 Stress-energy tensor of a nonminimally coupled scalar field

For action $S=\int \sqrt{-g}[-\frac{1}{2}(\nabla \Phi {)}^2-\xi R{\Phi }^2]d^{4}x$, metric variation defines $\delta S=\frac{1}{2}\int \sqrt{-g}{T}^{ab}\delta g_{ab}{d}^{4}x$ and gives the displayed tensor. The contracted Bianchi identity and the scalar derivative commutator yield ${\nabla }^a{T}_{ab}=(\square \Phi -2\xi R\Phi ){\nabla }_b\Phi$, so the stress-energy tensor is conserved on the field equation.