In this paper we discuss nondegeneracy and stability properties of some special minimal hypersurfaces which are asymptotic to a given Lawson cone \(C_{m,n}\) , for \(m,\,n\ge 2\) . Then we use such hypersurfaces to construct solutions to the Allen-Cahn equation \(-\Delta u=u-u^3\) in \(\mathbb {R}^{N+1}\) , \(N+1\ge 8\) , whose zero level set has exactly \(k\ge 2\) connected components and with infinite Morse index