Detecting Gapless Excitations above Ferromagnetic Domain Walls

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In a two or three dimensional ferromagnetic XXZ model, a low energy excitation mode above a magnetic domain wall is gapless, whereas all of the usual spin wave excitations moving around the whole crystal are gapful. Although this surprising fact was already proved in a mathematically rigorous manner, the gapless excitations have not yet been detected experimentally. For this issue, we show theoretically that the gapless excitations appear as the dynamical fluctuations of the experimental observable, magnetoresistance, in a ferromagnetic wire. We also discuss other methods (e.g., ferromagnetic resonance and neutron scattering) to detect the gapless excitations experimentally.