For a current loop, the magnetic dipole moment is
\[
\vec{\mu}= I\,\vec{A},
\]
where \(I\) (ampere) is the current and \(\vec{A}\) (m$^2$) is the area vector. Hence the SI unit is A\,m$^2$.
Option (i) A$\cdot$m corresponds to an obsolete pole–length model; (iii) and (iv) are dimensionally inconsistent with \(\mu=IA\).