homework and exercises - Noether's theorem for scale invariance

When we have the Lagrangian

$$\mathcal{L} = \frac{1}{2} \partial _\mu \phi\partial^\mu \phi \tag{1}$$ We have a symmetry given by $$x^\mu\mapsto e^\alpha x^\mu, \qquad\phi\mapsto e^{-\alpha} \phi.\tag{2}$$ I'm struggling to find the Noether charge for this symmetry. The formula is $$j^\mu=\frac{\partial \mathcal{L}}{\partial\partial_\mu\phi}\delta\phi-k^\mu\tag{3}$$ where $$\delta \phi=-\phi \tag{4}$$ in this case, but I can't find $k^\mu$ such that $$\delta \mathcal {L}=\partial _\mu k^\mu .\tag{5}$$