Effective field theories and spin-wave excitations in helical magnets

We consider two classes of helical magnets. The first class has magnetic ordering close to that of an antiferromagnet and the second class has magnetic ordering close to that of a ferromagnet. The first case is relevant to cuprate superconductors and the second case is realized in FeSrO(3) and FeCaO(3). We derive the effective field theories for these cases and calculate the corresponding excitation spectra. We demonstrate that the hourglass spin-wave dispersion observed experimentally in the cuprates is a fingerprint of the antiferromagnetic spin spiral state. We also show that quantum fluctuations are important for the ferromagnetic spin spiral, as they influence qualitative features of the spin-wave dispersion.