Thom isomorphisms in triangulated motivic categories

We show that a triangulated motivic category admits categorical Thom isomorphisms for vector bundles with an additional structure if and only the generalized cohomology theory represented by tensor unit object classes. also stable $\mathbb{A}^1$-derived does not admit oriented and, more generally, symplectic bundles. In order to do so we compute first homology sheaves of sphere spectrum class in coefficient ring $\mathbb{A}^1$-homology corresponding second Hopf map $\nu$ is nonzero which provides obstruction existence reasonable classes $\mathbb{A}^1$-cohomology.