  Multiple-$Q$ magnetic states often induce nontrivial topological spin
textures, such as a skyrmion and a hedgehog. We theoretically investigate yet
another multiple-$Q$ state with topological defects, a meron-antimeron crystal
(MAX), represented by a periodic array of the meron and antimeron with a
half-integer skyrmion number. Performing simulated annealing for an effective
spin model of noncentrosymmetric itinerant magnets on a triangular lattice, we
show that rectangular-shaped and triangular-shaped MAXs are stabilized by the
interplay between the biquadratic interaction arising from the spin-charge
coupling and the Dzyaloshinskii-Moriya interaction arising from the spin-orbit
coupling. We also discuss the effect of a magnetic field on the triangular MAX,
where highly anisotropic responses against a field direction are found. In
particular, we show that the triangular MAX turns into the skyrmion crystal for
the fields along the $y$ and $z$ directions, while it is replaced by another
chiral state for the field along the $x$ direction. These results would inspire
further experimental investigation of the MAXs in itinerant magnets.
