  Isochronous mass spectrometry has been applied in the storage ring CSRe to
measure the masses of the neutron-rich $^{\operatorname{52-54}}$Sc and
$^{54,56}$Ti nuclei. The new mass excess values $ME$($^{52}$Sc) $=$
$-40525(65)$ keV, $ME$($^{53}$Sc) $=$ $-38910(80)$ keV, and $ME$($^{54}$Sc) $=$
$-34485(360)$ keV, deviate from the Atomic Mass Evaluation 2012 by 2.3$\sigma$,
2.8$\sigma$, and 1.7$\sigma$, respectively. These large deviations
significantly change the systematics of the two-neutron separation energies of
scandium isotopes. The empirical shell gap extracted from our new experimental
results shows a significant subshell closure at $N = 32$ in scandium, with a
similar magnitude as in calcium. Moreover, we present $ab$ $initio$
calculations using the valence-space in-medium similarity renormalization group
based on two- and three-nucleon interactions from chiral effective field
theory. The theoretical results confirm the existence of a substantial $N = 32$
shell gap in Sc and Ca with a decreasing trend towards lighter isotones, thus
providing a consistent picture of the evolution of the $N = 32$ magic number
from the $pf$ into the $sd$ shell.
