The layer between the asthenosphere and the outer core is the mesosphere, also known as the lower mantle.

Here's a breakdown of the Earth's structure:

* Crust: The thin, outermost layer of the Earth.

* Upper Mantle: Includes the lithosphere (rigid, outermost part) and the asthenosphere (partially molten, flowing layer).

* Mesosphere (Lower Mantle): This layer is solid but can deform under pressure. It is much hotter and denser than the upper mantle.

* Outer Core: Liquid layer of iron and nickel.

* Inner Core: Solid ball of iron and nickel.

So, to answer your question: The mesosphere, or lower mantle, lies between the asthenosphere and the outer core.