  A design of a magnonic phase shifter operating without an external bias
magnetic field is proposed. The phase shifter uses a localized collective spin
wave mode propagating along a domain wall "waveguide" in a dipolarly-coupled
magnetic dot array existing in a chessboard antiferromagnetic (CAFM) ground
state. It is demonstrated numerically that remagnetization of a single magnetic
dot adjacent to the domain wall waveguide introduces a controllable phase shift
in the propagating spin wave mode without significant change of the mode
amplitude. It is also demonstrated that a logic XOR gate can be realized in the
same system.
