Hourglass-shaped magnetic excitation

Spin-Wave Spectrum in the Presence of Spin Vortices The Origin of an Hourglass-Shaped Magnetic Excitation Spectrum... 

The magnetic excitation spectrum has an hourglass shape . The dispersion at high energies is very similar to the one arising from antiferromagnetic spin-wave... 

In Fig. 15, magnetic excitation spectra calculated by the spin-vortex model are depicted. Results obtained by the Holstein-Primakoff method are also depicted. The dispersions exhibit hourglass-shapes. As the number of spin-vortices are increased, the peaks of the dispersion become blur. The neck energy increases with the increase of the number of holes in agreement with experiment. 

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