  Antiferromagnets (AFMs) exhibit intrinsic magnetization when the order
parameter spatially varies. This intrinsic spin is present even at equilibrium
and can be interpreted as a twisting of the homogeneous AFM into a state with a
finite spin. Because magnetic moments couple directly to external magnetic
fields, the intrinsic magnetization can alter the dynamics of antiferromagnetic
textures under such influence. Starting from the discrete Heisenberg model, we
derive the continuum limit of the free energy of AFMs in the exchange
approximation and explicitly rederive that the spatial variation of the
antiferromagnetic order parameter is associated with an intrinsic magnetization
density. We calculate the magnetization profile of a domain wall and discuss
how the intrinsic magnetization reacts to external forces. We show
conclusively, both analytically and numerically, that a spatially inhomogeneous
magnetic field can move and control the position of domain walls in AFMs. By
comparing our model to a commonly used alternative parametrization procedure
for the continuum fields, we show that the physical interpretations of these
fields depend critically on the choice of parametrization procedure for the
discrete-to-continuous transition. This can explain why a significant amount of
recent studies of the dynamics of AFMs, including effective models that
describe the motion of antiferromagnetic domain walls, have neglected the
intrinsic spin of the textured order parameter.
