  Results from the study of $\beta^-$-decay of $^{45}$Cl, produced in the
fragmentation of a 140-MeV/u $^{48}$Ca beam, are presented. The half-life for
$^{45}$Cl $\beta$-decay is measured to be 513(36) ms. The $\beta^-$ and
$\beta^- 1n$ decay of $^{45}$Cl populated excited states in $^{45,44}$Ar,
respectively. On the basis of $\gamma$-ray singles and $\gamma$-$\gamma$
coincidence data, decay schemes for the two daughter nuclei have been
established. They are compared with shell model calculations using the FSU
interaction. The low-lying negative parity states for $^{45}$Ar are well
described by a single particle (neutron) occupying orbitals near the Fermi
surface, whereas neutron excitations across the $N = 20$ shell gap are needed
to explain the positive-parity states which are expected to be populated in
allowed Gamow-Teller $\beta$-decay of $^{45}$Cl. The highest $\beta$-feeding to
the 5/2$^+$ state in $^{45}$Ar from the ground state of $^{45}$Cl points
towards a 3/2$^+$ spin-parity assignment of the ground state of the parent over
the other possibility of 1/2$^+$. The high Q$_{\beta^-}$ value of $^{45}$Cl
decay allows for the population of $1p1h$ states above the neutron separation
energy in $^{45}$Ar leading to positive parity states of $^{44}$Ar being
populated by removal of one neutron from the $sd$ shell. The spin-parities of
the excited levels in $^{44}$Ar are tentatively assigned for the first time by
comparison with the shell model calculations. The 2978~keV level of $^{44}$Ar
is identified as the excited 0$^+$ level which could correspond to a different
configuration from the ground state.
