  We introduce a spin field approach, that is compatible with the Cartan moving
frame method, to describe the submanifold in a flat space. In fact, we consider
a kind of spin field $\psi$, that satisfies a Killing spin field equation
(analogous to a Killing spinor equation) written in terms of the Clifford
algebra, and we use the spin field to locally rotate the orthonormal basis
$\{\hat{e}_\mathtt{I}\}$. Then, the deformed orthonormal frame
$\{\tilde{\psi}\hat{e}_\mathtt{I}\psi\}$ can be seen as the moving frame of a
submanifold. We find some solutions to the Killing spin field equation and
demonstrate an explicit example. Using the product of the spin fields, one can
easily generate a new immersion submanifold, and this technique should be
useful for studies in geometry and physics. Through the spin field, we find a
linear relation between the connection and the extrinsic curvature of the
submanifold. We propose a conjecture that any solution of the Killing spin
field equation can be locally written as the product of the solutions we find.
