic lattice-- that was present in certain undoped copper oxide insulators-- becomes frustrated, thus leading to short range antiferromagnetic fluctuations, symmetry breaking and high temperature superconductivity.