  We examine charmed-strange mesons within the framework of the constituent
quark model, focusing on the states with L=1. We are particularly interested in
the mixing of two spin-states that are involved in $D_{s1}(2536)$ and the
recently discovered $D_{sJ}(2460)$. We assume that these two mesons form a pair
of states with J=1. These spin-states are mixed by a type of the spin-orbit
interaction that violates the total-spin conservation. Without assuming
explicit forms for the interactions as functions of the interquark distance, we
relate the matrix elements of all relevant spin-dependent interactions to the
mixing angle and the observed masses of the L=1 quartet. We find that the
spin-spin interaction, among various types of the spin-dependent interactions,
plays a particularly interesting role in determining the spin structure of
$D_{s1}(2536)$ and $D_{sJ}(2460)$.
