  We study the generation of defects when a quantum spin system is quenched
through a multicritical point by changing a parameter of the Hamiltonian as
$t/\tau$, where $\tau$ is the characteristic time scale of quenching. We argue
that when a quantum system is quenched across a multicritical point, the
density of defects ($n$) in the final state is not necessarily given by the
Kibble-Zurek scaling form $n \sim 1/\tau^{d \nu/(z \nu +1)}$, where $d$ is the
spatial dimension, and $\nu$ and $z$ are respectively the correlation length
and dynamical exponent associated with the quantum critical point. We propose a
generalized scaling form of the defect density given by $n \sim
1/\tau^{d/(2z_2)}$, where the exponent $z_2$ determines the behavior of the
off-diagonal term of the $2 \times 2$ Landau-Zener matrix at the multicritical
point. This scaling is valid not only at a multicritical point but also at an
ordinary critical point.
