1 Magnons and magnon dispersion
Magnons are defined as collective excitations of a magnetic lattice that possesses long range
magnetic order; more specifically, a single magnon excitation corresponds 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-linear or non-constant relation
between the transferred momentum and the transferred energy of the magnetic lattice upon its
excitation. Typical values for the peak(s) of the transferred energy are on the order of 0.5 eV to 2
eV.
Two- and mutiple- magnon dispersion phenomena have been reported, and were recently employed
to explain the nonlinear dispersion behavior of both crystalline and non-crystalline systems with
long range ordering compared with the atomic scale.
1.1 Experimental observation of the 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 Kα edge resonant inelastic X-ray scattering (RIXS), spectra were also
reported for crystaline materials such as the undoped antiferromagnetic cuprates below 20
K.
1.2 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 in a 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.
