Anomalous tunneling of spin wave in heisenberg ferromagnet

The ferromagnetic spin wave (FSW) in classical Heisenberg chain exhibits the perfect transmission in the long-wavelength limit in the transmission-reflection problem with an inhomogeneity of exchange integral. In the presence of local magnetic field, on the other hand, FSW undergoes the perfect reflection in the long-wavelength limit. This difference in the long-wavelength limit is attributed to the symmetry property of the scatterers; it is crucial whether the potential preserves or breaks the spin rotation symmetry. Our result implies that the anomalous tunneling (i.e., perfect transmission in the low-energy limit) found both in scalar and spinor BECs is not specific to gapless modes in superfluids but is a common property shared with generic Nambu-Goldstone modes in the presence of a symmetry-preserving potential scatterer.