  We consider a topological coupling between a pseudo-scalar field and a 3-form
gauge field in ${\cal N}=1$ supersymmetric higher derivative 3-form gauge
theories in four spacetime dimensions. We show that ghost/tachyon-free higher
derivative Lagrangians with the topological coupling can generate various
potentials for the pseudo-scalar field by solving the equation of motion for
the 3-form gauge field. We give two examples of higher derivative Lagrangians
and the corresponding potentials: one is a quartic order term of the field
strength and the other is the term which can generate a cosine-type potential
of the pseudo-scalar field.
