The Killing-Ricci spinors

Question

Let $(M,g)$ be a spin manifold with Ricci curvature $Ric$ and spinorial connection $\nabla$, I define a Killing-Ricci spinor $\psi$ by the equation:

$$\nabla_X \psi= \mu X.\psi+ \mu' Ric(X).\psi$$

If $\cal D$ is the Dirac operator, we have:

$${\cal D}\psi=-(\mu n+\mu' r) .\psi$$

where $r$ is the scalar curvature.

What is the space of the Killing-Ricci spinors?